U.S. patent number RE47,157 [Application Number 15/620,417] was granted by the patent office on 2018-12-11 for discriminating electromagnetic radiation based on angle of incidence.
This patent grant is currently assigned to Massachusetts Institute of Technology. The grantee listed for this patent is Massachusetts Institute of Technology. Invention is credited to Peter Bermel, Ivan Celanovic, Michael Ghebrebrhan, Rafif E. Hamam, John D. Joannopoulos, Marin Soljacic, Adrian Y. X. Yeng.
United States Patent |
RE47,157 |
Hamam , et al. |
December 11, 2018 |
Discriminating electromagnetic radiation based on angle of
incidence
Abstract
The present invention provides systems, articles, and methods
for discriminating electromagnetic radiation based upon the angle
of incidence of the electromagnetic radiation. In some cases, the
materials and systems described herein can be capable of inhibiting
reflection of electromagnetic radiation (e.g., the materials and
systems can be capable of transmitting and/or absorbing
electromagnetic radiation) within a given range of angles of
incidence at a first incident surface, while substantially
reflecting electromagnetic radiation outside the range of angles of
incidence at a second incident surface (which can be the same as or
different from the first incident surface). A photonic material
comprising a plurality of periodically occurring separate domains
can be used, in some cases, to selectively transmit and/or
selectively absorb one portion of incoming electromagnetic
radiation while reflecting another portion of incoming
electromagnetic radiation, based upon the angle of incidence. In
some embodiments, one domain of the photonic material can include
an isotropic dielectric function, while another domain of the
photonic material can include an anisotropic dielectric function.
In some instances, one domain of the photonic material can include
an isotropic magnetic permeability, while another domain of the
photonic material can include an anisotropic magnetic permeability.
In some embodiments, non-photonic materials (e.g., materials with
relatively large scale features) can be used to selectively absorb
incoming electromagnetic radiation based on angle of incidence.
Inventors: |
Hamam; Rafif E. (Toronto,
CA), Bermel; Peter (Cambridge, MA), Celanovic;
Ivan (Cambridge, MA), Soljacic; Marin (Belmont, MA),
Yeng; Adrian Y. X. (Somerville, MA), Ghebrebrhan;
Michael (Cambridge, MA), Joannopoulos; John D. (Belmont,
MA) |
Applicant: |
Name |
City |
State |
Country |
Type |
Massachusetts Institute of Technology |
Cambridge |
MA |
US |
|
|
Assignee: |
Massachusetts Institute of
Technology (Cambridge, MA)
|
Family
ID: |
44511501 |
Appl.
No.: |
15/620,417 |
Filed: |
June 12, 2017 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
|
|
61365732 |
Jul 19, 2010 |
|
|
|
Reissue of: |
13186159 |
Jul 19, 2011 |
9057830 |
Jun 16, 2015 |
|
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
B82Y
20/00 (20130101); G02B 6/1225 (20130101); G02B
6/1225 (20130101); B82Y 20/00 (20130101); H01L
31/02168 (20130101); H02S 10/30 (20141201); H01L
31/02168 (20130101); H02S 10/30 (20141201); Y02E
10/50 (20130101); Y02E 10/50 (20130101) |
Current International
Class: |
G02B
27/42 (20060101); H01L 31/0232 (20140101); G02B
6/122 (20060101); B82Y 20/00 (20110101); H02S
10/30 (20140101); H01L 31/0216 (20140101); H01L
31/04 (20140101) |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
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101431109 |
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May 2009 |
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CN |
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WO 2009/036154 |
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Mar 2009 |
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WO |
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WO 2011/146843 |
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Nov 2011 |
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WO |
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WO 2012/012450 |
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Jan 2012 |
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WO |
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WO 2013/054115 |
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Apr 2013 |
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WO |
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WO 2015/178982 |
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Nov 2015 |
|
WO |
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|
Primary Examiner: Diamond; Alan
Attorney, Agent or Firm: Wolf, Greenfield & Sacks,
P.C.
Government Interests
GOVERNMENT SPONSORSHIP
.[.This invention was made with government support under Contract
No. W911NF-07-D-0004 awarded by the Army Research Office, Contract
No. DE-SC0001299 awarded by the Department of Energy, and Contract
No. DMR0819762 awarded by the National Science Foundation. The
government has certain rights in this invention..]. .Iadd.This
invention was made with Government support under Grant Nos.
DE-SC0001299 and DE-FG02-09ER46577 awarded by the Department of
Energy, under Grant No. DMR0819762 awarded by the National Science
Foundation, and under Contract No. W911NF-07-D-0004 awarded by the
Army Research Office. The Government has certain rights in the
invention. .Iaddend.
Parent Case Text
RELATED APPLICATIONS
.[.This application claims priority under 35 U.S.C. .sctn.119(e) to
U.S. Provisional Patent Application Ser. No. 61/365,732, filed Jul.
19, 2010, and entitled "Discriminating Electromagnetic Radiation
Based on Angle of Incidence," which is incorporated herein by
reference in its entirety for all purposes..]. .Iadd.This
application is a reissue of U.S. Pat. No. 9,057,830, issued on Jun.
16, 2015, filed as U.S. patent application Ser. No. 13/186,159 on
Jul. 19, 2011, and entitled "Discriminating Electromagnetic
Radiation Based on Angle of Incidence," which claims priority under
35 U.S.C. .sctn. 119(e) to U.S. Provisional Patent Application Ser.
No. 61/365,732, filed Jul. 19, 2010, and entitled "Discriminating
Electromagnetic Radiation Based on Angle of Incidence," each of
which is incorporated herein by reference in its entirety for all
purposes. .Iaddend.
Claims
What is claimed is:
1. An article, comprising: a photonic material comprising a
plurality of periodically occurring separate layers, including at
least a first layer and a second layer disposed over the first
layer, wherein: the first or second layer has an isotropic
dielectric function while the other of the first and second layers
has an anisotropic dielectric function; the first .[.or second.].
layer has an isotropic magnetic permeability while the .[.other of
the first and.]. second .[.layers.]. .Iadd.layer .Iaddend.has an
anisotropic magnetic permeability; .[.and.]. the first and second
layers are part of a 1-dimensionally periodic photonic crystal
comprising a periodic assembly of layers, wherein the
1-dimensionally periodic photonic crystal is arranged in such a way
that a line along a first coordinate direction within the
1-dimensionally periodic photonic crystal passes through multiple
layers while lines along second and third orthogonal coordinate
directions, each of the second and third orthogonal coordinate
directions being orthogonal to the first coordinate direction
within the 1-dimensionally periodic photonic crystal, do not pass
through multiple layers.Iadd.; and the second layer comprising the
anisotropic magnetic permeability comprises a combination of at
least two materials arranged to have an anisotropic effective
magnetic permeability.Iaddend..
2. The article of claim 1, wherein the first layer has an isotropic
dielectric function, and the second layer has an anisotropic
dielectric function.
3. The article of claim 1, wherein the first layer has an
anisotropic dielectric function, and the second layer has an
isotropic dielectric function.
.[.4. The article of claim 1, wherein the first layer has an
isotropic magnetic permeability, and the second layer has an
anisotropic magnetic permeability..].
.[.5. The article of claim 1, wherein the first layer has an
anisotropic magnetic permeability, and the second layer has an
isotropic magnetic permeability..].
6. The article of claim 2, wherein the second layer comprising an
anisotropic dielectric function comprises a .Iadd.single
.Iaddend.material having an anisotropic dielectric function.
7. The article of claim 6, wherein the .Iadd.single
.Iaddend.material having an anisotropic dielectric function
comprises TiO.sub.2, calcite, calomel, beryl, lithium niobate,
zircon, .[.and/or.]. .Iadd.or .Iaddend.mica.
8. The article of claim 2, wherein the second layer comprising an
anisotropic dielectric function comprises a combination of at least
two materials arranged to have an anisotropic effective dielectric
function.
9. The article of claim 8, wherein the combination of at least two
materials arranged to have an anisotropic effective dielectric
function form a 2-dimensionally periodic photonic crystal.
.[.10. The article of claim 4, wherein the second layer comprising
an anisotropic magnetic permeability comprises a combination of at
least two materials arranged to have an anisotropic effective
magnetic permeability..].
11. The article of claim .[.10.]. .Iadd.1.Iaddend., wherein the
second layer comprising an anisotropic magnetic permeability
comprises a combination of a metal and a second material.
12. The article of claim 11, wherein the second material comprises
a dielectric material.
13. The article of claim .[.10.]. .Iadd.1.Iaddend., wherein the
combination of at least two materials arranged to have an
anisotropic effective magnetic permeability form a 2-dimensionally
periodic photonic crystal.
14. The article of claim 1, wherein, when the photonic material is
exposed to electromagnetic radiation, at least about 75% of the
electromagnetic radiation within a range of wavelengths that
contacts an incident surface of the photonic material within a
range of angles of incidence is transmitted through the photonic
material, and at least about 75% of the electromagnetic radiation
within the range of wavelengths that contacts the incident surface
outside the range of angles of incidence is reflected by the
photonic material.
15. The article of claim 1, further comprising an energy conversion
device configured to produce electricity from electromagnetic
radiation received from the photonic material.
.[.16. The article of claim 15, wherein the energy conversion
device comprises a photovoltaic cell..].
.[.17. The article of claim 16, wherein the photovoltaic cell
comprises a solar photovoltaic cell..].
.[.18. The article of claim 16, wherein the photovoltaic cell is a
thermophotovoltaic cell..].
.[.19. The article of claim 16, wherein the energy conversion
device comprises a heat engine..].
.[.20. The article of claim 1, wherein the 1-dimensionally periodic
photonic crystal is configured to selectively transmit
electromagnetic radiation based upon the angle of incidence of the
electromagnetic radiation..].
.Iadd.21. An article, comprising: a plurality of separate layers,
including at least a first layer and a second layer disposed over
the first layer, wherein: the first or second layer has an
isotropic dielectric function while the other of the first and
second layers has an anisotropic dielectric function; the first and
second layers are part of a structure arranged in such a way that a
line along a first coordinate direction within the structure passes
through multiple layers while lines along second and third
orthogonal coordinate directions, each of the second and third
orthogonal coordinate directions being orthogonal to the first
coordinate direction within the structure, do not pass through
multiple layers; and the article is configured to selectively
transmit electromagnetic radiation based upon the angle of
incidence of the electromagnetic radiation such that at least about
75% of the electromagnetic radiation between 400 nm and 760 nm that
contacts an incident surface of the article at an angle of
incidence within 5.degree. of the 0.degree. angle normal to the
incident surface is not reflected by the article, and at least
about 75% of the electromagnetic radiation between 400 nm and 760
nm that contacts the incident surface of the article at an angle of
incidence outside 45.degree. of the 0.degree. angle normal to the
incident surface is reflected by the article..Iaddend.
.Iadd.22. The article of claim 21, wherein the article is
configured to selectively transmit electromagnetic radiation based
upon the angle of incidence of the electromagnetic radiation such
that at least about 75% of the electromagnetic radiation between
400 nm and 760 nm that contacts an incident surface of the article
at an angle of incidence within 5.degree. of the 0.degree. angle
normal to the incident surface is transmitted by the article, and
at least about 75% of the electromagnetic radiation between 400 nm
and 760 nm that contacts the incident surface of the article at an
angle of incidence outside 45.degree. of the 0.degree. angle normal
to the incident surface is reflected by the article..Iaddend.
.Iadd.23. The article of claim 21, further comprising: a third
layer disposed over the first layer and the second layer; and a
fourth layer disposed over the first layer, the second layer, and
the third layer, wherein: the first layer has an isotropic
dielectric function, the second layer has an anisotropic dielectric
function, the third layer has an isotropic dielectric function, and
the fourth layer has an anisotropic dielectric
function..Iaddend.
.Iadd.24. An article, comprising: a plurality of separate layers,
including at least a first layer and a second layer disposed over
the first layer, wherein: the first layer has an isotropic
dielectric function; the second layer has an anisotropic dielectric
function; and the article is configured to selectively transmit
electromagnetic radiation based upon the angle of incidence of the
electromagnetic radiation such that at least about 75% of the
electromagnetic radiation between 400 nm and 760 nm that contacts
an incident surface of the article at an angle of incidence within
5.degree. of the 0.degree. angle normal to the incident surface is
not reflected by the article, and at least about 75% of the
electromagnetic radiation between 400 nm and 760 nm that contacts
the incident surface of the article at an angle of incidence
outside 45.degree. of the 0.degree. angle normal to the incident
surface is reflected by the article..Iaddend.
.Iadd.25. The article of claim 24, wherein the article is
configured to selectively transmit electromagnetic radiation based
upon the angle of incidence of the electromagnetic radiation such
that at least about 75% of the electromagnetic radiation between
400 nm and 760 nm that contacts an incident surface of the article
at an angle of incidence within 5.degree. of the 0.degree. angle
normal to the incident surface is transmitted by the article, and
at least about 75% of the electromagnetic radiation between 400 nm
and 760 nm that contacts the incident surface of the article at an
angle of incidence outside 45.degree. of the 0.degree. angle normal
to the incident surface is reflected by the article..Iaddend.
.Iadd.26. The article of claim 21, wherein the article comprises a
material having a first index of refraction and is configured to be
exposed to electromagnetic radiation from a medium having a second
index of refraction that is smaller than the first index of
refraction..Iaddend.
.Iadd.27. The article of claim 22, wherein the article comprises a
material having a first index of refraction and is configured to be
exposed to electromagnetic radiation from a medium having a second
index of refraction that is smaller than the first index of
refraction..Iaddend.
.Iadd.28. The article of claim 21, wherein the article is
configured to selectively transmit electromagnetic radiation based
upon the angle of incidence of the electromagnetic radiation such
that at least about 75% of said electromagnetic radiation that
contacts an incident surface of the article at an angle of
incidence within 5.degree. of the 0.degree. angle normal to the
incident surface is transmitted through the article, and at least
about 75% of said electromagnetic radiation that contacts the
incident surface of the article at an angle of incidence outside
5.degree. of the 0.degree. angle normal to the incident surface is
reflected by the article..Iaddend.
.Iadd.29. The article of claim 26, wherein the article is
configured to selectively transmit electromagnetic radiation based
upon the angle of incidence of the electromagnetic radiation such
that at least about 75% of said electromagnetic radiation that
contacts an incident surface of the article at an angle of
incidence within 5.degree. of the 0.degree. angle normal to the
incident surface is transmitted through the article, and at least
about 75% of said electromagnetic radiation that contacts the
incident surface of the article at an angle of incidence outside
5.degree. of the 0.degree. angle normal to the incident surface is
reflected by the article..Iaddend.
