U.S. patent application number 13/219296 was filed with the patent office on 2012-03-01 for negative refractive index materials and methods for making same.
This patent application is currently assigned to TRITON SYSTEMS, INC.. Invention is credited to Alkim Akyurtlu, Keith A. Higginson, Adil-Gerai Kussow.
Application Number | 20120050878 13/219296 |
Document ID | / |
Family ID | 42265660 |
Filed Date | 2012-03-01 |
United States Patent
Application |
20120050878 |
Kind Code |
A1 |
Higginson; Keith A. ; et
al. |
March 1, 2012 |
NEGATIVE REFRACTIVE INDEX MATERIALS AND METHODS FOR MAKING SAME
Abstract
Embodiments of the invention described herein include
metamaterials that exhibit negative permittivity and negative
permeability at optical frequencies, methods for preparing such
materials, and devices prepared from same.
Inventors: |
Higginson; Keith A.;
(Leominster, MA) ; Akyurtlu; Alkim; (Arlington,
MA) ; Kussow; Adil-Gerai; (Beverly, MA) |
Assignee: |
TRITON SYSTEMS, INC.
Chelmsford
MA
|
Family ID: |
42265660 |
Appl. No.: |
13/219296 |
Filed: |
August 26, 2011 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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12626173 |
Nov 25, 2009 |
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13219296 |
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61118123 |
Nov 26, 2008 |
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Current U.S.
Class: |
359/652 ;
252/582; 359/642; 428/220; 428/221; 428/336; 977/773; 977/834 |
Current CPC
Class: |
Y10T 428/25 20150115;
B29D 11/0074 20130101; C01B 32/956 20170801; G02B 1/007 20130101;
Y10T 428/249921 20150401; Y10T 428/265 20150115; B82Y 20/00
20130101; G02B 1/00 20130101 |
Class at
Publication: |
359/652 ;
359/642; 428/221; 428/220; 428/336; 252/582; 977/773; 977/834 |
International
Class: |
G02B 3/00 20060101
G02B003/00; C09K 3/00 20060101 C09K003/00; B32B 5/16 20060101
B32B005/16 |
Claims
1.-50. (canceled)
51. A metamaterial comprising: a matrix material having a negative
permittivity (.di-elect cons.) at optical frequencies; and
nanoparticles having a high dielectric constant structured to cause
negative permeability (.mu.) at optical frequencies due to a
scattering resonance.
52. The metamaterial of claim 51, wherein the matrix material is
metallic with a plasmon resonance.
53. The metamaterial of claim 51, wherein the matrix material is
one or more materials that exhibit negative permittivity and a low
Drude loss factor.
54. The metamaterial of claim 51, wherein the matrix material
comprises one or more transition metals and metal alloys
thereof.
55. The metamaterial of claim 51, wherein the matrix material is
polycrystalline magnesium diboride (MgB.sub.2).
56. The metamaterial of claim 51, wherein the matrix material
comprises nanoparticles of material selected from gold (Au),
platinum (Pt), copper (Cu), silver (Ag), nickel (Ni), palladium
(Pd), cadmium (Cd), zinc (Zn), and combinations thereof.
57. The metamaterial of claim 56, wherein the matrix material
further comprises one or more polymeric materials.
58. The metamaterial of claim 51, wherein the nanoparticles
comprise one or more transition metal oxides.
59. The metamaterial of claim 51, wherein the nanoparticles are
selected from silicon carbide (SiC) nanoparticles, titanium oxide
(TiO.sub.2), zirconium oxide (ZrO.sub.2), and combinations
thereof.
60. The metamaterial of claim 51, wherein the nanoparticles have a
particle size of from about 10 nm to about 1000 nm.
61. The metamaterial of claim 51, wherein the nanoparticles have a
spherical, pyramidal, cylindrical, or tetrahedral shape.
62. The metamaterial of claim 51, wherein the nanoparticles are in
a regular arrangement.
63. The metamaterial of claim 51, wherein the nanoparticles are in
a random arrangement.
64. The metamaterial of claim 51, wherein the nanoparticles are
arranged in a gradient.
65. The metamaterial of claim 64, wherein the nanoparticles
comprise spherical nanoparticles of various sizes.
66. The metamaterial of claim 64, wherein the gradient provides a
negative gradient index of refraction.
67. The metamaterial of claim 51, wherein the nanoparticles are
from about 10% by volume to about 50% by volume of the
metamaterial.
68. The metamaterial of claim 51, further comprising a surfactant,
binder, or combination thereof.
69. The metamaterial of claim 68, wherein the surfactant, binder,
or combination thereof comprises less than about 25% by volume of
the metamaterial.
70. The metamaterial of claim 51, wherein the metamaterial is a
film having a thickness of from less than about 10 .mu.m to about
25 mm.
71. The metamaterial of claim 51, wherein the metamaterial is a
coating having a thickness less than about 10 .mu.m.
72. The metamaterial of claim 51, wherein the metamaterial exhibits
a negative refractive index within the visible spectrum.
73. The metamaterial of claim 51, wherein the metamaterial exhibits
one or more negative refractive index band from about 250 nm to
about 1500 nm.
74. The metamaterial of claim 51, wherein the Drude loss factor of
the matrix material is less than about 0.1.