.Iadd.30. The article of claim 24, wherein the article comprises a
material having a first index of refraction and is configured to be
exposed to electromagnetic radiation from a medium having a second
index of refraction that is smaller than the first index of
refraction..Iaddend.
.Iadd.31. The article of claim 25, wherein the article comprises a
material having a first index of refraction and is configured to be
exposed to electromagnetic radiation from a medium having a second
index of refraction that is smaller than the first index of
refraction..Iaddend.
.Iadd.32. The article of claim 24, wherein the article is
configured to selectively transmit electromagnetic radiation based
upon the angle of incidence of the electromagnetic radiation such
that at least about 75% of said electromagnetic radiation that
contacts an incident surface of the article at an angle of
incidence within 5.degree. of the 0.degree. angle normal to the
incident surface is transmitted through the article, and at least
about 75% of said electromagnetic radiation that contacts the
incident surface of the article at an angle of incidence outside
5.degree. of the 0.degree. angle normal to the incident surface is
reflected by the article..Iaddend.
.Iadd.33. The article of claim 30, wherein the article is
configured to selectively transmit electromagnetic radiation based
upon the angle of incidence of the electromagnetic radiation such
that at least about 75% of said electromagnetic radiation that
contacts an incident surface of the article at an angle of
incidence within 5.degree. of the 0.degree. angle normal to the
incident surface is transmitted through the article, and at least
about 75% of said electromagnetic radiation that contacts the
incident surface of the article at an angle of incidence outside
5.degree. of the 0.degree. angle normal to the incident surface is
reflected by the article..Iaddend.
Description
FIELD OF INVENTION
Articles, systems, and methods for discriminating electromagnetic
radiation based on angle of incidence are generally described.
BACKGROUND
Materials and structures that discriminate electromagnetic
radiation based on one or more of its properties (e.g.
polarization, frequency) can be useful in a wide range of systems.
For example, polarizers can discriminate (e.g., transmit and/or
absorb vs. reflect) electromagnetic radiation based on its
polarization, irrespective of the angle of incidence, over a wide
range of frequencies. Photonic crystals (PhCs) can reflect
electromagnetic radiation of certain frequencies irrespective of
the angle of incidence and irrespective of the polarization. A
material system that could transmit and/or absorb electromagnetic
radiation based on the angle of incidence could have a wide range
of uses.
SUMMARY OF THE INVENTION
Discriminating electromagnetic radiation based on the angle of
incidence, and associated articles, systems, and methods, are
generally described. The subject matter of the present invention
involves, in some cases, interrelated products, alternative
solutions to a particular problem, and/or a plurality of different
uses of one or more systems and/or articles.
In one aspect, a photonic material is described. In some
embodiments, the photonic material comprises a periodic assembly of
domains having different dielectric properties, the periodic
assembly of domains comprising a material having a first index of
refraction and configured to be exposed to electromagnetic
radiation from a medium having a second index of refraction that is
smaller than the first index of refraction. In some embodiments, at
least about 75% of a first portion of the electromagnetic radiation
that contacts a first incident surface of the photonic material at
an angle of incidence within a range of angles of incidence
spanning about 45.degree. or less is not reflected by the photonic
material, and at least about 75% of a second portion of the
electromagnetic radiation that contacts a second incident surface
of the photonic material at an angle of incidence outside the range
is reflected by the photonic material.
In one aspect, a system is provided. The system comprises, in some
embodiments, an electromagnetic radiation discriminator configured
to absorb and/or transmit electromagnetic radiation, the
discriminator comprising a material with a first index of
refraction and configured to be exposed to electromagnetic
radiation from a medium having a second index of refraction that is
smaller than the first index of refraction; an energy conversion
device configured to produce electricity from electromagnetic
radiation and/or heat received from the electromagnetic radiation
discriminator, wherein at least about 75% of a first portion of the
electromagnetic radiation that contacts a first incident surface of
the electromagnetic radiation discriminator at an angle of
incidence within a range of angles of incidence spanning about
45.degree. or less is absorbed and/or transmitted through the
radiation discriminator, and at least about 75% of a second portion
of electromagnetic radiation that contacts a second incident
surface of the electromagnetic radiation discriminator at an angle
of incidence outside the range is reflected by the article.
In some embodiments, the system comprises a transmitter comprising
a material with a first index of refraction configured to be
exposed to electromagnetic radiation from a medium in contact with
the transmitter having a second index of refraction that is smaller
than the first index of refraction; and an absorber configured to
absorb at least a portion of the electromagnetic radiation
transmitted through the transmitter; wherein at least about 75% of
a first portion of the electromagnetic radiation that is incident
upon a first incident surface of the transmitter at an angle of
incidence within a range of angles of incidence spanning about
45.degree. or less is transmitted through the transmitter, and at
least about 75% of a second portion of the electromagnetic
radiation that is incident upon a second incident surface of the
transmitter at an angle of incidence outside the range is reflected
by the transmitter.
In one aspect, an article is described. In some embodiments, the
article comprises a photonic material comprising a plurality of
periodically occurring separate domains, including at least a first
domain and a second domain adjacent the first domain, wherein the
first or second domain has an isotropic dielectric function while
the other of the first and second domains has an anisotropic
dielectric function; and the first or second domain has an
isotropic magnetic permeability while the other of the first and
second domains has an anisotropic magnetic permeability.
In some embodiments, the article comprises a photonic material
comprising a plurality of periodically occurring separate domains,
including at least a first domain and a second domain adjacent the
first domain, wherein the first or second domain has an isotropic
dielectric function while the other of the first and second domains
has an anisotropic dielectric function; and a polarizer configured
to produce TM-polarized electromagnetic radiation from the incoming
electromagnetic radiation such that the TM-polarized
electromagnetic radiation is incident on the photonic material.
Other advantages and novel features of the present invention will
become apparent from the following detailed description of various
non-limiting ornbodiments of the invention when considered in
conjunction with the accompanying figures. In cases where the
present specification and a document incorporated by reference
include conflicting and/or inconsistent disclosure, the present
specification shall control.
BRIEF DESCRIPTION OF THE DRAWINGS
Non-limiting embodiments of the present invention will be described
by way of example with reference to the accompanying figures, which
are schematic and are not intended to be drawn to scale. In the
figures, each identical or nearly identical component illustrated
is typically represented by a single numeral. For purposes of
clarity, not every component is labeled in every figure, nor is
every component of each embodiment of the invention shown where
illustration is not necessary to allow those of ordinary skill in
the art to understand the invention. In the figures:
FIGS. 1A-1B are exemplary schematic illustrations of articles that
can be used to discriminate electromagnetic radiation based on
angle of incidence, according to some embodiments;
FIG. 2 is an exemplary schematic illustration showing an incident
surface, according to some embodiments;
FIGS. 3A-3C show, according to some embodiments, exemplary
schematic diagrams of a macroscale filter used to discriminate
electromagnetic radiation based on angle of incidence;
FIGS. 4A-4B are exemplary schematic diagrams of a selective
absorber, according to some embodiments;
FIGS. 5A-5C are exemplary schematic diagrams of energy generation
systems, according to one set of embodiments;
FIGS. 6A-6E are, according to some embodiments, (A, C, and D)
schematic diagrams illustrating exemplary 1-dimensionally periodic
photonic crystals and (B and E) exemplary plots of transmission as
a function of frequency;
FIGS. 7A-7C are (A-B) schematic diagrams illustrating exemplary
1-dimensionally periodic photonic crystals and (C) an exemplary
contour plot of the change in the size of a bandgap as a function
of the incidence angle and the degree of anisotropy, according to
some embodiments;
FIGS. 8A-8C are, according to some embodiments, exemplary plots of
transmission as a function of frequency;
FIGS. 9A-9F are exemplary schematic diagrams of a macroscale
transmitter, according to some embodiments;
FIG. 10 is an exemplary schematic illustration of a
thermophotovoltaic system, according to one set of embodiments;
FIGS. 11A-11B are, according to some embodiments, exemplary plots
of (A) system efficiency and (B) area ratio as a function of
undesired emissivity;
FIGS. 12A-12B are exemplary contour plots of overall system
efficiency as a function of temperature and TPV bandgap, according
to some embodiments;
FIG. 13 is an exemplary plot of emissivity as a function of polar
angle, according to some embodiments;
FIG. 14 is an exemplary plot of system efficiency as a function of
temperature; and
FIG. 15 is an exemplary plot of emissivity as a function of
wavelength.
DETAILED DESCRIPTION
The present invention provides systems, articles, and methods for
discriminating electromagnetic radiation based upon the angle of
incidence of the electromagnetic radiation. In some cases, the
materials and systems described herein can be capable of inhibiting
reflection of electromagnetic radiation (e.g., the materials and
systems can be capable of transmitting and/or absorbing
electromagnetic radiation) within a given range of angles of
incidence at a first incident surface, while substantially
reflecting electromagnetic radiation outside the range of angles of
incidence at a second incident surface (which can be the same as or
different from the first incident surface). A photonic material
comprising a plurality of periodically occurring separate domains
can be used, in some cases, to selectively transmit and/or
selectively absorb one portion of incoming electromagnetic
radiation while reflecting another portion of incoming
electromagnetic radiation, based upon the angle of incidence. In
some embodiments, one domain of the photonic material can include
an isotropic dielectric function, while another domain of the
photonic material can include an anisotropic dielectric function.
In some instances, one domain of the photonic material can include
an isotropic magnetic permeability, while another domain of the
photonic material can include an anisotropic magnetic permeability.
In some embodiments, non-photonic materials (e.g., materials with
relatively large scale features) can be used to selectively absorb
incoming electromagnetic radiation based on angle of incidence.
In some applications, it would be beneficial if electromagnetic
radiation incident at a particular angle (or a range of angles)
would be inhibited from being reflected (e.g., it would be
transmitted and/or absorbed), while other angles of incidence would
be substantially reflected (e.g., nearly perfectly reflected),
independent of the incoming polarization, and for as wide a range
of frequencies as possible. Such materials could be useful in a
wide variety of applications including, for example, solar energy
applications, producing a highly enhanced green-house effect. As
one specific, non-limiting example, such materials could be used to
discriminate sunlight, which travels along a relatively
well-defined direction and, accordingly, has a relatively
well-defined angle of incidence. When sunlight interacts with
components of solar-energy conversion devices (e.g., solar
absorbers, selective emitters, photovoltaic (PV) cells, etc.), a
portion of sunlight can be reflected from one or more components of
the solar-energy conversion device, while another portion can be
re-radiated (e.g., because of radiative recombination, or in
solar-thermal systems because of thermal emission). Reflection and
re-radiation result in energy losses, which can often be
substantial and can lower the overall efficiency of the
solar-energy conversion device. If one could place a material
proximate an absorber, selective emitter, and/or a PV cell (e.g., a
solar cell) that would substantially inhibit reflection of (e.g.,
substantially transmit and/or substantially absorb) electromagnetic
radiation at a particular angle (e.g., the angle coming from the
sun) or range of angles, while substantially reflecting
electromagnetic radiation emerging from the solar-energy conversion
device (most of which propagates at angles that are different from
the angle at which the electromagnetic radiation approaches from
the sun) back to the solar-energy conversion device, the efficiency
of the energy-conversion system could be greatly improved.
In some embodiments, the devices and systems described herein make
use of photonic materials. As used herein, the terms "photonic
material" and "photonic crystal" are given their ordinary meaning
in the art, and refer to a material that can control the
propagation of electromagnetic radiation based on a periodic
assembly of domains having different dielectric properties. In some
embodiments, the photonic crystals include domains with one or more
dimensions of the same order of magnitude as the wavelength(s) of
the electromagnetic radiation the photonic crystal is configured to
control the propagation of. "Photonic crystal" and "photonic
material" are used interchangeably herein, and refer to the same
class of materials.
The photonic materials described herein can have, in some cases,
1-dimensional and/or 2-dimensional periodicity. One of ordinary
skill in the art would be able to determine the dimensionality of
the periodicity of a photonic crystal upon inspection. For example,
1-dimensionally periodic photonic crystals include materials
arranged in such a way that a line along a first coordinate
direction within the photonic crystal passes through multiple
domains while lines along second and third orthogonal coordinate
directions, each of the second and third coordinate directions
being orthogonal to the first coordinate direction within the
photonic crystal, do not pass through multiple domains. In some
embodiments, the index of refraction at least one point within the
1-dimensionally periodic photonic crystal varies along a first
coordinate direction and does not substantially vary along second
and third orthogonal coordinate directions, each of the second and
third coordinate directions being orthogonal to the first
coordinate direction. For example, a 1-dimensionally periodic
photonic crystal can include two or more materials and/or
metamaterials arranged in a stack such that a line along a first
coordinate direction passes through multiple layers while lines
along second and third coordinate directions (each orthogonal to
the first coordinate direction) remain within a single layer. An
example of a 1-dimensionally periodic photonic crystal is shown as
photonic crystal 118 in FIG. 1A.
2-dimensionally periodic photonic crystals include materials
arranged in such a way that lines along first and second orthogonal
coordinate directions within the photonic crystal pass through
multiple domains while a line along a third coordinate direction,
orthogonal to the first and second coordinate directions, does not
pass through multiple domains. In some embodiments, the index of
refraction within the volume of a 2-dimensionally periodic photonic
crystal varies along first and second orthogonal coordinate
directions, but does not substantially vary along a third
coordinate direction orthogonal to the first and second coordinate
directions. For example, a 2-dimensionally periodic photonic
crystal can include two or more materials arranged such that at
least one material forms a series of elongated rods that extend
through the thickness of another material. An example of a
2-dimensionally periodic photonic crystal is shown in FIGS. 4A-4B
and on the left side of FIG. 6A.
As noted above, various aspects are related to distinguishing
electromagnetic radiation based on angle of incidence. As used
herein, the "angle of incidence" between electromagnetic radiation
and a given article (e.g., an incident surface of the article)
refers to the smallest angle formed between the vector along which
electromagnetic radiation travels and the line extending
perpendicularly from the incident surface from the point at which
the electromagnetic radiation intersects the incident surface of
the article. For example, in the set of embodiments illustrated in
FIG. 1A, the angle of incidence 192 between incoming
electromagnetic radiation 190 and incident surface 150 is measured
relative to line 161 normal to incident surface 150 and originating
from point 162, where electromagnetic radiation 190 intersects
incident surface 150.
In this context, an "incident surface" of an article refers to the
geometric surface of the article, which will be understood by those
of ordinary skill in the art to refer to the surface defining the
outer boundaries of the article on which electromagnetic radiation
is incident, and does not include surfaces lying within the
external boundaries of the article. For example, the incident
surface would include the area that may be measured by a
macroscopic measuring tool (e.g., a ruler), but would not include
surfaces formed by pores or holes formed within the article. In
some cases (e.g., when an article has a relatively smooth,
non-porous exterior surface), the incident surface of an article
corresponds to a physical surface of the article. For example, in
the set of embodiments illustrated in FIG. 1A, incident surface 150
of photonic crystal 118 corresponds to the top surface of photonic
crystal 118. In other embodiments (e.g., when the external surface
of the object includes pores, holes, and/or other discontinuities
passing through it), the incident surface is an imaginary surface
that spans the outermost points of the object. For example, in the
set of embodiments illustrated in FIG. 2, incident surface of
article 200 corresponds to imaginary surface 210. In this set of
embodiments, the angle of incidence between electromagnetic
radiation 212 and article 200 corresponds to angle 214, even though
electromagnetic radiation 212 does not contact article 200 until
point 220. In FIG. 2, angle 214 is the smallest angle between the
vector along which electromagnetic radiation 212 travels and a line
216 that is perpendicular to surface 210 and originates from the
point 218 at which electromagnetic radiation 212 intersects surface
210.
In some embodiments, the articles described herein can be
configured to inhibit reflection of electromagnetic radiation
(e.g., transmit and/or absorb electromagnetic radiation) that
contacts a first incident surface of the article at an angle of
incidence within a range of angles. For example, in some
embodiments, the article can be configured such that at least about
75%, at least about 85%, at least about 95%, at least about 99%, at
least about 99.9%, or substantially all of the electromagnetic
radiation that contacts the first incident surface at an angle of
incidence within a range of angles of incidence spanning about
45.degree. or less, about 30.degree. or less, about 15.degree. or
less, about 5.degree. or less, about 2.degree. or less, or about
1.degree. or less is not reflected by the article (e.g., is
transmitted through the article and/or is absorbed by the article).
A range of angles of incidence is said to span X.degree. when the
range includes all incidence angles from Y.degree. to Z.degree.,
wherein the difference between Z and Y is X. For example, a range
of angles of incidence spanning 30.degree. could include all
incidence angles between 0.degree. and 30.degree. (where, according
to the description above, Y=0 and Z=30), all incidence angles
between 15.degree. and 45.degree., all incidence angles between
30.degree. and 60.degree., etc. In some embodiments, the range of
angles of incidence over which reflection of the electromagnetic
radiation is inhibited includes the 0.degree. angle normal to an
incident surface. In some embodiments, and as described in more
detail below, the range of angles of incidence over which
reflection of electromagnetic radiation is inhibited does not
include the 0.degree. angle normal to the incident surface.
In some embodiments, the articles described herein can be
configured to substantially reflect electromagnetic radiation that
contacts a second incident surface of the article at an angle of
incidence outside the range of angles over which reflection was
inhibited. For example, in some embodiments, the article can be
configured such that at least about 75%, at least about 85%, at
least about 95%, at least about 99%, at least about 99.9%, or
substantially all of the electromagnetic radiation that contacts
the second incident surface outside the range of angles of
incidence spanning about 45.degree. or less, about 30.degree. or
less, about 15.degree. or less, about 5.degree. or less, about
2.degree. or less, or about 1.degree. or less is reflected by the
article.
In some embodiments, the first incident surface and the second
incident surface are the same. For example, in some articles
described herein, the top surface of the article can be configured
such that it inhibits reflection of electromagnetic radiation
within a given range of angles of incidence and substantially
reflects electromagnetic radiation outside that range of angles of
incidence. In some embodiments, the first incident surface and the
second incident surface are different. For example, in some
embodiments (e.g., in some cases in which a selective transmitter
is employed), the first incident surface is the top surface of the
article (e.g., a surface exposed to incoming electromagnetic
radiation from a source such as the sun), which can be configured
to inhibit reflection of incoming electromagnetic radiation within
a given range of angles of incidence. In some such embodiments, the
second incident surface is the bottom surface of the article (e.g.,
a surface exposed to reflected and/or re-emitted radiation from a
selective emitter, TPV cell, etc.) which can be configured to
reflect incident electromagnetic radiation with an angle of
incidence outside the given range of angles.
In some embodiments in which the first and second incident surfaces
are different, the second incident surface can be substantially
parallel to the first incident surface. In some embodiments, the
first incident surface and the second incident surfaces face in
opposite directions (e.g., incident surfaces 150 and 151 in FIG.
1A).
In some embodiments, at least some (and, in some cases, all) of the
material within the articles used to discriminate electromagnetic
radiation has an index of refraction that is greater than the index
of refraction of a medium in contact with the article and through
which electromagnetic radiation (e.g., discriminated
electromagnetic radiation) passes to contact the article. For
example, in many embodiments described herein, the electromagnetic
radiation is transported through air (which has an index of
refraction of about 1.0003) prior to contacting the article, and
the article includes a material having an index of refraction
greater than that of air (e.g., tungsten, which has an index of
refraction of about 2). One of ordinary skill in the art would be
capable of measuring the index of refraction of an article using an
ellipsometer. The articles described herein can be configured to
discriminate electromagnetic radiation over a relatively broad
range of wavelengths, in some embodiments. For example, in some
cases, the articles described herein can be configured to
discriminate electromagnetic radiation (e.g., inhibit reflection of
and/or substantially reflect electromagnetic radiation to any of
the extents mentioned herein and/or within/outside any of the
ranges of angles of incidence mentioned herein) based on the angle
of incidence over a range of wavelengths of between about 100 nm
and about 300 micrometers, between about 100 nm and about 100
micrometers, between about 100 nm and about 10 micrometers, or
between about 100 nm and about 1 micrometer. In some embodiments,
the articles described herein can be configured to discriminate
visible electromagnetic radiation (e.g., between about 400 nm and
about 760 nm), ultraviolet electromagnetic radiation (e.g., between
about 100 nm and about 400 nm), and/or infrared electromagnetic
radiation (e.g., between about 760 nm and about 300 micrometers).
In some embodiments, the electromagnetic radiation includes a
wavelength that interacts photonically with a photonic material in
the article configured to discriminate electromagnetic
radiation.
As noted above, in some embodiments, articles for discriminating
electromagnetic radiation based upon the angle of incidence (i.e.,
electromagnetic radiation angular discriminators) are provided. In
some embodiments, an article can discriminate electromagnetic
radiation such that a relatively large percentage of incident
radiation within a range of angles of incidence is transmitted
through the article and a relatively large percentage of the
incident radiation outside the range of angles of incidence is
reflected by the article. FIG. 1A includes an exemplary schematic
illustration of article 100, which can be used to substantially
reflect or substantially transmit electromagnetic radiation based
upon the angle of incidence, according to some embodiments. In FIG.
1A, article 100 includes a plurality of periodically occurring
separate domains, including first domain regions 110 and second
domain regions 112. The first and second domain regions can be
adjacent each other. For example, in some embodiments, one or more
materials (e.g., an adhesion promoter) that does not affect the
functionality of a photonic crystal defined by regions 110 and 112
can be positioned between regions 110 and 112). In some
embodiments, such as those illustrated in FIG. 1A, the first and
second domain regions can be in physical contact with each
other.
In some embodiments, the first domain regions comprise a first
material and the second domain regions comprise a second material
that has at least one property (e.g., index of refraction) that is
different from the first material. The first and second domains can
form a plurality of bilayers, each bilayer having a period equal to
the thickness of the bilayer. For example, in FIG. 1A, domains 110
and 112 form bilayers 114, 115, and 116. The first and second
domains can be arranged, in some instances, such that they form a
photonic material. For example, in the set of embodiments
illustrated in FIG. 1A, domains 110 and 112 are arranged such that
they form a 1-dimensionally periodic photonic crystal 118. The
photonic materials (or stacks within a photonic material) described
herein can include any suitable number of bilayers (e.g., at least
2, at least 3, at least 5, at least 10, at least 20, or more).
In some embodiments, the first or second domain has an isotropic
dielectric function while the other of the first and second domains
has an anisotropic dielectric function. One of ordinary skill in
the art would understand the meaning of the terms "isotropic
dielectric function" and "anisotropic dielectric function." The
dielectric function of a domain made of a single material
corresponds to the dielectric function of that material. The
dielectric function of a domain including multiple materials
corresponds to the overall dielectric function of the domain (also
referred to as an "effective dielectric function"), rather than the
dielectric functions of the individual materials within the domain.
The dielectric function of a domain (including one material or
including multiple materials) can be measured using an
ellipsometer. In some embodiments, the dielectric function of a
domain along a first coordinate direction can be at least about 5%,
at least about 10%, at least about 25%, at least about 50%, or at
least about 100% different than the dielectric function of the
domain along a second and/or third coordinate direction, the second
and third coordinate directions orthogonal to each other and to the
first coordinate direction. In some cases, the first domain (e.g.,
domains 110 in FIG. 1A) has an isotropic dielectric function and
the second domain (e.g., domains 112 in FIG. 1A) has an anisotropic
dielectric function. In other cases, the first domain (e.g.,
domains 110 in FIG. 1A) can have an anisotropic dielectric function
while the second domain (e.g., domains 112 in FIG. 1A) has an
isotropic dielectric function.
By arranging the domains such that they have alternating
isotropic/anisotropic dielectric functions, one can discriminate
TM-polarized electromagnetic radiation based upon the angle of
incidence. For example, in some embodiments, the thicknesses and/or
dielectric functions of domains 110 and 112 can be configured such
that a high percentage (e.g., at least about 75%, at least about
85%, at least about 95%, at least about 99%, at least about 99.9%,
or substantially all) of the TM-polarized electromagnetic radiation
that contacts a first incident surface of article 100 (e.g.,
incident surface 150 and/or incident surface 151) at an angle of
incidence within a given range of angles of incidence (e.g., a
range of angles of incidence spanning about 45.degree. or less,
about 30.degree. or less, about 15.degree. or less, about 5.degree.
or less, about 2.degree. or less, or about 1.degree. or less) will
be transmitted through the photonic material, while a relatively
high percentage (e.g., any of the percentages mentioned above) of
the TM-polarized electromagnetic radiation that contacts a second
incident surface of article 100 (e.g., surface 150 and/or surface
151) at an angle of incidence outside the given range of angles of
incidence will be reflected by the photonic material. In the set of
embodiments illustrated in FIG. 1A, range 120 includes a range of
angles of incidence that spans about 30.degree. (it includes all
angles of incidence between 0.degree. and 30.degree., thus spanning
a range of about 30.degree.). In the set of embodiments illustrated
in FIG. 1A, photonic crystal 118 can be configured such that a high
percentage of incident TM-polarized electromagnetic radiation with
an angle of incidence of 30.degree. or less (i.e., within range
120) is transmitted through photonic crystal 118, while incident
TM-polarized electromagnetic radiation with an angle of incidence
greater than 30.degree. (i.e., outside range 120) is reflected by
photonic crystal 118.
One can construct a domain with an anisotropic dielectric function
in a number of ways. In some cases, the domain comprising an
anisotropic dielectric function can comprise a material that has an
anisotropic dielectric function (also sometimes referred to as
birefringent materials) such as, for example, TiO.sub.2, calcite,
calomel (mercury chloride), beryl, lithium niobate, zircon, mica,
and/or mixtures of these. One of ordinary skill in the art would be
capable of selecting other materials with anisotropic dielectric
functions suitable for use with the embodiments described herein.
In some embodiments, a domain comprising an anisotropic dielectric
function comprises a combination of at least two materials arranged
to have an anisotropic effective dielectric function. For example,
in some cases, a combination of at least two materials can be
arranged to form a 2-dimensionally periodic photonic crystal. FIG.
6A includes one example of a 2-dimensionally periodic photonic
crystal suitable for use as a domain comprising an anisotropic
dielectric function. One of ordinary skill in the art, given the
present disclosure, would be capable of using a screening test to
select materials and/or configure a multi-material system to
achieve a desired anisotropic dielectric function within a domain
by, for example, fabricating a domain out of a selected material
and/or fabricating a multi-material domain and measuring the
dielectric function of the domain from various angles to determine
whether the domain has an anisotropic dielectric function.
In some embodiments, the first or second domain can have an
isotropic magnetic permeability while the other of the first and
second domains has an anisotropic magnetic permeability. One of
ordinary skill in the art would understand the meaning of the terms
"isotropic magnetic permeability" and "anisotropic magnetic
permeability." The magnetic permeability of a domain made of a
single material corresponds to the magnetic permeability of that
material. The magnetic permeability of a domain including multiple
materials corresponds to the overall magnetic permeability of the
domain (also referred to as an "effective magnetic permeability"),
rather than the magnetic permeabilities of the individual materials
within the domain. The magnetic permeability of a domain (including
one material or including multiple materials) can be measured
using, for example, a superconductive magnet or a balance, such as
an Evans balance or a Gouy balance. In some embodiments, the
magnetic permeability of a domain along a first coordinate
direction can be at least about 5%, at least about 10%, at least
about 25%, at least about 50%, or at least about 100% different
than the magnetic permeability of the domain along a second and/or
third coordinate direction, the second and third coordinate
directions orthogonal to each other and to the first coordinate
direction. In some cases, the first domain (e.g., domain 110 in
FIG. 1A) has an isotropic magnetic permeability and the second
domain (e.g., domain 112 in FIG. 1A) has an anisotropic magnetic
permeability. In some instances, the first domain (e.g., domain 110
in FIG. 1A) has an anisotropic magnetic permeability and the second
domain (e.g., domain 112 in FIG. 1A) has an isotropic magnetic
permeability.
One might construct a domain with an anisotropic magnetic
permeability in a number of ways. For example, a domain comprising
an anisotropic magnetic permeability might comprise a combination
of at least two materials arranged to have an anisotropic effective
magnetic permeability. The two materials might comprise, for
example, a metal and a second material (e.g., a metal and a
dielectric material). For example, metallo-dielectric materials are
described in Pendry, et al., IEEE transactions on microwave theory
and techniques, 47, No. 11, November 1999. In some cases, the
domain comprising an anisotropic magnetic permeability might
comprise a 2-dimensionally periodic photonic crystal. As another
example, metamaterials are described in Li et al., "Large Absolute
Band Gap in 2D Anisotropic Photonic Crystals," Physical Review
Letters, 81, No. 12, 21 Sep. 1998. One of ordinary skill in the
art, given the present disclosure, would be capable of using a
screening test to select materials and/or configure a
multi-material system to achieve a desired anisotropic magnetic
permeability within a domain by, for example, fabricating a domain
out of a selected material and/or fabricating a multi-material
domain and measuring the magnetic permeability of the domain from
various angles to determine whether the domain has an anisotropic
magnetic permeability. In some embodiments, a multi-material system
can be designed using rigorous simulations of Maxwell's equations
to achieve certain effective dielectric constants along particular
directions, resulting in a certain degree of anisotropy.