75. The metamaterial of claim 51, wherein the material is optically
isotropic.
76. A lens comprising: a matrix material having a negative
permittivity (.di-elect cons.) at optical frequencies; and
nanoparticles having a high dielectric constant structured to cause
negative permeability (.mu.) at optical frequencies due to a
scattering resonance.
77. The lens of claim 76, wherein the nanoparticles are arranged in
a gradient.
78. The lens of claim 76, wherein the lens exhibits a negative
index of refraction.
79. A method for focusing parallel beams of light comprising
directing a beam of light through a lens having a negative gradient
of refraction.
80. The method of claim 79, wherein the lens comprises: a matrix
material having a negative permittivity (.di-elect cons.) at
optical frequencies; and nanoparticles having a high dielectric
constant structured to cause negative permeability (.mu.) at
optical frequencies due to a scattering resonance arranged in a
gradient.
81. The method of claim 79, wherein the beam of light emanates from
an object in far field of the lens.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application claims priority from U.S. Provisional
Application No. 61/118,123 entitled "Negative Refractive Index
Materials and Methods for Making Same" filed Nov. 26, 2008, the
contents of which are incorporated herein by reference in their
entirety.
GOVERNMENT INTERESTS
[0002] Not applicable
PARTIES TO A JOINT RESEARCH AGREEMENT
[0003] Not applicable
INCORPORATION BY REFERENCE OF MATERIAL SUBMITTED ON A COMPACT
DISC
[0004] Not applicable
BACKGROUND
[0005] Negative refractive index materials (NIMs) have
extraordinary promise in imaging and lithography applications.
Unlike a conventional lens, a negative refractive index implies
that when a material refracts an incoming light ray, the refracted
ray will be deviated at a negative angle to the normal according to
Snell's law, as shown in FIG. 1. This seemingly trivial observation
has profound consequences because, as implied by the figure,
focusing can be accomplished by a slab of material rather than a
conventionally-shaped lens. More subtly, lenses made from NIMs can
be much more compact than conventional lenses, and wave vector
components along the optical axis can be used for imaging since
evanescent waves grow in NIMs instead of decay. In contrast, these
components decay at distances very close to the lens surface (the
near field) in conventional optics accounting for a loss of imaging
information and, ultimately, loss of resolution. Furthermore, a
negative index implies that the phase of a wave decreases through
NIMs rather than advances. A material with n=-1 can be considered
to reverse the effect of propagation through an equivalent
thickness of vacuum. Consequently, negative index materials have a
potential advantage of forming highly efficient low reflectance
surfaces by canceling the scattering properties of other materials,
and if the material is isotropic, these effects occur regardless of
the direction of the incident wave creating what theoreticians have
called this the perfect lens: a planar slab, without reflective
losses, which could focus both the propagating and evanescent
components of an object and achieve sub-wavelength imaging.
[0006] Negative index of refraction metamaterials can be obtained
when the electrical permittivity (.di-elect cons.) is less than 0
and magnetic permeability (.mu.) is less than 0. Typically these
are achieved when there is resonance behavior in the material.
Electrical resonances are common in metals at optical frequencies,
but magnetic resonant conditions do not occur in natural materials
at these frequencies, therefore the construction of metamaterials
involves engineering a negative permeability material using
non-magnetic materials. At radio frequencies, this can be done
using small (mm-scaled) metallic inclusions to achieve negative
effective value for .mu. to create structures that have a negative
index of refraction in certain microwave bands. These are usually
ring-shaped strips of metal, and the magnitude of the magnetic
moment that forms from the induced current becomes large (positive
or negative) under resonance conditions. More recently, it has been
possible to lithographically define tiny optical-frequency
resonators in materials, which have resulted in negative index
behavior in the visible and near-infrared spectrum. Still, these
materials are (1) not isotropic, i.e., the features are planar, and
the index varies with orientation, and (2) most of these materials
exhibit large optical losses.
[0007] Properties that can be exploited using NIMs include:
[0008] Reversal of Snell's Law: When light passes through NIMs, the
sign on the relationship between incident and refracted light rays
changes. Therefore, light is refracted away from the normal instead
of toward it. This allows devices such as a flat lens, which may
lead to more compact optics, and in curved lenses, NIMs may focus
light to a much shorter focal length using less material. There is
not a near-field limitation implied with the reversal of Snell's
law.
[0009] Evanescent Field Grows Instead of Decays: A very interesting
consequence of negative index is that the evanescent field within
the light will grow exponentially instead of decay as in
conventional lenses. As illustrated in FIG. 2, evanescent waves may
originate from three interfaces: the object, where it decays; the
front of the lens at the aperture, where it begins to grow; and
from the back of the lens, where it again decays. In an NIM lens,
optical information at the interface is not lost, but can be
reconstructed at the image plane. In principle, the resolution of
the reconstructed image may be better than the diffraction limit
creating a phenomenon known as super-resolution.
[0010] A super-resolution lens can be constructed so that the
information at the aperture is completely reconstructed, such that
there is improved imaging at the plane of the detector of the light
that is received. This may create a smaller spot size eliminating
some limitations of conventional lenses and allowing for smaller
pixels in the detector (or that finer features may be obtained in
optical lithography). The image plane created by a NIM lens is in
the near field, which is applicable in some applications, but
techniques are being developed to project the information at the
aperture onto an image plane in the far field as well, e.g., with a
grating coupled to the NIM.