By arranging the domains such that they have alternating
isotropic/anisotropic magnetic permeabilities, one can discriminate
TE-polarized electromagnetic radiation based upon the angle of
incidence. For example, in some embodiments, the thicknesses and/or
magnetic permeabilities of domains 110 and 112 can be configured
such that a high percentage (e.g., at least about 75%, at least
about 85%, at least about 95%, at least about 99%, at least about
99.9%, or substantially all) of the TE-polarized electromagnetic
radiation that contacts a first incident surface of photonic
crystal 118 (e.g., incident surface 150 and/or incident surface
151) at an angle of incidence within a given range of angles of
incidence (e.g., a range of angles of incidence spanning about
45.degree. or less, about 30.degree. or less, about 15.degree. or
less, about 5.degree. or less, about 2.degree. or less, or about
1.degree. or less) will be transmitted through the photonic
material while a relatively high percentage (e.g., any of the
percentages mentioned above) of the TE-polarized electromagnetic
radiation that contacts a second incident surface of article 100
(e.g., surface 150 and/or surface 151) at an angle of incidence
outside the given range of angles of incidence will be reflected by
the photonic material. In the set of embodiments illustrated in
FIG. 1A, photonic crystal 118 can be configured such that a high
percentage of incident TE-polarized electromagnetic radiation with
an angle of incidence within range 120 (which, as mentioned above,
spans about 30.degree.) is transmitted through photonic material
118, while a high percentage of incident TE-polarized
electromagnetic radiation with an angle of incidence outside range
120 is reflected by photonic material 118.
The ability to discriminate both TM-polarized and TE-polarized
electromagnetic radiation based upon angle of incidence can allow
one to discriminate incident electromagnetic radiation based on
angle of incidence regardless of polarization. In some embodiments,
at least about 75%, at least about 85%, at least about 95%, at
least about 99%, at least about 99.9%, or substantially all of the
electromagnetic radiation that contacts a first incident surface
(e.g., surface 150 and/or surface 151 in FIG. 1A) of the photonic
material within a range of angles of incidence is transmitted
through the photonic material. In some embodiments, at least about
75%, at least about 85%, at least about 95%, at least about 99%, at
least about 99.9%, or substantially all of the electromagnetic
radiation that contacts a second incident surface (e.g., surface
150 and/or surface 151 in FIG. 1A) of the photonic material outside
a range of angles of incidence is reflected by the photonic
material. In some embodiments, the range of angles of incidence
spans about 45.degree. or less, about 30.degree. or less, about
15.degree. or less, about 5.degree. or less, about 2.degree. or
less, or about 1.degree. or less. The spacing and/or material
properties of the domains can be selected, in some cases, to tailor
the range of incident angles over which electromagnetic radiation
is transmitted through the photonic crystal.
As noted above, in the set of embodiments illustrated in FIG. 1A,
the range 120 of the angles of incidence over which incoming
electromagnetic radiation is transmitted through photonic material
118 spans about 30.degree.. Physically, the range of angles of
incidence illustrated in FIG. 1A would correspond to a cone with an
angle at its apex of about 60.degree. (since angles formed on
either side of line 160 would fall within the 30.degree. span of
angles of incidence). In some embodiments, the range of angles of
incidence over which electromagnetic radiation is transmitted
through the photonic material can include the 0.degree. angle
normal to an incident surface (e.g., indicated by line 160 in FIG.
1A). As noted above, in some embodiments, the range of angles of
incidence over which electromagnetic radiation is transmitted
through the photonic material does not include the 0.degree. angle
normal to the incident surface. For example, the photonic crystal
illustrated in FIG. 1B transmits electromagnetic radiation within
range 180 of angles of incidence, which spans 30.degree. and
includes angles of incidence between about 15.degree. and about
45.degree.. Range 180 in FIG. 1B does not include the 0.degree.
angle normal to the incident surface.
In some embodiments, the frequency range over which light is
absorbed within a given range of angles of incidence can be
broadened by including multiple stacks of to bilayers within the
photonic material. For example, in some cases, the photonic
material can comprise at least 2, at least 5, at least 10, at least
20, at least 50, at least 100, or more stacks of bilayers. In some
embodiments, the bilayers within each of the stacks might have
different periods. For example, in some embodiments, the photonic
material can comprise a first stack of bilayers with a first
period, which can be used to discriminate electromagnetic radiation
with wavelengths within a first range of wavelengths, and a second
stack of bilayers with a second period, which can be used to
discriminate electromagnetic radiation with wavelengths within a
second range of wavelengths. One of ordinary skill in the art,
given the present disclosure, would be capable of using a screening
test to adjust the period(s) of bilayer(s) to achieve a desired
angular selectivity over a desired range of wavelengths by, for
example, fabricating a stack of bilayers, exposing the bilayers to
electromagnetic radiation of a wavelength one desires to
discriminate at a variety of angles of incidence, and measuring the
amount of the electromagnetic radiation that is transmitted and/or
absorbed by the bilayers.
In some cases (e.g., in some instances where domains with
anisotropic magnetic permeabilities are not used), the system can
include an optional polarizer configured to produce TM-polarized
electromagnetic radiation from the incoming electromagnetic
radiation such that the TM-polarized electromagnetic radiation is
incident on the photonic material. For example, in the set of
embodiments illustrated in FIG. 1A, optional polarizer 130 can be
positioned proximate photonic crystal 118. As incoming
electromagnetic radiation 132 is transmitted through polarizer 130,
TM-polarized electromagnetic radiation 134 and TE-polarized
electromagnetic radiation 136 can be produced. In some cases, an
optional rotator can be provided, which can be configured to rotate
at least a portion of (e.g., at least 50%, at least about 75%, at
least about 90%, at least about 99%, or substantially all of) the
TE-polarized electromagnetic radiation from the polarizer into
TM-polarized electromagnetic radiation, which can then be
transmitted to the photonic material. For example, in FIG. 1A,
optional rotator 138 can be used to rotate at least a portion of
TE-polarized electromagnetic radiation 136 into TM-polarized
electromagnetic radiation 140, which is then transmitted to
photonic material 118.
In addition to 1-dimensionally periodic photonic crystals,
selective transmission of incident electromagnetic radiation can be
achieved using non-photonic articles with relatively large-scale
features. For example, in some embodiments, selective transmission
of incident electromagnetic radiation can be achieved using a
macroscale filter, optionally made of a reflective material,
comprising a plurality of elongated channels formed through the
filter. Electromagnetic radiation that intersects an incident
surface of the macroscale filter proximate the channel openings and
that propagates parallel to or nearly parallel to the channels in
the macroscale filter can be transmitted through the macroscale
filter. On the other hand, electromagnetic radiation that is
incident on reflective portions of the incident surface of the
macroscale filter and/or electromagnetic radiation that travels at
angles that are far from parallel to the channels within the
macroscale filter can be reflected from, rather than transmitted
through, the macroscale filter.
FIGS. 3A-3B are schematic illustrations of an exemplary macroscale
filter 300, which can be used to selectively transmit
electromagnetic radiation based on angle of incidence. FIG. 3A is a
top-view of the filter, while FIG. 3B is a side-view of a
cross-section of the filter taken along plane 301. Filter 300
includes a reflective portion 310 and a plurality of elongated
channels 312 extending through the thickness 314 of filter 300.
Elongated channels 312 include a material that is transparent to
incoming electromagnetic radiation so that the electromagnetic
radiation can be transmitted through the macroscale filter via
channels 312. As shown in FIG. 3B, electromagnetic radiation 316A
is nearly parallel to channels 312 in macroscale filter 300. In
addition, electromagnetic radiation 316A intersects incident
surface 318 of macroscale filter 300 proximate channel opening 320.
Accordingly, electromagnetic radiation 316A is transmitted through
macroscale filter 300.
Electromagnetic radiation 316B in FIG. 3B is incident upon portion
322 of incident surface 318, which is formed, at least partially,
of a reflective material. Accordingly, even though electromagnetic
radiation 316B is propagated in a direction that is substantially
parallel to channels 312, electromagnetic radiation 316B is
reflected back toward the source and is not transmitted through
filter 300.
Electromagnetic radiation 316C in FIG. 3B is propagated at an angle
relative to incident surface 318 of filter 300, such that
electromagnetic radiation 316C and incident surface 318 define
incidence angle 319. Electromagnetic radiation 316C is partially
transmitted through channel 312B and contacts internal surface
portion 324A of filter 300. In FIG. 3B, a portion of
electromagnetic radiation 316C is subsequently reflected from
portions 324B, 324C, and 324D of channel 312B, and transmitted
through filter 300. Another portion of electromagnetic radiation
316C, on the other hand, will be absorbed by the walls of channel
312B or reflected at angles that prevent the transmission of the
electromagnetic radiation through the filter. Accordingly, only a
portion of electromagnetic radiation 316C that intersects incident
surface 318 will be transmitted through filter 300. In the system
illustrated in FIGS. 3A-3B, electromagnetic radiation defining a
relatively large angle of incidence will be transmitted to a lesser
extent than electromagnetic radiation defining a relatively small
angle of incidence. For example, for the set of embodiments
illustrated in FIG. 3B, the larger angle 319 is, the less
electromagnetic radiation will be transmitted through the
filter.
While channels 312 illustrated in FIGS. 3A-3B have substantially
circular cross-sectional shapes and are substantially cylindrical,
other cross-sectional shapes can be employed. In some embodiments,
one or more channels formed within a macroscale filter can have a
cross-sectional shape that is essentially a circle, essentially an
ellipse, essentially an ellipsoid, essentially a polygon (regular
or irregular, and including shapes that are essentially triangles,
quadrilaterals (including rectangles and squares), pentagons,
hexagons, etc.), irregular, or any other suitable cross-sectional
shape.
The cross-sectional shape of the channels within the macroscale
filter can be, in some cases, substantially constant along their
lengths. In some embodiments, at least some of the channels (e.g.,
at least about 50%, at least about 75%, at least about 90%, at
least about 95%, or at least about 99%) have a substantially
constant cross-sectional shape along essentially the entire length
of the channel. For example, in the set of embodiments illustrated
in FIGS. 3A-3B, each of channels 312 has a substantially constant
cross-sectional shape (substantially circular) along the entire
length of the channel.
In some embodiments, the channels within the macroscale filter can
have relatively large cross-sectional diameters. As used herein,
the "cross-sectional diameter" of a channel is measured
perpendicular to the length of the channel. The cross-sectional
diameter of a cylindrical channel is the cross-sectional diameter
of that cylinder. For example, in the set of embodiments
illustrated in FIGS. 3A-3B, the cross-sectional diameters of the
channels correspond to dimension 315. For non-cylindrical channels,
the cross-sectional diameter corresponds to the cross-sectional
diameter of a theoretical cylinder with the same volume and length
as the non-cylindrical channel. In some embodiments, the
cross-sectional diameter of at least one channel (e.g., at least
about 10%, at least about 25%, at least about 50%, at least about
75%, at least about 90%, at least about 95%, or at least about 99%
of the channels) in the macroscale filter is at least about 1
micrometer, at least about 10 micrometers, at least about 100
micrometers, at least about 1 mm, or at least about 10 mm. In some
embodiments, the average and/or the median of the cross-sectional
diameters of the channels in the filter can be at least about 1
micrometer, at least about 10 micrometers, at least about 100
micrometers, at least about 1 mm, or at least about 10 mm.
As noted above, the channels in the macroscale filter can be
elongated and can, in some embodiments, have a relatively large
aspect ratio. The aspect ratio of a channel is calculated by
dividing the length of the channel by the cross-sectional diameter
of the channel. For example, in the set of embodiments illustrated
in FIGS. 3A-3B, the aspect ratios of the channels can be calculated
by dividing the channel lengths (corresponding to dimension 314) by
the channel cross-sectional dimensions 315. In some embodiments,
the aspect ratio of at least one channel (e.g., at least about 10%,
at least about 25%, at least about 50%, at least about 75%, at
least about 90%, at least about 95%, or at least about 99% of the
channels) in the macroscale filter is at least about 3, at least
about 5, at least about 10, at least about 50, at least about 100,
at least about 250, at least about 400, between about 3 and about
500, between about 5 and about 500, between about 50 and about 500,
or between about 100 and about 500. In some embodiments, the
average and/or the median of the aspect ratios of the channels in
the filter can be at least about 3, at least about 5, at least
about 10, at least about 50, or at least about 100, at least about
250, at least about 400, between about 3 and about 500, between
about 5 and about 500, between about 50 and about 500, or between
about 100 and about 500.
In some embodiments, the macroscale filter can be configured such
that a relatively small portion of the surface area of at least one
incident surface (e.g., incident surface 318 and/or incident
surface 321) is occupied by reflective material. For the filter
illustrated in FIGS. 3A-3B, the portion of the surface area of the
incident surface occupied by the reflective material corresponds to
the area of region 310 in FIG. 3A, while the portion of the surface
area of the incident surface occupied by the channels corresponds
to the sum of the areas of regions 312 in FIG. 3A. In some
embodiments, less than about 20%, less than about 10%, less than
about 5%, less than about 2%, or less than about 1% of the surface
area of an incident surface of the macroscale filter is occupied by
reflective material.
Configuring the macroscale filter such that a relatively small
portion of the surface area of the incident surface is occupied by
reflective material can reduce the amount of electromagnetic
radiation with an incidence angle of 0.degree. or close to
0.degree. that is reflected away from the filter (rather than being
transmitted through the filter), which can enhance the degree to
which the filter can discriminate incoming electromagnetic
radiation based on angle of incidence.
The portion of the surface area of the incident surface occupied by
reflective material can be configured to be relatively small by,
for example, configuring the channels within the macroscale filter
to have relatively large cross-sectional dimensions and/or by
configuring the reflective material separating the channels to
define thin walls. For example, FIG. 3C includes a top-view
schematic diagram of a macroscale filter that includes channels
arranged in a hexagonal tiling such that very thin inter-channel
wall thicknesses 330 are produced. While hexagonal tiling is
illustrated in FIG. 3C, other embodiments can include triangular
tiling, quadrilateral tiling (e.g., square tiling), pentagonal
tiling, octagonal tiling, or combinations of these and/or other
tiling configurations.
A variety of materials can be used to form the reflective portion
of the macroscale filter. For example, reflective portion 310 can
comprise a metal (e.g., steel, aluminum, gold, silver, nickel,
copper, platinum, or mixtures or alloys of these), dielectric
photonic crystal structures, or mixtures of these.
A variety of materials can be used to form channels in the
macroscale filter. In some embodiments, the channels in the
macroscale filter can comprise a material transparent to the
electromagnetic radiation the filter is designed to discriminate.
In some embodiments, the channels in the macroscale filter can
comprise a material with a relative low index of refraction (e.g.,
less than about 1.5, less than about 1.25, less than about 1.1, or
less than about 1.05). For example, the channels in the macroscale
filter can comprise a polymer, water, a glass, a gas (e.g., oxygen,
nitrogen, argon, helium, or mixtures of these such as air and/or
other mixtures), oxides (including metal oxides), and/or mixtures
of these. In some embodiments, the channels are fabricated from
material(s) selected to be at least partially transparent to the
electromagnetic radiation which the filter is designed to
discriminate. In some embodiments, at least a portion of the
material within the channel is the same as the ambient medium
material in which the macroscale filter is to be used. For example,
the macroscale filter can comprise holes formed through the
reflective portion of the filter, and the holes can be filled with
the material in which the filter is located (e.g., ambient air). As
one particular example, the macroscale filter can comprise holes
formed in a metal and can be used to filter incoming sunlight in an
outdoor location, in which case, the channels can be filled with
atmospheric air.
As noted above, macroscale filter 300 can be used to discriminate
electromagnetic radiation based on its angle of incidence. In some
embodiments, at least about 75%, at least about 85%, at least about
95%, at least about 99%, at least about 99.9%, or substantially all
of the electromagnetic radiation that contacts a first incident
surface (e.g., surface 318 and/or surface 321 in FIG. 3B) of the
macroscsale filter within a range of angles of incidence is
transmitted through the macroscsale filter. In some embodiments, at
least about 75%, at least about 85%, at least about 95%, at least
about 99%, at least about 99.9%, or substantially all of the
electromagnetic radiation that contacts a second incident surface
(e.g., surface 318 and/or surface 312 in FIG. 3B) of the
macroscsale filter outside a range of angles of incidence is
reflected by the macroscsale filter. In some embodiments, the range
of angles of incidence spans about 45.degree. or less, about
30.degree. or less, about 15.degree. or less, about 5.degree. or
less, about 2.degree. or less, or about 1.degree. or less. The
spacing and/or material properties of the reflective material
and/or the elongated channels can be selected, in some cases, to
tailor the range of incident angles over which electromagnetic
radiation is transmitted through the macroscale filter.
In some embodiments, articles that selectively absorb incident
electromagnetic radiation, are provided. For example, in some
embodiments, selective absorption of incident electromagnetic
radiation can be achieved using a 2-dimensionally periodic photonic
crystal. The 2-dimensionally periodic photonic crystal can comprise
a continuous region and a plurality of discontinuous regions formed
within the continuous region. In some embodiments, a relatively
large portion of the electromagnetic radiation that intersects the
incident surface of the selective absorber at an incidence angle
within a certain range can be absorbed by the selective absorber,
and a relatively large portion of the electromagnetic radiation
that intersects the incident surface of the selective absorber at
an incidence angle outside the range can be reflected by the
selective absorber.
FIGS. 4A-4B include perspective-view (FIG. 4A) and front-view (FIG.
4B) schematic illustrations of an exemplary selective absorber 400
that can be used to discriminate electromagnetic radiation based on
angle of incidence. Selective absorber 400 includes a
2-dimensionally periodic photonic crystal comprising a continuous
region 410 having a first index of refraction (or an effective
index of refraction when two or more materials are used to form
continuous region 410). In addition, selective absorber 400
includes a plurality of discontinuous regions 412 that have indices
of refraction (or effective indices of refraction when two or more
materials are used to form discontinuous regions 412) that are
different from the index of refraction of continuous region 410.
Accordingly, the index of refraction of selective absorber 400, as
illustrated in FIG. 4A, varies along orthogonal coordinate
directions 413 and 414, and does not substantially vary along
coordinate direction 415.
In some embodiments, the selective absorber can be configured to
include materials and/or dimensions that allow the selective
absorber to discriminate electromagnetic radiation based on the
angle of incidence. In some embodiments, at least about 75%, at
least about 85%, at least about 95%, at least about 99%, at least
about 99.9%, or substantially all of the electromagnetic radiation
that contacts a first incident surface (e.g., surface 418 and/or
surface 419 in FIG. 4B) of the selective absorber within a range of
angles of incidence is absorbed by the selective absorber. In some
embodiments, at least about 75%, at least about 85%, at least about
95%, at least about 99%, at least about 99.9%, or substantially all
of the electromagnetic radiation that contacts a second incident
surface (e.g., surface 418 and/or surface 419 in FIG. 4B) of the
selective absorber outside a range of angles of incidence is
reflected by the selective absorber. In some embodiments, the range
of angles of incidence spans about 45.degree. or less, about
30.degree. or less, about 15.degree. or less, about 5.degree. or
less, about 2.degree. or less, or about 1.degree. or less. The
spacing and/or material properties of the continuous domain and/or
the discontinuous domains can be selected, in some cases, to tailor
the range of incident angles over which electromagnetic radiation
is absorbed by the selective absorber.
For example, referring to FIG. 4B, selective absorber 400 can be
configured such that a relatively large portion of electromagnetic
radiation defining an angle of incidence 416 with incident surface
418 is absorbed by the selective absorber, regardless of whether
the electromagnetic radiation intersects incident surface 418
proximate the continuous region (e.g., surface portion 420 of
incident surface 418) or proximate a discontinuous region (e.g.,
surface portion 422 of incident surface 418). In some embodiments,
selective absorber 400 can be configured such that a relatively
large portion of electromagnetic radiation defining an angle of
incidence 417, which is greater than angle of incidence 416, is
reflected by the selective absorber, regardless of whether the
electromagnetic radiation intersects incident surface 418 proximate
the continuous region or proximate a discontinuous region.
Regions 412 of the 2-dimensionally periodic photonic crystal can
include at least one cross sectional dimension with a length that
is less than 3 times, less than 2 times, or less than 1 time the
maximum wavelength of the electromagnetic radiation the filter is
configured to discriminate. Not wishing to be bound by any
particular theory, it is believed that selective absorption can be
achieved by configuring the photonic crystal to include features
(e.g., regions 412) that establish discontinuities in the
dielectric function having cross-sectional dimensions on the order
of the wavelengths of electromagnetic radiation the selective
absorber is configured to discriminate, and that if the period of
the structure is much greater than the wavelength of light being
discriminated, then the interactions between the holes will be
changed.
In some embodiments, the discontinuous regions 412 within the
selective absorber 400 can have relatively small cross-sectional
diameters and/or lengths. As used herein, the "cross-sectional
diameter" of a discontinuous region is measured in a direction
parallel to the incident surface of the selective absorber. The
cross-sectional diameter of a cylindrical discontinuous region is
the cross-sectional diameter of that cylinder. For non-cylindrical
discontinuous regions, the cross-sectional diameter corresponds to
the cross-sectional diameter of a theoretical cylinder with the
same volume and length (measured parallel to the thickness of the
layer in which the discontinuous region is formed) as the
non-cylindrical discontinuous region. In some embodiments, the
cross-sectional diameter of at least one discontinuous region
(e.g., at least about 10%, at least about 25%, at least about 50%,
at least about 75%, at least about 90%, at least about 95%, or at
least about 99% of the channels) in the selective absorber is less
than about 100 micrometers, less than about 50 micrometers, less
than about 10 micrometers, less than about 5 micrometers, less than
about 2 micrometers, or less than about 1 micrometer, and/or at
least about 10 nm, at least about 100 nm, or at least about 500 nm
(e.g., between about 10 nm and about 10 micrometers, between about
100 nm and about 5 micrometers, or between about 0.5 micrometers
and about 2 micrometers). In some embodiments, the average and/or
the median of the cross-sectional diameters of the discontinuous
regions in the selective absorber can be less than about 100
micrometers, less than about 50 micrometers, less than about 10
micrometers, less than about 5 micrometers, less than about 2
micrometers, or less than about 1 micrometer, and/or at least about
10 nm, at least about 100 nm, or at least about 500 nm (e.g.,
between about 10 nm and about 10 micrometers, between about 100 nm
and about 5 micrometers, or between about 0.5 micrometers and about
2 micrometers).
In some embodiments, continuous region 410 can be a thin film. For
example, in some cases, continuous region 410 can have an average
thickness 424 of less than about 100 micrometers, less than about
10 micrometers, less than about 1 micrometer, between about 100 nm
and about 10 micrometers, or between about 0.5 micrometers and
about 1.5 micrometers. One of ordinary skill in the art would be
capable of measuring the thicknesses (and calculating average
thicknesses) of thin films using, for example, an ellipsometer, a
spectrophotometer, an optical microscope, a transmission-electron
microscope, or other suitable method, depending on the type of
material from which the thin film is formed.
While discontinuous regions 412 illustrated in FIGS. 4A-4B have
substantially circular cross-sectional shapes and are substantially
cylindrical, other cross-sectional shapes can be employed. In some
embodiments, one or more discontinuous regions 412 formed within a
selective absorber can have a cross-sectional shape that is
essentially a circle, essentially an ellipse, essentially an
ellipsoid, essentially a polygon (regular or irregular, and
including shapes that are essentially triangles, quadrilaterials
(including rectangles and squares), pentagons, hexagons, etc.),
irregular, or any other suitable cross-sectional shape.
The cross-sectional shape of the discontinuous regions 412 within
the selective absorber 400 can be, in some cases, substantially
constant along their lengths. In some embodiments, at least some of
discontinuous regions 412 (e.g., at least about 50%, at least about
75%, at least about 90%, at least about 95%, or at least about 99%)
have a substantially constant cross-sectional shape along
essentially the entire length of the discontinuous region. For
example, in the set of embodiments illustrated in FIGS. 4A 4B, each
of discontinuous regions 412 has a substantially constant
cross-sectional shape (substantially circular) along the entire
length of the discontinuous region.
Discontinuous regions 412 can have a variety of aspect ratios. The
aspect ratio of regions 412 is calculated by dividing the length of
the discontinuous region (as measured in a direction parallel to
the thickness of the material in which the discontinuous region is
formed), to the cross-sectional diameter of the discontinuous
region. For example, in the set of embodiments illustrated in FIGS.
4A-4B, the aspect ratio of regions 412 is calculated by dividing
the length of dimension 424 by the length of cross-sectional
diameter 426. In some embodiments, the aspect ratio of at least one
discontinuous region 412 (e.g., at least about 10%, at least about
25%, at least about 50%, at least about 75%, at least about 90%, at
least about 95%, or at least about 99% of the discontinuous
regions) in the selective absorber is at least about 0.75, at least
about 2, at least about 5, at least about 10, at least about 20,
between about 0.75 and about 25, between about 2 and about 25, or
between about 5 and about 25.
In some embodiments, the average of the nearest neighbor distances
between regions 412 can be less than about 100 micrometers, less
than about 50 micrometers, less than about 10 micrometers, less
than about 5 micrometers, or less than about 2 micrometers, and/or
at least about 10 nm, at least about 100 nm, at least about 500 nm,
or at least about 1 micrometer (e.g., between about 10 nm and about
100 micrometers, between about 100 nm and about 10 micrometers, or
between about 0.5 micrometers and about 2 micrometers). The nearest
neighbor distance for a first discontinuous region is calculated as
the distance between the center of the first discontinuous region
and the center of the nearest discontinuous region relative to the
first discontinuous region. For example, in the set of embodiments
illustrated in FIG. 4A, dimension 440 is used to indicate the
nearest neighbor distance between regions 412A and 412B. The
average of the nearest neighbor distances of multiple discontinuous
regions is calculated as the number average.
In some embodiments, discontinuous regions 412 can include one or
more materials positioned within voids of the continuous region
410. For example, voids can be formed within continuous region 410,
and one or more materials can be deposited into the voids to form
discontinuous regions 412. In some cases, discontinuous regions 412
can comprise openings formed within continuous region 410. In some
such embodiments, the chemical composition of discontinuous regions
412 can be substantially the same as the chemical composition of
the environment surrounding the selective absorber (e.g., vacuum,
ambient air, etc.).
Selective absorber 400 can include a variety of types of materials.
Examples of materials that can be used to form the continuous
region 410 of the 2-dimensionally periodic photonic crystal
include, but are not limited to, metals (e.g., tungsten (e.g.,
single-crystal tungsten), tantalum, platinum, palladium, silver,
gold, etc.), semiconductors (e.g., silicon, germanium, etc.), or
dielectric materials (e.g., titania, zirconia). In one particular
set of embodiments, a 2-dimensionally periodic photonic crystal can
comprise a layer of tungsten in which holes are formed. In some
embodiments, the selective absorber can be formed of a material
with a relatively low emissivity. In some embodiments, the
selective absorber can comprise a material with an emissivity of
less than about 0.3, less than about 0.2, less than about 0.1, or
less than about 0.05, for example at the temperature at which the
selective absorber is designed to operate and at the wavelength(s)
of electromagnetic radiation the selective absorber is configured
to absorb.
Structures capable of discriminating electromagnetic radiation
based on the angle of incidence could find uses in a wide variety
of applications. For example, articles capable of selectively
absorbing and/or transmitting electromagnetic radiation based upon
the angle of incidence can be useful in applications where it is
desirable to "trap" incoming electromagnetic radiation of a known
incidence angle. One example of such an application is solar energy
conversion. In many commercial solar conversion systems (e.g.,
solar to thermal to electrical conversion systems, concentrated
solar photovoltaic systems, etc.) incident angle of the sun can be
controlled for. For example, solar to electrical photovoltaic
conversion panels and concentrated solar photovoltaic system panels
can be configured to track the motion of the sun. In many systems
currently in use, a portion of the incident solar energy is
typically reflected or reemitted from the receiving device (e.g.,
the photovoltaic panel, the absorber, etc.), which results in
(often substantial) losses. Since the angle of outgoing
electromagnetic radiation reflected from the receiving device is
typically substantially different than the angle of the incoming
electromagnetic radiation from the sun, articles capable of
selectively transmitting electromagnetic radiation based on the
angle of incidence could be used to "trap" the reflected radiation,
redirecting it back towards the receiving device. In addition,
selective absorbers could be used to produce a relatively large
amount of heat, without the need for concentrators such as lenses,
mirrors, or other devices.
Accordingly, in some embodiments, the articles described herein
(including article 100, macroscale filter 300, and/or selective
absorber 400) can be configured such that they transmit the
electromagnetic radiation incident on the article and/or heat
derived from the electromagnetic radiation incident on the article
to a system capable of producing energy (e.g., in the form of
electricity) from the electromagnetic radiation and/or heat
transmitted from the article. In some cases, the photonic
materials, articles, and systems described herein can be configured
to transmit electromagnetic radiation to and/or be a part of a
photovoltaic cell (e.g., a solar photovoltaic cell, a
thermophotovoltaic cell, etc.). In some cases, the photonic
materials, articles, and systems described herein can be configured
to transmit heat to and/or be a part of an absorber (e.g., an
absorber proximate an emitter configured to transmit
electromagnetic radiation emitted by the emitter to a photovoltaic
cell, an absorber configured to exchange heat with a device capable
of producing electricity from heat (e.g., a heat engine)).