[0011] NIM properties vary with wavelength: For most applications,
a broad band of negative index behavior is preferred, but these are
still designed around resonances, and in some cases, a very narrow
bandwidth may be desired. Under these conditions, transmission and
reflection properties will go through extremes of near-perfect
transmission or reflection, and at the proper wavelength can be
designed to have negligible reflectance at wavelengths of interest,
which is desired in certain optical systems.
BRIEF SUMMARY OF THE INVENTION
[0012] Various embodiments are directed to a metamaterial including
a matrix material having a negative permittivity (.di-elect cons.)
at optical frequencies and nanoparticles having a high dielectric
constant structured to cause negative permeability (.mu.) at
optical frequencies due to a scattering resonance.
[0013] In some embodiments, the matrix material may be a metallic
with a plasmon resonance, and in other embodiments, the matrix
material may be one or more materials that exhibit negative
permittivity and a low Drude loss factor. In such embodiments, the
matrix material may include one or more transition metals and metal
alloys thereof, and in some embodiments, the matrix material may be
polycrystalline magnesium diboride (MgB.sub.2). In other
embodiments, the matrix material may include nanoparticles of
material such as, but not limited to, gold (Au), platinum (Pt),
copper (Cu), silver (Ag), nickel (Ni), palladium (Pd), cadmium
(Cd), zinc (Zn), and combinations thereof. In still other
embodiments, the matrix material further can include one or more
polymeric materials.
[0014] In some embodiments, the nanoparticles may include one or
more transition metal oxides, and in certain embodiments, the
nanoparticles may be silicon carbide (SiC) nanoparticles, titanium
oxide (TiO.sub.2), zirconium oxide (ZrO.sub.2), and combinations
thereof. In such embodiments, the nanoparticles may have a particle
size of from about 10 nm to about 1000 nm, and may have a
spherical, pyramidal, cylindrical, or tetrahedral shape. In some
embodiments, the nanoparticles may be in a regular arrangement, and
in other embodiments, the nanoparticles may be in a random
arrangement. In still other embodiments, the nanoparticles may be
arranged in a gradient. In some embodiments, the gradient may
include spherical nanoparticles of various sizes, and in certain
embodiments, the gradient may provide a negative gradient index of
refraction. In some embodiments, the nanoparticles may make up from
about 10% by volume to about 50% by volume of the metamaterial.
[0015] In particular embodiments, the metamaterial may include a
surfactant, binder, or combination thereof and in some embodiments,
the surfactant, binder, or combination thereof may be less than
about 25% by volume of the metamaterial. In certain embodiments,
the metamaterial may be a film having a thickness of from less than
about 10 .mu.m to about 25 mm, and in other embodiments, the
metamaterial may be a coating having a thickness less than about 10
.mu.m. In some embodiments, the metamaterial may exhibit a negative
refractive index within the visible spectrum, and in particular
embodiments, the metamaterial may exhibit one or more negative
refractive index band from about 250 nm to about 1500 nm. In some
embodiments, the Drude loss factor of the matrix material may be
less than about 0.1, and in other embodiments, the material may be
optically isotropic.
[0016] Other embodiments include a lens including a matrix material
having a negative permittivity (.di-elect cons.) at optical
frequencies and nanoparticles having a high dielectric constant
structured to cause negative permeability (.mu.) at optical
frequencies due to a scattering resonance.
[0017] In particular embodiments, the nanoparticles may be arranged
in a gradient, and in some embodiments, the lens may exhibit a
negative index of refraction.
[0018] Still other embodiments include a method for producing a
metamaterial including the steps of combining a matrix material
having a negative permittivity (.di-elect cons.) at optical
frequencies and nanoparticles having a high dielectric constant
structured to cause negative permeability (.mu.) at optical
frequencies due to a scattering resonance to create a powder
mixture, encapsulating the powder mixture in a container, and
consolidating the powder mixture by hot isostatic pressing to form
a metamaterial billet.
[0019] In some embodiments, such methods may further include the
steps of cutting metamaterial billet. In other embodiments, the hot
isostatic pressing may be carried out at from about 600.degree. C.
to about 700.degree. C. In still other embodiments, the method may
further include the step of milling a matrix material and
nanoparticles to produce a milled powder.
[0020] Further embodiments include a method for producing a
metamaterial including the steps of combining a matrix material
having a negative permittivity (.di-elect cons.) at optical
frequencies and nanoparticles having a high dielectric constant
structured to cause negative permeability (.mu.) at optical
frequencies due to a scattering resonance to create a powder
mixture and sintering at reduced temperature to form a
consolidated, metamaterial film.
[0021] In some embodiments, the method may further include the
steps of dispersing the powder mixture in a solvent and allowing a
film of the powder mixture to form on a substrate before sintering
at reduced temperature. In some embodiment, the solvent may be
selected from, but not limited to ethanol, methanol, acetone, and
combinations thereof. In other embodiments, the substrate may be a
silicon wafer. In still other embodiments, the consolidated,
metamaterial film may be from about 100 nm to about 100 .mu.m
thick. In further embodiments, the sintering may be conducted using
an e-beam, and in some embodiments, the sintering may include a
dosage e-beam energy at an interval of from about 25,000 kGy to
about 150,000 kGy. In other embodiments, the reduced temperature
may be less than about 150.degree. C., and in particular
embodiments, the sintering may occur under nitrogen. In still other
embodiments, the method may further include the step of milling a
matrix material and nanoparticles to produce a milled powder.
[0022] Still further embodiments include a method for producing a
metamaterial including the steps of dispersing a magnesium salt in
organic solvent and reacting with a borohydride compound to form a
solution, adding water to the solution to form a second solution,
precipitating magnesium diboride from the second solution,
collecting the precipitate, and reacting under an atmosphere of
diborane.
[0023] In some embodiments, the magnesium salt may be magnesium
chloride or magnesium boride, and in other embodiments, the
borohydride may be sodium borohydride. In certain embodiments, the
method may further include the step of spin casting the
precipitate, and in other emodiments, the method may further
include reacting the precipitate under an atmosphere of
diborane.
[0024] Yet other embodiments are directed to a method for focusing
parallel beams of light comprising directing a beam of light
through a lens having a negative gradient of refraction. In some
embodiments, the lens may include a matrix material having a
negative permittivity (.di-elect cons.) at optical frequencies and
nanoparticles having a high dielectric constant structured to cause
negative permeability (.mu.) at optical frequencies due to a
scattering resonance arranged in a gradient. In other embodiments,
the beam of light emanates from an object in far field of the
lens.
DESCRIPTION OF DRAWINGS
[0025] For a fuller understanding of the nature and advantages of
the present invention, reference should be made to the following
detailed description taken in connection with the accompanying
drawings, in which:
[0026] FIG. 1 shows a "perfect lens" of a negative index material
(NIM): (A) shows a flat slab of metamaterial (with greater allowed
resolution), (B) illustrates incident beams refracting at a
negative angle to the normal, and (C) shows a metamaterial
consisting of a distribution of nanoparticles randomly distributed
in a matrix material.
[0027] FIG. 2 shows an evanescent field is amplified within a
NIM.
[0028] FIG. 3A shows scanning electron micrographs of commercially
available 130 nm .beta.-SiC nanoparticles and FIG. 3B shows
scanning electron micrographs of commercially available ultrafine
.beta.-SiC nanoparticles.
[0029] FIG. 4 shows the real part of n.sub.eff and the loss ratio,
calculated using the ellipsometric data of the MgB.sub.2 made by
HIP, and assuming randomly distributed SiC spheres (500 nm diameter
and filled at 30 vol %).
[0030] FIG. 5 shows an exemplary lens designed with a gradient
index of refraction.
[0031] FIG. 6 shows an exemplary variation of the real part of the
negative index of refraction for a gradient index of refraction
lens.
[0032] FIG. 7 shows FDTD analysis of nanoparticles having different
shapes embedded in MgB.sub.2 for real and imaginary parts of the
index of refraction.
[0033] FIG. 8 shows a metamaterial comprised of SiC spheres with a
volume fraction of about 30% randomly distributed in an MgB.sub.2
matrix. Particle sizes may range from 130-500 nm, depending on the
properties of the MgB.sub.2 and which plasmon band is
exploited.
[0034] FIG. 9 shows the effective index of refraction and the loss
ratio calculated for the low-energy plasmon dielectric function of
MgB.sub.2. The loss ratio is the imaginary part of the refractive
index divided by the real part (|Im(n)/Re(n)|). These calculations
assume Drude loss factors for MgB.sub.2, .gamma.=0.01 (low loss,
consistent with literature values) and 0.25 eV (high loss).
[0035] FIG. 10 shows (A) real and imaginary parts of the effective
negative index of refraction using two different models, and (B)
results for the real and imaginary parts of n.sub.eff. The sizes of
nanoparticles and their fill factors are: r.sub.Au=10 nm,
r.sub.SiC=65 nm, f.sub.Au=0.46, f.sub.SiC=0.3.
[0036] FIG. 11 shows a photograph of a finished billet, and a
micrograph (1000.times. magnification) showing the polycrystalline
nature, and also the anisotropic reflectivity of single grains.
Feature size is about 1-2 .mu.m.
[0037] FIG. 12 shows a scanning electron micrograph (SEM) of
MgB.sub.2/SiC metamaterial prepared using hot isostatic
pressing.
[0038] FIG. 13 shows MgB.sub.2/SiC films prepared by e-beam
sintering. At a dose of 150,000 kGy, the MgB.sub.2 appears to be
melted around non-aggregated SiC spheres, but the film is not yet
fully dense.
[0039] FIG. 14 shows reflectivity curves measured by ellipsometry
at different angles. (2 eV=621 nm).
[0040] FIG. 15 shows the complex index of refraction derived from
the ellipsometric data. The real index is in red, and the imaginary
part is the green dashed line. The plasma energy is 2.1 eV, or
about 600 nm.
[0041] FIG. 16 shows spectrometer normal incidence reflection data
(blue line) vs. reflection calculated using ellipsometer data
(yellow line).
[0042] FIG. 17 shows an SPR apparatus. In a NIM, surface plasmons
will be excited for both s- and p-polarized light. In a normal
conductor, only the p-polarization can excite a surface
plasmon.