In some embodiments, the systems, articles, and methods described
herein can be used in photovoltaic energy generation systems. FIG.
5A includes an exemplary schematic diagram of a photovoltaic energy
generation system 500 comprising a selective transmitter 510 (e.g.,
article 100 and/or macroscale filter 300) and a photovoltaic cell
512 configured to receive electromagnetic radiation from selective
transmitter 510 and convert the electromagnetic radiation to
electricity. In this set of embodiments, electromagnetic radiation
514 (from a source such as the sun, which is not illustrated) is
incident on incident surface 515 of selective transmitter 510.
Because electromagnetic radiation 514 establishes an normal
incidence angle (i.e., an incidence angle of 0.degree.) with
incident surface 515 of selective transmitter 510, electromagnetic
radiation 514 is transported through selective transmitter 510.
Upon reaching photovoltaic cell 512, at least a portion of
electromagnetic radiation 514 is absorbed by photovoltaic cell 512.
Another portion 516 of electromagnetic radiation 514 is reflected
by photovoltaic cell 512 at an angle different from the original
incidence angle of electromagnetic radiation 514. Selective
transmitter 510 can be configured such that, when electromagnetic
radiation portion 516 reaches incident surface 517 of selective
transmitter 510, a relatively large portion 518 of electromagnetic
radiation 516 is reflected back to photovoltaic cell (e.g., because
the incidence angle 519 is relatively large). Eventually, portion
518 of electromagnetic radiation reaches photovoltaic cell 512,
where at least some of portion 518 is absorbed. In the absence of
selective transmitter 510, the electromagnetic radiation from
portion 518 that is absorbed by photovoltaic cell 512 would have
been reflected out of the system, thereby reducing system
efficiency. Accordingly, in this set of embodiments, the use of
selective transmitter 510 increases the overall system
efficiency.
In some embodiments, the systems, articles, and methods described
herein can be used in thermophotovoltaic systems. In
thermophotovoltaic systems, electromagnetic radiation (e.g.,
sunlight) is not absorbed directly by a photovoltaic material, but
rather, is absorbed by an absorber. In some cases, the absorber can
selectively emit and/or be thermally coupled to a selective
emitter, which then thermally radiates electromagnetic radiation.
The electromagnetic radiation emitted by the emitter can then be
absorbed by a photovoltaic cell.
FIG. 5B includes an exemplary schematic diagram of a
thermophotovoltaic energy generation system 530, according to one
set of embodiments. In this set of embodiments, selective absorber
532 (e.g., selective absorber 400 as shown in FIG. 4) is configured
to absorb electromagnetic radiation to generate heat. In this set
of embodiments, electromagnetic radiation 514 (from a source such
as the sun, which is not illustrated) is incident on incident
surface 533 of selective absorber 532. Because electromagnetic
radiation 514 establishes an normal incidence angle (i.e., an
incidence angle of 0.degree.) with incident surface 533 of
selective absorber 532, at least a portion of electromagnetic
radiation 514 is absorbed by selective absorber 532.
Electromagnetic radiation 534, on the other hand, establishes a
relatively large angle of incidence 535 with incident surface 533.
Accordingly, a large portion (or all) of electromagnetic radiation
534 is reflected from incident surface 533 of selective absorber
532. By absorbing electromagnetic radiation incident only over a
narrow range of angles of incidence, absorber 532 can be heated to
a relatively high temperature. Not wishing to be bound by any
particular theory, it is believed that selective absorption leads
to higher temperatures because heat escapes much more slowly in
selective absorbers than in non-selective absorbers, as predicted
by Kirchoff's Law.
Although selective absorber 532 and selective emitter 536 are
illustrated as being in direct contact in FIG. 5B, in other
embodiments, one or more materials (e.g., a thermally conductive
material such as a metal) can be positioned between selective
absorber 532 and selective emitter 536. Selective absorber 532 can
be configured to transfer heat to selective emitter 536, for
example, by placing the absorber and the emitter in direct contact,
by positioning one or more heat exchangers between the absorber and
the emitter, or by any other suitable method.
In some embodiments, selective emitter 536 is configured to emit
electromagnetic radiation when it is heated. For example, selective
emitter 536 can comprise a material having a relatively high
emissivity (e.g., a material having an emissivity of at least about
0.7, at least about 0.8, or at least about 0.9, for example at the
temperature at which the selective emitter is designed to operate
and at the wavelength(s) of electromagnetic radiation the selective
emitter is configured to radiate). Exemplary high emissivity
materials include, but are not limited to, quartz, silicon carbon
(e.g., graphite, carbon black, etc.), carbide, oxidized steel, and
the like. In FIG. 5B, electromagnetic radiation 538 emitted from
selective emitter 536 is absorbed by thermophotovoltaic cell 540,
which generates energy (e.g., in the form of electricity).
In some embodiments, rather than heating a selective emitter,
selective absorber 532 can be used to heat a working fluid, which
can be used to power a heat engine. FIG. 5C is a schematic
illustration of an energy generation system 550 in which selective
absorber 532 is configured to provide heat to a working fluid
within conduit 552. The fluid within conduit 552 can be a gas
(e.g., to power a gas turbine or other energy generation device
using gas as the working fluid) or a liquid (e.g., to power a steam
turbine or other energy generation device in which the working
fluid is a liquid at some point in the energy generation
process).
Generally, thermophotovoltaic systems and heat engine-based systems
are more efficient when they operate at high temperatures. In many
previous systems, high temperatures can be achieved by using
lenses, mirrors, or other suitable devices to focus the
electromagnetic radiation (e.g., sunlight) onto the absorber. The
selective transmitters and absorbers described herein can be used
to replace traditional concentrators in many such systems and/or
enhance their effect, thereby improving system performance.
In some embodiments, the articles for discriminating
electromagnetic radiation based on angle of incidence described
herein can comprise a refractory metal (e.g., niobium, molybdenum,
tantalum, tungsten, osmium, iridium, ruthenium, zirconium,
titanium, vanadium, chromium, rhodium, hafnium, and/or rhenium)
and/or another refractory material. The use of refractory materials
can allow one to fabricate a articles that are capable of
withstanding relatively high temperatures (e.g., at least about
1000.degree. C., at least about 1500.degree. C., or at least about
2000.degree. C.). In some embodiments, the article for
discriminating electromagnetic radiation can comprise compounds
such as tungsten carbide, tantalum hafnium carbide, and/or tungsten
boride. In some embodiments, the article for discriminating
electromagnetic radiation can comprise noble metals, including
noble metals with high melting points (e.g., platinum, palladium,
gold, and silver), diamond, and/or cermets (i.e., compound
metamaterials including two or more materials (e.g., tungsten and
alumina) which can be, in some embodiments, broken up into pieces
smaller than the wavelength of visible light). In some embodiments,
the article for discriminating electromagnetic radiation can
comprise a combination of two or more of these materials.
The present invention also relates to methods for discriminating
electromagnetic radiation based on the angle of incidence. The
methods can comprise, for example, exposing any of the articles
described herein to electromagnetic radiation and discriminating
the electromagnetic radiation to any of the extents described
herein. In some embodiments, the methods comprise configuring other
components (e.g., absorbers, energy conversion devices such as
photovoltaic cells, heat engines, etc.) to receive heat and/or
electromagnetic radiation from an article configured to
discriminate electromagnetic radiation, for example, as part of an
energy generation system. Methods of the invention also include
methods for fabricating the articles used to discriminate
electromagnetic radiation described herein.
A variety of methods, according to certain aspects of the
invention, can be used to form the articles for discriminating
electromagnetic radiation based on angle of incidence described
herein. In some embodiments, various components can be formed from
solid materials, in which materials (e.g., layers of materials),
holes, discontinuous regions, and the like can be formed via
micromachining; film deposition processes such as spin coating,
chemical vapor deposition, and/or physical vapor deposition
(including sputtering); laser fabrication; photolithographic
techniques; etching methods including wet chemical or plasma
processes; electrochemical processes; and the like. See, for
example, "Silicon Micromechanical Devices" by Angell et al.,
Scientific American, Vol. 248, pages 44-55, 1983. For example, at
least a portion of a 1-dimensionally periodic photonic crystal can
be formed by depositing multiple thin-films of material via, for
example, sputtering. As another example, in one set of embodiments,
at least a portion of a 2-dimensionally periodic photonic crystal
can be formed by etching (e.g., laser etching) features into a
substrate and/or layer such as a metal substrate and/or layer
(e.g., aluminum, steel, copper, tungsten, and the like). In some
embodiments, the articles described herein can be fabricated using
milling techniques (including relatively large-scale milling
techniques), sheet material (e.g., sheet metal) working, and the
like. Technologies for precise and efficient fabrication of various
material layers and/or devices described herein are known to those
of ordinary skill in the art.
U.S. Provisional Patent Application Ser. No. 61/365,732, filed Jul.
19, 2010, and entitled "Discriminating Electromagnetic Radiation
Based on Angle of Incidence" is incorporated herein by reference in
its entirety for all purposes. All patents, patent applications,
and documents cited herein are hereby incorporated by reference in
their entirety for all purposes.
The following examples are intended to illustrate certain
embodiments of the present invention, but do not exemplify the full
scope of the invention.
Example 1
This example describes numerical simulations of a class of material
systems that discriminate electromagnetic radiation (including
visible light) based on the angle of incidence of the
electromagnetic radiation on the material, over a broad range of
frequencies, and irrespective of the polarization of the
electromagnetic radiation. Unique properties of these systems
emerge from exploring photonic crystals whose constituents have
anisotropic dielectric permeabilities. Among other potential uses,
such systems could be of interest for solar energy applications,
where they could enable a highly enhanced green-house effect.
In some cases, it would be beneficial if electromagnetic radiation
(e.g., visible light) incident at a particular angle (or a range of
angles) would be nearly perfectly transmitted, while other angles
of incidence would be nearly perfectly reflected, independent of
the incoming polarization, and for as wide a range of frequencies
as possible. This example presents a system that precisely opens
such desired angular gaps. Using realistic constituent material
parameters, numerical calculations are presented that demonstrate a
system in which electromagnetic radiation close to normal incidence
is nearly perfectly transmitted for a wide range of frequencies,
independent of the polarization. In contrast, electromagnetic
radiation with incidence angles further from the normal (e.g.
22.5.degree.-90.degree.) can be nearly perfectly reflected over a
fractional frequency bandgap of greater than 100%. In some cases,
the structures can include photonic crystals whose constituents
have an anisotropic dielectric function and/or an anisotropic
magnetic permeability.
The system described in this example for opening an angular
photonic gap includes a one-dimensionally (1D) periodic photonic
crystal whose constituents possess anisotropic properties. To
demonstrate the fundamental physics principle at work in this
system, FIG. 6A includes a specific example of such a metamaterial
that opens an angular gap for the TM polarization (i.e., the
electric field is in the plane of incidence) only. Later in this
example, a generalized approach will be shown for both
polarizations and wide frequency ranges. Angular discrimination of
TM electromagnetic radiation can be achieved by introducing
anisotropy in the dielectric function (.di-elect cons.) of one of
the layers (e.g., layer A). In this first example, one can assume
that layer A has an anisotropic effective dielectric function
.di-elect cons..sub.A=(1.23, 1.23, 2.43) whereas layer B has an
isotropic effective dielectric function .di-elect cons..sub.B=1.23.
To accomplish this anisotropy, one could use naturally existing
materials with anisotropic dielectric functions, such as TiO.sub.2
(.di-elect cons..sub.TiO.sub.2=(2.6.sup.2, 2.6.sup.2, 2.9.sup.2) at
590 nm), and/or explore a metamaterial approach.
An example of a metamaterial system that in the long wavelength
limit possesses an effective epsilon of (1.23, 1.23, 2.43) is shown
on the left-hand side of FIG. 6A, which includes a two dimensional
(2D) periodic square lattice of dielectric rods having radius r=0.2
d where d (the in-plane period) can be calculated as: d=0.1 a.
Here, a corresponds to the thickness of each bilayer. Since it is
known that a TM reflection window opens at 45.degree., one can
choose the thickness of layer A (h.sub.A) such that the size of the
TM fractional gap is maximized, which happens at the quarter-wave
condition (h.sub.An.sub.A.sup.TM
cos(.theta..sub.A.sup.TM).omega..sub.o/c=h.sub.Bn.sub.B.sup.TM
cos(.theta..sub.B.sup.TM).omega..sub.o/c), where .omega..sub.o is
the frequency at the center of the gap, h.sub.A is the thickness of
layer A, h.sub.B is the thickness of layer B, n.sub.A.sup.TM is the
index of refraction of TM polarized electromagnetic radiation in
material A, n.sub.B.sup.TM is the index of refraction of TM
polarized electromagnetic radiation in material B,
.theta..sub.A.sup.TM is the angle that TM polarized electromagnetic
radiation makes with respect to the normal of layer A,
.theta..sub.B.sup.TM is the angle of incidence that TM polarized
electromagnetic radiation makes with respect to the normal of layer
B, and c is the speed of light in a vacuum (i.e., about
3.times.10.sup.8 m/s). This results in h.sub.A=0.46a. The
metamaterial system shown to the left of FIG. 6A also includes rods
formed of an isotropic material, with the dielectric function of
the rods being 12.25 (.di-elect cons..sub.rods=12.25). In a 2D
square lattice of dielectric rods, modes having their E-field along
the rods are substantially more concentrated inside the rods and
therefore experience the high E of the rods. On the other hand,
modes having their E-field in the periodicity plane experience
average E smaller than that along the rods, hence the anisotropy in
effective epsilon of the entire layer. Frequency domain simulations
(not discussed here) show that in the low frequency limit, the
metamaterial has effective E=(1.23, 1.23, 2.43).
The right-hand side of FIG. 6A is a schematic diagram of normally
incident TM-polarized and TE-polarized electromagnetic radiation;
originating from air, incident on the above-described multilayer
structure (with period a, .di-elect cons..sub.A=(1.23, 1.23, 2.43),
and .di-elect cons..sub.B=1.23). Since {right arrow over (E)} lies
in the xy-plane, both polarizations experience n.sub.A=n.sub.B=
{square root over (1.23)}, so there is no index contrast. Because
of the absence of any contrast in the refractive index, there is no
photonic bandgap and normally incident electromagnetic radiation of
all frequencies and both polarizations is transmitted through this
metamaterial structure, apart from the small reflections at
boundaries between the structure and air.
FIG. 6B illustrates transmission spectra for TE-polarized and
TM-polarized electromagnetic radiation, normally incident from air
on 30 bilayers of the structure in FIG. 6A. The transmission
spectra shown in FIG. 6B were obtained using the Transfer Matrix
Method (TMM) as described in Pochi Yeh, Optical Waves in Layered
Media, Chapter 5 (pages 102-110) and Chapter 6 (pages 118-128)
(John Wiley & Sons Inc., 1988), which is incorporated herein by
reference. As seen in FIG. 6B, when the angle of incidence is
non-zero (i.e., incident electromagnetic radiation makes an angle
.theta..sub.inc.noteq.0 with the normal), different effects are
observed relative to situations in which the angle of incidence is
zero (i.e., incident electromagnetic radiation is normal to the
surface). FIGS. 6C and 6D are schematic diagrams showing
TM-polarized (in FIG. 6C) and TE-polarized (in FIG. 6D)
electromagnetic radiation incident at a nonzero angle from air
(n.sub.inc=1) on the structure in FIG. 6A. As illustrated in the
schematic of FIG. 6C, TM-polarized electromagnetic radiation
incident at .theta..sub.inc.noteq.0 now has E.sub.Z.noteq.0, and
thus experiences an index contrast
(n.sub.A.sup.TM.noteq.n.sub.B.sup.TM= {square root over (1.23)});
therefore, one expects a photonic bandgap (of a certain frequency
width) and hence strong reflections for TM-polarized
electromagnetic radiation in this bandgap. In contrast,
TE-polarized electromagnetic radiation incident at an angle
.theta..sub.inc.noteq.0 still has E.sub.Z=0 and thus experiences no
index contrast as shown in FIG. 6D (n.sub.A=n.sub.B= {square root
over (1.23)}); therefore, it is transmitted for all frequencies.
Therefore, normally incident TM-polarized electromagnetic radiation
is transmitted, while TM-polarized electromagnetic radiation
incident at nonzero angles is reflected in a certain frequency
range. FIG. 6E includes transmission spectra (obtained from TMM)
for TE-polarized and TM-polarized polarized electromagnetic
radiation incident at 45.degree. from air on 30 bilayers of the
structure in FIG. 6A, in the case when anisotropic layer A is made
from a homogeneous material. From FIG. 6E, it can be seen that
TM-polarized electromagnetic radiation incident at nonzero angles
is reflected in a frequency range of 9.3%. Generally, a frequency
bandgap of X % is calculated by dividing .DELTA..OMEGA. by
.OMEGA..sub.mid, wherein .DELTA..OMEGA. is the difference between
the highest and lowest frequencies in the bandgap and
.OMEGA..sub.mid is the average of the highest and lowest
frequencies in the bandgap.
FIG. 6E also includes a transmission spectrum (obtained from the
FDTD method described in Oskooi et al., "MEEP: A flexible
free-software package for electromagnetic simulations by the FDTD
method," Computer Physics Communications, 181, pp. 687-702 (2010))
for TM-polarized electromagnetic radiation incident at 45.degree.
from air on 30 bilayers of the structure in FIG. 6A, in the case
when anisotropic layer A is not made from a homogeneous material,
but is made from a metamaterial including a square lattice of
dielectric rods. In this case, a TM photonic bandgap opens and
closely overlaps with the TM gap obtained from TMM for the uniform
dielectric case. The above explains the physical mechanism based on
which the proposed structures described herein discriminate
electromagnetic radiation with respect to the angle of incidence in
that particular frequency range.
Before discussing numerical results for transmission of various
angles, polarizations, and frequencies from this multilayer
structure, analytical expressions for the refractive index n.sub.A
of the anisotropic layer are provided. A simple calculation
starting from Maxwell's equations yields the following refractive
indices (n=C/v.sub.phase, wherein c is the speed of light in a
vacuum (about 3.times.10.sup.8 m/s) and v.sub.phase is the speed of
light in the phase for which the refractive index is being
determined) experienced by TE-polarized and TM-polarized
electromagnetic radiation respectively in the anisotropic layer
A:
.times..times..times..times..theta..mu..times..times..mu..times..times..t-
imes..times..times..times..theta..mu..times..times..mu..times..times..time-
s..times..times..times..theta..mu..times..times..mu..times..times..times..-
times..times..times..theta..mu..times..times..mu..times..times.
##EQU00001## where .theta..sub.A.sup.TE and .theta..sub.A.sup.TM
are the angles that TE-polarized and TM-polarized electromagnetic
radiation, respectively, make with respect to the normal as they
propagate in layer A, .mu..sub.xx.sup.A is the magnetic
permeability of material A in the x-direction, .mu..sub.yy.sup.A is
the magnetic permeability of material A in the y-direction,
.mu..sub.zz.sup.A is the magnetic permeability of material A in the
z-direction, .di-elect cons..sub.xx.sup.A is the dielectric
function of material A in the x-direction, .di-elect
cons..sub.yy.sup.A is the dielectric function of material A in the
y-direction, .di-elect cons..sub.zz.sup.A is the dielectric
function of material A in the z-direction, .di-elect cons..sub.o is
the dielectric function of vacuum, and .mu..sub.o is the magnetic
permeability of vacuum. .mu..sub.xx.sup.B is the magnetic
permeability of material B in the x-direction, .mu..sub.yy.sup.B is
the magnetic permeability of material B in the y-direction,
.mu..sub.zz.sup.B is the magnetic permeability of material B in the
z-direction, .di-elect cons..sub.xx.sup.B is the dielectric
function of material B in the x-direction, .di-elect
cons..sub.yy.sup.B is the dielectric function of material B in the
y-direction, .di-elect cons..sub.zz.sup.B is the dielectric
function of material B in the z-direction. These values can be
obtained from Snell's law, which in this anisotropic case is:
n.sub.A.sup.TE sin 0.sub.A.sup.TE=n.sub.air sin 0.sub.inc (3)
n.sub.A.sup.TM sin .theta..sub.A.sup.TM=n.sub.air sin
.theta..sub.inc (4)
From the expressions for n.sub.A.sup.TE and n.sub.A.sup.TM, one can
see that TE-polarized electromagnetic radiation is affected only by
.di-elect cons..sub.yy.sup.A, .mu..sub.xx.sup.A, and
.mu..sub.zz.sup.A, while TM-polarized electromagnetic radiation is
affected only by .mu..sub.yy.sup.A, .di-elect cons..sub.xx.sup.A
and .di-elect cons..sub.zz.sup.A. In particular, TM-polarized
electromagnetic radiation is affected by .di-elect
cons..sub.zz.sup.A, while TE-polarized electromagnetic radiation is
not. One can also observe that for angles .theta..sub.A close to
the normal, sin .theta..sub.A.apprxeq.0. Accordingly, in view of
Equations 1 and 2, n.sub.A increases only slightly with increasing
anisotropy. However, for incidence angles not close to the normal,
n.sub.A increases more rapidly with increasing anisotropy, and
therefore higher anisotropy in .di-elect cons. or .mu. results in
higher index contrast and wider frequency gaps at those angles.
The multilayer structure illustrated in FIG. 6A discriminates
angles only for TM-polarized electromagnetic radiation. One can
generalize this structure and design a different multilayer
structure which is capable of discriminating angles of incidence
irrespective of the polarization of the electromagnetic radiation.
Such a multilayer structure can include anisotropy in both the
dielectric function and in the magnetic permeability. More
specifically, the proposed structure can have .di-elect
cons..sub.B=.mu..sub.A=.gamma..sub.1 while .di-elect
cons..sub.A=.mu..sub.B=(.gamma..sub.1,.gamma..sub.1,.gamma..sub.2).
Note that a structure having .di-elect
cons..sub.A=.mu..sub.A=(.gamma..sub.1,.gamma..sub.1,.gamma..sub.2)
and .di-elect cons..sub.B=.mu..sub.B=.gamma..sub.1 would work
equally well and would have a larger fractional frequency gap (at
the quarter-wave condition which is satisfied differently at
different incidence angles). The structure illustrated and analyzed
in FIGS. 7A-7C can offer somewhat more flexibility in material
choice, in the sense that anisotropic .di-elect cons. and .mu.
would not have to occur in the same material.
For simplicity, we consider the case .di-elect
cons..sub.inc=.mu..sub.inc=.gamma..sub.1 in this example. FIGS.
7A-7B includes schematic diagrams showing (A) TM-polarized and (B)
TE-polarized electromagnetic radiation incident at nonzero angles
from .di-elect cons..sub.inc=.mu..sub.inc=.gamma..sub.1 on an
anisotropic multilayer structure with .di-elect
cons..sub.A=.mu..sub.B=(.gamma..sub.1,.gamma..sub.1,.gamma..sub.2),
.di-elect cons..sub.B=.mu..sub.A=.gamma..sub.1. Here,
.gamma..sub.2.noteq..gamma..sub.1. In both of these cases,
electromagnetic radiation experiences index contrasts and hence
photonic bandgaps. For example, as shown in the schematic of FIG.
7A, TM-polarized electromagnetic radiation incident from air at a
nonzero angle on this structure experiences a photonic bandgap
because according to Eq. (2), n.sub.B.sup.TM= {square root over
(.gamma..sub.1)} while n.sub.A.sup.TM.noteq. {square root over
(.gamma..sub.1)}. On the other hand, TE-polarized electromagnetic
radiation incident (from air) at the same nonzero angle also
experiences an index contrast because according to Eq. (1),
n.sub.A.sup.TE= {square root over (.gamma..sub.1)} while
n.sub.B.sup.TE.noteq. {square root over (.gamma..sub.1)}. FIG. 7C
includes a contour plot showing how the relative size of the TE
(and also TM) photonic bandgap changes with .theta..sub.inc and
with the degree of anisotropy .gamma..sub.2/.gamma..sub.1 for
electromagnetic radiation incident from .di-elect
cons..sub.inc=.mu..sub.inc=.gamma..sub.1 on the anisotropic
multilayer structure of FIG. 7A. This result was obtained using
TMM, and the thickness of layers A and B were chosen to be equal
(h.sub.A=h.sub.B=0.5a) so that the structure discriminates
different angles over the same frequency interval and for both
polarizations simultaneously. Note that this choice of
h.sub.A=h.sub.B does not result in the largest possible fractional
gap for either polarization, which actually occurs at the
quarter-wave condition, satisfied non-simultaneously for the two
different polarizations when .di-elect
cons..sub.A=.mu..sub.B=(.gamma..sub.1,.gamma..sub.1,.gamma..sub.2.noteq..-
gamma..sub.1).
From the contour plot in FIG. 7C, one can observe that the size of
the fractional gap increases only slightly with increasing
anisotropy .gamma..sub.2/.gamma..sub.1 beyond
.gamma..sub.2/.gamma..sub.1.apprxeq.2, which can also be seen by
inspection of Equation 1 and Equation 2, and noticing that the
achievable index contrast "saturates" for large
.gamma..sub.2/.gamma..sub.1 anisotropy values. Therefore, materials
with very large anisotropy do not necessarily lead to much larger
bandgap in these structures. This is somewhat contrary to
conventional photonic crystals where substantially large index
contrast typically lead to substantially larger bandgaps. Note also
that the size of the fractional frequency gap also increases with
.theta..sub.inc.
The structures described above allow one to open an angular gap for
both TE and TM polarizations over a certain frequency range. One
might also consider how to enlarge the frequency range over which
this angular discrimination is exhibited. To achieve a relatively
large fractional frequency gap that occurs simultaneously for both
polarizations, one can operate at the quarter-wave condition (the
structure obeying the quarter-wave condition at 45.degree. is used
in the calculations of FIG. 8A, While the structure obeying the
quarter-wave condition at 22.5.degree. is used in FIGS. 8B and 8C).
In this case, anisotropic .di-elect cons..sub.A=.mu..sub.A is used
(as opposed to the previously considered case when anisotropic
.di-elect cons..sub.A=.mu..sub.B). One can start with a single
stack consisting of 30 homogeneous bilayers with .di-elect
cons..sub.A=.mu..sub.A=(1.23, 1.23, 2.43) and .di-elect
cons..sub.B=.mu..sub.B=1.23. The size of each bilayer in this stack
is a. Electromagnetic radiation incident at 45.degree. (from air)
on this stack experiences a simultaneous TE and TM photonic bandgap
having a fractional frequency width of 6.94% (at quarter-wave
condition). To widen this fractional frequency range, one can
consider a multilayer consisting of 17 such stacks, each stack
being made out of 30 bilayers, however the period of each stack is
chosen so that frequency gaps of different stacks are contiguous
and merge together, resulting in a much larger frequency gap
(.apprxeq.17 times the size of the gap in the single gap case). In
the system analyzed for this example, the period a.sub.i of the
i.sup.th stack (i=1, 2, . . . , 17) was chosen to be
a.sub.i=1.0694.sup.(i-1)a, where a is the period of the first stack
facing the incident electromagnetic radiation. The thickness
h.sub.A.sup.i of layer A in the i.sup.th stack was chosen to be
0.473a.sub.i so that the quarter-wave condition (which maximizes
the relative size of the frequency gap) is satisfied. FIG. 8A
includes a transmission spectrum, obtained using TMM, for
electromagnetic radiation incident from air at an angle of
incidence of 45.degree. (i.e., 45.degree. from normal) on the
17-stack multilayer structure described above. As shown in FIG. 8A,
a reflection window with a relative frequency size of about 104%
was observed for both TE and TM polarizations simultaneously.
FIG. 8B includes additional transmission spectra obtained using
TMM. The TMM results in FIG. 8B show a 107% wide frequency gap for
both TE-polarized and TM-polarized electromagnetic radiation
incident at 22.5.degree. from the normal, irrespective of its
polarization. This structure analyzed in FIG. 8B includes 71 stacks
each consisting of 130 bilayers each having .di-elect
cons..sub.A=.mu..sub.A=(1.23, 1.23, 2.43), .di-elect
cons..sub.B=.mu..sub.B=1.23, and a.sub.i=1.0164.sup.(i-1)a. The
thickness h.sup.i.sub.A of layer A was 0.494a.sub.i in this case
(which satisfies the quarter-wave condition).
FIG. 8C includes TMM transmission spectra for electromagnetic
radiation incident at 45.degree. on the structure described in
association with FIG. 8B. In the case illustrated in FIG. 8C, there
is reflection at all frequencies that fall inside the reflection
window shown in FIG. 8B for 22.5.degree. incidence. That is, the
structure designed to reflect 22.5.degree.-incident electromagnetic
radiation in the frequency range (0.13c/a.fwdarw.0.43c/a)
irrespective of its polarization, is also capable of reflecting
electromagnetic radiation incident at all angles greater than
22.5.degree. in this same frequency range and irrespective of the
polarization; after all, bandgap of each stack is larger for
45.degree. incidence than for 22.5.degree. incidence.