[0043] FIG. 18 shows the behavior of a conductor in an SPR
experiment. There is no dip for s-polarized light (red curve), but
a surface plasmon is absorbed for p-polarized radiation. Here the
air gap is zero, and the material is Au on a SiO.sub.2
dielectric.
[0044] FIG. 19 shows reflection of MgB.sub.2 as a function of
incident angle and width of air gap in p-polarization.
[0045] FIG. 20 shows reflection of MgB.sub.2 as a function of
incident angle and width of air gap in s-polarization.
[0046] FIG. 21 shows reflection of MgB.sub.2/SiC as a function of
incident angle, for both polarizations. The sample is made by HIP,
using 500 nm diameter SiC particles. Surface plasmons are excited
by both s- and p-polarized light, indicative of both .di-elect
cons.<0 and .mu.<0, conditions of negative index of
refraction.
[0047] FIG. 22 shows the results of surface plasmon coupling.
Coupling is observed for both electric and magnetic plasmons.
[0048] FIG. 23 shows the microstructure of Au/SiC material. For a
real material, at the necessary density, the voids will not be free
space.
[0049] FIG. 24 shows the calculated reflection and extinction
spectra for Au/SiC metamaterials where f.sub.Au varies from 34% to
46%.
[0050] FIG. 25 shows the real and imaginary parts of the refractive
index near 6 .mu.m wavelengths.
[0051] FIG. 26 shows the complex effective refractive index
[n.sub.eff] and figure of merit [FOM=|Re(n.sub.eff)|/Im(n.sub.eff)]
for a Ag/SiC metamaterial where r.sub.SiC=75 nm; r.sub.Ag=10 nm;
f.sub.SiC=30%; f.sub.Ag=48%.
[0052] FIG. 27 shows the relationship between image plane distance,
resolution factor, and imaginary part of the refractive index at
193 nm where S=10 implies .lamda./20 resolution.
DETAILED DESCRIPTION
[0053] It must also be noted that as used herein and in the
appended claims, the singular forms "a", "an", and "the" include
plural reference unless the context clearly dictates otherwise.
Thus, for example, reference to a "cell" is a reference to one or
more cells and equivalents thereof known to those skilled in the
art, and so forth. Unless defined otherwise, all technical and
scientific terms used herein have the same meanings as commonly
understood by one of ordinary skill in the art. Although any
methods and materials similar or equivalent to those described
herein can be used in the practice or testing of embodiments of the
present invention, the preferred methods, devices, and materials
are now described. All publications mentioned herein are
incorporated by reference. Nothing herein is to be construed as an
admission that the invention is not entitled to antedate such
disclosure by virtue of prior invention.
[0054] As used herein, the term "about" means plus or minus 10% of
the numerical value of the number with which it is being used.
Therefore, about 50% means in the range of 45%-55%.
[0055] The invention described herein is generally directed to
optically isotropic metamaterials that are active in the visible
spectrum. Such materials may include a host material exhibiting
negative permittivity (.di-elect cons.) at optical frequencies, and
nanoparticles dispersed in the host material that exhibit a Mie
resonance that provides a negative permeability (.mu.).
[0056] Any host material that exhibits negative permittivity may be
used in various embodiments of the invention, and in particular
embodiments, the host material may also exhibit low dielectric
losses in the visible spectrum. For example, in some embodiments
the host material may exhibit negative permittivity and have a low
intrinsic (Drude) loss factor; and in other embodiments the host
material may be a composite material composed of more than one
material, and the composite may exhibit negative permeability
and/or low Drude loss. In some embodiments, such a host material
may include at least one transition metal including any material
between group 2 elements and group 13 elements on the periodic
table of elements; and in some embodiments, the host material may
include one or more noble metals. For example, in some embodiments,
the host material may be a substantially pure transition metal such
as, but not limited to, gold, Au; platinum, Pt; copper, Cu; silver,
Ag; nickel, Ni; palladium, Pd; mercury, Hg; cadmium, Cd; zinc, Zn;
magnesium, Mg; and the like and, in other embodiments, the matrix
material may include one or more polymeric materials. For example,
in some exemplary embodiments, the host material may be aggregated
nanoparticles, such as gold nanoparticles, and in other exemplary
embodiments the nanoparticles may be combined with a polymeric
material that fills voids within the material between
nanoparticles. In such embodiments, a dispersion of, for example,
gold nanoparticles host material may exhibit reduced dielectric
losses due to air, and in other such embodiments, a host material
may include a polymer with n>1 between gold nanoparticles. In
other embodiments, the host material may include one or more metal
alloys or superconducting materials including, for example, any
transition metal or noble metal provided above, such as, for
example, magnesium diboride (MgB.sub.2).
[0057] Similarly, nanoparticles of any composition and structure
that exhibit negative permeability may be used in embodiments. In
some embodiments, the nanoparticles may be carbide containing
nanoparticles such as, for example, silicon carbide (SiC) and the
like. The magnetic response of the metamaterial is a result of
collective oscillations of charges in the random (or regular) array
of dielectric particles, as explained by Mie theory. A higher
dielectric constant implies that more current can be induced in the
particles and thus, SiC (.di-elect cons..about.6.5) may be
considered an appropriate material. However, dry SiC powders are
difficult to get into liquid suspension and may require excessive
surfactant in the final film formulation. Therefore, in other
embodiments, transition metal oxides such as, for example, titanium
oxide, TiO.sub.2: zirconium oxide, ZrO.sub.2: and the like may be
used as alternatives to SiC because, for example. TiO.sub.2, has an
c value of about 6.2 or 8.4 depending on the crystal phase and
sufficient current can be induced in such particles. Additionally,
transition metal oxide particles may allow fabrication strategies,
such as sol-gel synthesis, and suspension stabilization in aqueous
or alcoholic solvents by well-known techniques.
[0058] The size and shape of the nanoparticles of various
embodiments may vary. In general, the nanoparticles of embodiments
may have an average particle size from about 10 nm to about 1000
nm, and in some embodiments, the average particle size may be from
about 50 to about 800 nm, about 75 nm to about 750 nm, or about 100
to about 500 nm. In such embodiments, the particle size may be
uniform wherein each nanoparticle of the optically isotropic
metamaterials has substantially the same average particle size, and
in other embodiments, the particle size may not be uniform. For
example, in particular embodiments, a first portion of the
nanoparticles may have a first average particle size and one or
more other portions of the nanoparticles in metamaterial may have
smaller average particle sizes or larger average particle sizes
than the first average particle size.
[0059] The nanoparticles of such embodiments may be of any shape.
For example, in some embodiments, the nanoparticles may be
spherical or nearly spherical, and in other embodiments, the
nanoparticles may have a polyhedral shape such as, but not limited
to, cubical, cuboidal, rhomboidal, cylindrical, octahedral,
icosahedral, and the like. In still other embodiments, the
nanoparticles may have an irregular shape such that, for example, a
portion of the nanoparticle appears spherical and another portion
appears angular, forming a hemispherical structure, or various
edges or vertices of the polyhedron may be rounded, smoothed or
removed. In particular embodiments, the nanoparticles may be
present in an array of non-uniform shapes including any of those
shapes recited above. For example, scanning electron micrographs
(SEM) of exemplary SiC nanoparticles are provided in FIG. 3, which
illustrates the variety of shapes and sizes of nanoparticles. FIG.
3A shows 130 nm .beta.-SiC nanoparticles having a mean particle
diameter of about 190 nm with a standard deviation of about 50%,
and FIG. 3B shows ultrafine .beta.-SiC nanoparticles having a mean
particle diameter of about 500 nm with a standard deviation of
about 50%.
[0060] The arrangement of the nanoparticles in the host material
may also vary. For example, in some embodiments, the nanoparticles
may be regularly arranged, and in other embodiments, the
nanoparticles may be randomly arranged. In still other embodiments,
the nanoparticles of a portion of the material may be regularly
arranged, and the nanoparticles of another portion of the material
may be randomly arranged. The nanoparticles of various embodiments
may be dispersed uniformly throughout the material, or they may be
concentrated in one or more portion of the material. In still other
embodiments, the nanoparticles may be of a range of average
particle sizes.
[0061] Without wishing to be bound by theory, the position of the
negative .mu. band may be controlled by varying the size and volume
fraction nanoparticles. Thus, the nanoparticles of various
embodiments may be structured to cause negative permeability (.mu.)
at optical frequencies. Moreover, the nanoparticles can be
engineered to coincide with the negative .di-elect cons. band
originating from the host material. For example, as shown in FIG.
4, there is a region where the real part of the refractive index is
negative, and in this region, the imaginary part is close to zero.
Therefore, for thin samples, the material should be highly
transmissive because the imaginary part of the index is close to
zero. In particular embodiments, multiple bands of negative
refractive index and low optical losses can be engineered in the
same material. For example, FIG. 4 shows multiple bands of negative
index calculated for a MgB.sub.2/SiC metamaterial made by hot
isostatic pressing, using measured optical properties of
MgB.sub.2.
[0062] In certain embodiments, the nanoparticles may be provided in
a gradient within the host material. For example, in some
embodiments, nanoparticles of various sizes may be provided in a
gradient, as illustrated in FIG. 5, in which the nanoparticles are
arranged in a gradient of small to large nanoparticles. In other
embodiments, nanoparticles of similar sizes may be used to create a
concentration gradient within the host material. Without wishing to
be bound by theory, a gradient of nanoparticles may create a
gradient negative index of refraction within the material, and
while the random or regular arrays of nanoparticles described above
may allow for a superlensing effect when both object and image are
in the near-field of the superlens, gradient negative index
refraction materials may allow for a superlens that achieves
sub-wavelength resolution when the object is in the far-field. The
proposed mechanism is based on the phase correction which arises
from the different optical lengths of parallel beams of light as
they travel through different parts of the slab with different
indices of refraction. This should lead to focusing of the parallel
beams of light emanating from the far-field object similar to a
conventional convex lens. If the gradient index of refraction is
negative, such materials may allow for focusing of parallel beams
of light emanated from a source far from the lens, i.e. far-field,
and provide a superlens which allows for subdiffraction size
imaging.