Electromagnetic radiation incident close-to-normal on this same
structure is transmitted irrespective of its polarization. In fact,
this proposed structure exhibits an angular gap (for
.theta..sub.inc between 22.5.degree. and 90.degree.) for both
polarizations simultaneously over a 107% wide frequency range.
A variety of materials can be used to achieve the above-described
concepts. As seen in FIG. 6A, dielectric metamaterial approaches
could be used for TM-polarized electromagnetic radiation. For TE
polarization (where anisotropic p can be used), one option is to
use metallo-dielectric metamaterials as described, for example, in
J. B. Pendry, A. J. Holden, D. J. Roddins, and W. J. Stewart, IEEE
transactions on microwave theory and techniques, Vol. 47, No. 11,
November 1999. In some cases, one might split incoming
electromagnetic radiation according to polarization before it
enters the structure, rotate TE polarization into TM polarization,
and only then allow it to continue to the structure (see e.g.,
Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X.
Kaertner, E. P. Ippen, and H. I. Smith, Nature Photonics, 1, pp
57-60, (2007)).
Example 2
This example describes the design and performance of a macroscale
filter used to discriminate electromagnetic radiation based on
angle of incidence. In this example, a 2-dimensional array of
channels is formed in a reflective material to produce the
structure illustrated in FIGS. 9A-9F. FIG. 9A is a schematic
illustration of the incident surface of the structure (i.e., a top
view of the structure). FIGS. 9B-9F are schematic illustrations of
the structure in FIG. 9A from various incidence angles. FIG. 9B is
a view of the structure from an incidence angle of 15.degree., FIG.
9C is a view from an incidence angle of 30.degree., FIG. 9D is a
view from an incidence angle of 45.degree., FIG. 9E is a view from
an incidence angle of 60.degree., and FIG. 9F is a view from an
incidence angle of 75.degree..
The macroscale filter illustrated in FIGS. 9A-9F includes a
periodic array of cylinders formed in a reflective material such as
a metal. Each of the holes has a cross-sectional diameter and a
length (corresponding to the thickness of the reflective material)
such that the aspect ratios of the cylinders are 10:1 (i.e., the
channel lengths are 10 times greater than the channel
cross-sectional diameters). The holes are spaced such that they
have a nearest neighbor distance of 1.05 times the cross-sectional
diameters of the holes (i.e., the hole cross-sectional diameters
are 95% of the nearest neighbor distances).
The amount of incident electromagnetic radiation that is reflected
from the device illustrated in FIGS. 9A-9F is dependent upon the
angle of incidence. For angles of incidence less than or equal to
.theta..sub.m (which corresponds to the maximum polar angle at
which electromagnetic radiation is exchanged with the environment),
the percentage of electromagnetic radiation that will be reflected
from the macroscale filter is calculated as: %
Reflected=R.sub.o+asin(.theta.) [5] where R.sub.o represents
reflection at normal incidence, a represents angular sensitivity
(which depends on the geometry), and .theta. is the angle of
incidence. For angles of incidence greater than .theta..sub.m, the
percentage of electromagnetic radiation that will be reflected from
the macroscale filter is calculated as: %
Reflected=R.sub.o+asin(.theta..sub.m) [6]
For the macroscale filter illustrated in FIGS. 9A-9F, at an angle
of incidence of 0.degree., about 16% of the electromagnetic
radiation incident on the incident surface is reflected by the
filter. At an incidence angle of 75.degree., roughly 90% of the
electromagnetic radiation incident on the incident surface is
reflected by the filter.
Example 3
This example describes the enhancement in the performance in a
solar thermophotovoltaic (TPV) system that can be achieved using a
2-dimensionally periodic photonic crystal to selectively absorb
electromagnetic radiation. In this example, the theoretical
performance of a standard solar TPV system without an angularly
selective absorber is analyzed, both in the ideal case and with a
realistic amount of long-wavelength emissivity. Next, the
improvement that can be achieved in a structure with
long-wavelength emissivity using an angle-sensitive design, as
illustrated in FIG. 10, is described.
The energy conversion efficiency of a solar TPV system such as the
system illustrated in FIG. 10 is defined to be:
.eta..times..times..times..times..times..times. ##EQU00002## where
I.sub.m and V.sub.m are the current and voltage of the
thermophotovoltaic diode at the maximum power point, C is the
concentration in suns relative to the solar constant I.sub.s
(usually taken to be 1 kW/m.sup.2), and A.sub.s is the surface area
of the selective solar absorber. This system can conceptually be
decomposed into two halves: the selective solar absorber front end
and the selective emitter plus TPV diode back end. Each half can be
assigned its own efficiency: .eta..sub.t and .eta..sub.p,
respectively. The system efficiency can then be rewritten as:
.eta.=.eta..sub.t(T).eta..sub.p(T) [8] where T is the equilibrium
temperature of the selective absorber and emitter region. The
efficiency of each subsystem can be further decomposed into its
component parts. In particular, the selective solar absorber
efficiency can be represented by:
.eta..function..times..times..times..times..alpha..times..times.
.times..times..sigma..times..times. ##EQU00003## where B is the
window transmissivity, .infin. is the spectrally averaged
absorptivity, .di-elect cons. is the spectrally averaged
emissivity, and B is the Stefan-Boltzmann constant.
The TPV diode backend efficiency can be represented by
.eta..times..times..times..times.
.times..times..times..times..sigma..times..times. ##EQU00004##
where .di-elect cons..sub.E E and A.sub.E are the effective
emissivity and area of the selective emitter, respectively.
First, one can consider the situation where absorptivity for both
the selective absorber and emitter is unity within a certain
frequency range, and .delta. otherwise. .delta. corresponds to the
emissivity which cannot be suppressed due to fabrication and/or
material constraints, which one would generally like to be as small
as possible. The ranges for the selective absorbers and emitters
are optimized separately, and the lower end of the selective
emitter frequency range equals the TPV diode bandgap frequency
w.sub.g. If one considers the case of unconcentrated sunlight, the
limit .delta..fwdarw.0 implies a decoupling between the selective
absorber and emitter, where the selective absorber is kept
relatively cool to maximize .eta..sub.t, while the selective
emitter acts as if it were much hotter with a bandgap frequency
.omega..sub.g well over the blackbody peak predicted by Wien's law.
However, this also leads to declining effective emissivity
.di-elect cons..sub.E, (which varies proportionally with .delta.),
and thus A.sub.E/A.sub.s varies proportionally with 1/.delta.. This
expectation is supported by the numerical calculations shown in
FIGS. 11A-11B, which demonstrate both that efficiency slowly
increases with decreasing .delta., while the area ratio increases
rapidly as 1/.delta.. The limit where .delta..fwdarw.0 and
A.sub.E/A.sub.s.fwdarw..infin. is unphysical, both because the time
to establish equilibrium in an arbitrarily large system is
arbitrarily long, and a perfectly sharp emissivity cutoff requires
a step function in the imaginary part of the dielectric constant of
the underlying material. However, the latter is inconsistent with
the Kramers-Kronig relations for materials, which derive from
causality.
Based on previous comprehensive reviews of selective solar
absorbers, typical spectrally averaged selective solar absorber
emissivities .di-elect cons. are about 0.05 at a temperature of
approximately 373 K. Assuming .delta.=0.05 as well, this implies a
maximum system efficiency of 10.5% (T=720 K, .eta..sub.t=0.6937,
.eta..sub.p=0.1510, and A.sub.E=A.sub.s=0.75), as illustrated in
FIG. 12A. While a physically relevant result, this efficiency is
unfortunately less than a quarter of the asymptotic efficiency
calculated above as .delta..fwdarw.0.
In order to bridge the gap between performance of solar TPV in the
cases where .delta.=0.05 and .delta..fwdarw.0, one can employ an
absorber with a specific form of angular selectivity. The
expression used in this example is as follows: .di-elect
cons.(.omega.,.theta.)=[1-(.theta./.theta..sub.max.sup.2][.delta.+(1-.del-
ta.).PI..sub..omega.1,.omega.2(.omega.) [11] where
.PI..sub..omega.1,.omega.2 is the tophat function (equal to 1 if
.omega..sub.1<.omega.<.omega..sub.2 and 0 otherwise),
.theta..sub.max is the maximum polar angle at which electromagnetic
radiation is exchanged with the environment, and .omega..sub.1 and
.omega..sub.2 are the range of absorbed wavelengths. FIG. 13
includes a plot of emissivity as a function of polar angle .theta.
for frequencies within the window of the top hat. Inserting
Equation 11 into Equation 10 and setting .delta.=0.05 yields the
results in FIG. 12B, where the maximum efficiency is 37.0% (T=1600
K, .eta..sub.t=0.7872, .eta..sub.p=0.4697, A.sub.E/A.sub.s=0.05).
This is 3.5 times higher than the result illustrated in FIG. 12A,
and is fairly close to the asymptotic limit where .delta..fwdarw.0,
without the physically unreasonable requirement of a perfectly
sharp emissivity cutoff (which is inconsistent with causality).
This result also exceeds the Shockley-Quiesser limit for
photovoltaic energy conversion in unconcentrated sunlight of 31%
efficiency. Furthermore, as illustrated in FIG. 14, photovoltaic
diodes made from group IV compounds such as silicon and germanium
have bandgaps that would allow for the system to continue to exceed
the Shockley-Quiesser limit. Finally, the much lower area ratio
A.sub.E/A.sub.s=0.05 implies that the angle-selective solar
absorber illustrated in FIG. 10 would serve as a sort of thermal
concentrator, thus allowing for much less thermophotovoltaic area
to be used compared to previous designs.
One structure capable of providing the top-hat functionality
described above is a 2-dimensionally periodic photonic crystal
configured to selectively absorb incident electromagnetic
radiation. The 2-dimensionally periodic photonic crystal considered
in this example is formed in a 4244 nm-thick layer of
single-crystal tungsten. The tungsten layer comprises a plurality
of cylindrical holes with a radius of 795 nm (corresponding to
cross-sectional diameters of 1590 nm) formed within the layer. The
holes have an average nearest neighbor distance of 1591 nm, and are
arranged periodically similar to the arrangement illustrated in
FIG. 4A. The cylindrical holes have lengths of 4244 nm,
corresponding to the thickness of the tungsten layer in which they
were formed.
The performance of the 2-dimensionally periodic photonic crystal
described above was simulated using S-matrix code as described in
Whittaker and Culshaw, "Scattering-matrix treatment of patterned
multilayer photonic structures," Phys Rev B, 60, 2610 (1999). As
shown in FIG. 15, the 2-dimensionally periodic photonic crystal
exhibits decreasing average emissivity with increasing incident
angle. In particular, at a 75.degree. incident angle, the average
emissivity is 60% lower than at normal incidence (i.e., an incident
angle of 0.degree.).
While several embodiments of the present invention have been
described and illustrated herein, those of ordinary skill in the
art will readily envision a variety of other means and/or
structures for performing the functions and/or obtaining the
results and/or one or more of the advantages described herein, and
each of such variations and/or modifications is deemed to be within
the scope of the present invention. More generally, those skilled
in the art will readily appreciate that all parameters, dimensions,
materials, and configurations described herein are meant to be
exemplary and that the actual parameters, dimensions, materials,
and/or configurations will depend upon the specific application or
applications for which the teachings of the present invention
is/are used. Those skilled in the art will recognize, or be able to
ascertain using no more than routine experimentation, many
equivalents to the specific embodiments of the invention described
herein. It is, therefore, to be understood that the foregoing
embodiments are presented by way of example only and that, within
the scope of the appended claims and equivalents thereto, the
invention may be practiced otherwise than as specifically described
and claimed. The present invention is directed to each individual
feature, system, article, material, kit, and/or method described
herein. In addition, any combination of two or more such features,
systems, articles, materials, kits, and/or methods, if such
features, systems, articles, materials, kits, and/or methods are
not mutually inconsistent, is included within the scope of the
present invention.
The indefinite articles "a" and "an," as used herein in the
specification and in the claims, unless clearly indicated to the
contrary, should be understood to mean "at least one."
The phrase "and/or," as used herein in the specification and in the
claims, should be understood to mean "either or both" of the
elements so conjoined, i.e., elements that are conjunctively
present in some cases and disjunctively present in other cases.
Other elements may optionally be present other than the elements
specifically identified by the "and/or" clause, whether related or
unrelated to those elements specifically identified unless clearly
indicated to the contrary. Thus, as a non-limiting example, a
reference to "A and/or B," when used in conjunction with open-ended
language such as "comprising" can refer, in one embodiment, to A
without B (optionally including elements other than B); in another
embodiment, to B without A (optionally including elements other
than A); in yet another embodiment, to both A and B (optionally
including other elements); etc.
As used herein in the specification and in the claims, "or" should
be understood to have the same meaning as "and/or" as defined
above. For example, when separating items in a list, "or" or
"and/or" shall be interpreted as being inclusive, i.e., the
inclusion of at least one, but also including more than one, of a
number or list of elements, and, optionally, additional unlisted
items. Only terms clearly indicated to the contrary, such as "only
one of" or "exactly one of," or, when used in the claims,
"consisting of," will refer to the inclusion of exactly one element
of a number or list of elements. In general, the term "or" as used
herein shall only be interpreted as indicating exclusive
alternatives (i.e. "one or the other but not both") when preceded
by terms of exclusivity, such as "either," "one of," "only one of,"
or "exactly one of." "Consisting essentially of," when used in the
claims, shall have its ordinary meaning as used in the field of
patent law.
As used herein in the specification and in the claims, the phrase
"at least one," in reference to a list of one or more elements,
should be understood to mean at least one element selected from any
one or more of the elements in the list of elements, but not
necessarily including at least one of each and every element
specifically listed within the list of elements and not excluding
any combinations of elements in the list of elements. This
definition also allows that elements may optionally be present
other than the elements specifically identified within the list of
elements to which the phrase "at least one" refers, whether related
or unrelated to those elements specifically identified. Thus, as a
non-limiting example, "at least one of A and B" (or, equivalently,
"at least one of A or B," or, equivalently "at least one of A
and/or B") can refer, in one embodiment, to at least one,
optionally including more than one, A, with no B present (and
optionally including elements other than B); in another embodiment,
to at least one, optionally including more than one, B, with no A
present (and optionally including elements other than A); in yet
another embodiment, to at least one, optionally including more than
one, A, and at least one, optionally including more than one, B
(and optionally including other elements); etc.
In the claims, as well as in the specification above, all
transitional phrases such as "comprising," "including," "carrying,"
"having," "containing," "involving," "holding," and the like are to
be understood to be open-ended, i.e., to mean including but not
limited to. Only the transitional phrases "consisting of" and
"consisting essentially of" shall be closed or semi-closed
transitional phrases, respectively, as set forth in the United
States Patent Office Manual of Patent Examining Procedures, Section
2111.03.
* * * * *
References