[0063] Such superlenses may exhibit negative permeability and
negative permittivity which may allow for better control of the
negative index of refraction and may provide a broader frequency
regime when the index of refraction is negative. Such superlenses
may further exhibit low losses, and in some embodiments, the low
losses may be a function of the spatial coordinates of the
nanoparticles in the host material. For example, in such
embodiments, nanoparticles of various sizes may be positioned some
distance apart from one another. The nanoparticles must be smaller
that the wavelength of the incidence light. However, the wavelength
of the incidence light cannot be too large, since the waves passing
through the lens decay exponentially and must not be damped
entirely.
[0064] In certain embodiments, the nanoparticles of a superlens may
include spheres of varying sizes and may be ordered as illustrated
in FIG. 5. Without wishing to be bound by theory, such superlens
may exhibit an effective negative epsilon and an effective negative
permeability, which may lead to a low-loss negative index of
refraction. The resulting gradient negative index may be similar to
the waveforms shown in FIG. 6 for different focal lengths. Thus, in
some embodiments, the materials having a gradient negative index of
refraction may be useful for providing sub-wavelength resolution of
objects in the far-field that are projected in the near field. In
other embodiments, materials having a gradient index of refraction
may include surface plasmon coupling (via the grating) to project
an far-field object into the far-field.
[0065] In particular embodiments, the host material may MgB.sub.2
or gold and the nanoparticles may be SiC, and in some embodiments,
the host material may be gold nanoparticles encompassed by a
polymeric material and the nanoparticles may be SiC. Therefore, the
metamaterial of embodiments may be MgB.sub.2/SiC, Au/SiC, or
Au/polymer/SiC. The SiC nanoparticles may be of any shape or a
variety of shapes and may have either a regular or random
distribution in the host material, and in certain embodiments, the
nanoparticles may be regularly dispersed in the host material.
[0066] The suggested structure of optically isotropic metamaterials
including a matrix or host material of polycrystalline magnesium
diboride in a normal state, at room temperature, with randomly
embedded spherical nanoparticles of SiC, is provided in FIG. 6.
which are active in the visible spectrum described above. An
alternate material consists of Au and SiC nanoparticles of
different sizes, with air, or another low-index material, in the
interstices filling voids between the particles. Such metamaterials
may exhibit negative refraction index behavior with extremely low
losses, and in the case of MgB.sub.2/SiC, this result stands for
both random and regular distribution of SiC nanoparticles in the
MgB.sub.2 matrix.
[0067] Negative refractive index can be predicted using either the
effective medium theories or numerical methods such as the rigorous
FDTD method or a combination thereof. Effective medium theories,
including the extended Maxwell-Garnett theory for random
arrangements, may be used to consider the effects of the collective
scattering behavior of the particles and to properly adjust the
parameters of the metamaterial. FDTD simulations may be used to
validate the results and to gain further insight through full-wave
simulations. The Mie resonance due to inclusions of SiC or other
dielectric nanoparticle may be observed at some frequency range,
.DELTA..omega..sub..mu.eff<0, with the effective permeability
.mu..sub.eff<0. Due to Drude-like behavior of the matrix, the
effective permittivity .di-elect cons..sub.eff<0 occurs at
frequencies below the material's plasmon resonance. By the
self-consistent adjustment of the fill factor, f, and the radius of
the dielectric spheres, a set of conditions can be reached where
these regions overlap, and negative refraction index occurs within
the visible region when both .di-elect cons..sub.eff and
.mu..sub.eff are simultaneously negative.
[0068] At optical frequencies, the matrix of the NIM (which
controls the permittivity) should satisfy two requirements. First,
the permittivity .di-elect cons.(.omega.) should obey the
Drude-like (or similar) behavior (Eq. 1) with a plasmon frequency,
.omega..sub.p, within an optical range. Secondly, the losses,
.gamma., should be small.
( .omega. ) = .infin. - .omega. p 2 .omega. 2 + .gamma..omega. ( 1
) ##EQU00001##
Many recently reported NIMs in optical range exhibit large losses,
mostly due to the fact that noble metals (Au, Ag), which have
considerable plasmon losses, were utilized as the components of the
NIMs. The metamaterial of embodiments of the invention utilizes a
superconductor material, MgB.sub.2, instead of a noble metal as a
matrix, which has both theoretically and experimentally verified
low losses. These, however, can be very sensitive to the defect
structure of the MgB.sub.2. For purposes of the discussion herein,
"defects" have been lumped into the Drude loss factor, .gamma.. The
loss factor can be increased to generate a perhaps more realistic
picture of the MgB.sub.2. Calculations have shown that even with a
modest loss factor, the material still generates NIM bands with
relatively low overall losses. FIG. 7 shows calculations with a
favorable (.gamma.=0.01 eV) and unfavorable (.gamma.=0.25 eV) value
of the loss factor. Also, there are at least two Drude-like regions
of behavior of MgB.sub.2, and a NIM can be designed around the UV
or the visible plasmon resonance, each may require differently
sized SiC inclusions.
[0069] The dielectric behavior of the host material contributes
most strongly to the effective permittivity of the NIM, but it is
not independent of the properties of the guest. The effective
magnetic properties of the NIM come about exclusively from the
collective scattering of the inclusions. For illustration, the
effective permittivity (.di-elect cons..sub.eff) and permeability
(.mu..sub.eff) can be averaged according to extended
Maxwell-Garnett theory, which describes the scattering of light
(with the wavelength .lamda.) by particles of finite size
(subscript s) randomly distributed in a host (subscript h). The
effective parameters are given by the following formulas:
eff = h x 3 - 3 fT I E x 3 + 3 2 fT I E ( 2 ) .mu. eff = .mu. h x 3
- 3 fT I H x 3 + 3 2 fT I H ( 3 ) ##EQU00002##
where f is the volume fraction, and T.sub.1.sup.E and T.sub.1.sup.H
are the elements of the scattering matrix for single spheres, given
by:
T I E = [ j 1 ( x s ) [ xj 1 ( x ) ] ' s - j 1 ( x s ) [ x s j 1 (
x s ) ] ' ] h h 1 ( x ) [ x s j 1 ( x s ) ] ' h - j 1 ( x s ) [ xh
1 ( x ) ] ' ] s ] , T I H = [ j 1 ( x s ) [ xj 1 ( x ) ] ' .mu. s -
j 1 ( x s ) [ x s j 1 ( x s ) ] ' ] .mu. h h 1 ( x ) [ x s j 1 ( x
s ) ] ' .mu. h - j 1 ( x s ) [ xh 1 ( x ) ] ' ] .mu. s ] . ( 4 )
##EQU00003##
in which x.sub.s (=2.pi.r(.di-elect
cons..sub.s.mu..sub.s).sup.1/2/.lamda.) and x (=2.pi.r(.di-elect
cons..sub.h.mu..sub.h).sup.1/2/.lamda.) are dimensionless radii,
j.sub.1 and h.sub.1 are spherical Bessel and Hankel functions of
the first kind, and the prime indicates a derivative. In these
calculations, the radius of SiC and the fill factor constitute the
design parameters, and they can be used to find a negative index
band at certain particle radius and volume fraction.
[0070] In various embodiments, it may be assumed that dielectric
properties are averaged over three dimensions, that is, that the
MgB.sub.2 host material is polycrystalline, with no alignment of
the crystal axes. FIG. 9 displays the results of calculation using
the lower-energy (.omega..sub.p=2.1 eV) dielectric function for
MgB.sub.2, considering the worst case for defects, averaged
according to the extended Maxwell-Garnett and Lewin effective
medium models. This uses our most conservative estimate for the
loss factor, .gamma.=0.25 eV., corresponding to a highly defected
matrix, and (in this case) r.sub.SiC=150 nm, a volume fraction of
0.3, and literature values of .di-elect cons..sub.SiC=6.8+0.01i.
Even with extremely high losses, both the models used predict a NIM
region within the .about.700-850 nm, and 700-825 nm, respectively.
The loss ratio is the ratio of the real and imaginary part of the
effective refractive index (|Im(n.sub.eff)/Re(n.sub.eff)|). A loss
ratio below one means that a wave will propagate through the medium
faster than it is absorbed. The loss ratios of both the models are
less than 1 in the entire NIM band, and less than 0.5 within most
of the NIM region, even for the highly defective matrix.
[0071] In other embodiments, the metamaterial may include randomly
distributed small gold nanoparticles in free space, constituting
the host medium, with spherical SiC nanoparticles embedded in this
host. The theoretical analysis of this material is similar to that
presented above, although the losses are expected to be higher, in
general due to the intense scattering of gold and indicates that
this metamaterial also exhibits isotropic negative refraction in
the visible spectrum. The numerical analysis includes both the
effective medium theories and FDTD simulations. It should be noted
that preliminary calculations done during this program suggest that
an interstitial medium other than "free space" will also result in
a negative index band.
[0072] It can be inferred from FIG. 10 that the loss factor, i.e.,
the ratio of magnitudes for the real and imaginary parts of
n.sub.eff, in the negative index band of the Au/SiC material is
more modest than for the MgB.sub.2/SiC material, even in the best
case considered.
[0073] As described above, calculations for theoretical
MgB.sub.2/SiC, and Au/SiC indicate that such materials will exhibit
the qualities of a NIM. Such calculations assume that spherical SiC
nanoparticles are randomly distributed with a particular fill
factor, which specifies distance between the particles because
highly aggregated SiC nanoparticles would negate the resonance
effects that cause negative effective magnetic permeability.
Additionally, simulations with two similarly sized SiC nanoparticle
spheres, which very roughly approximating a size dispersion,
indicate that the negative refractive index effect observed in
simulations of spherical nanoparticles of a single size would not
be cancelled. Moreover, calculations made for SiC nanoparticles of
different shapes, e.g., cylinders, tetrahedra, verify that such
materials exhibit a similar negative index band as predicted for
spheres although the losses and band position may be different.
[0074] Real SiC nanoparticles are not uniformly spherical and are
polydisperse, see, FIG. 3. Moreover, SiC nanoparticles can be any
combination of amorphous and two crystal (.alpha. and .beta.),
which fortunately have similar dielectric properties, and most
commercially available SiC nanopowders are produced by grinding
larger particles to create nanoparticles having a smallest particle
sizes of about 0.25 .mu.m (250 nm). However, particles made by
grinding are more irregularly shaped than those condensed from the
gas phase. Accordingly, simulations using Finite Difference Time
Domain (FDTD) code were carried out to test whether different
shapes would result in similar bands of negative index of
refraction. As illustrated in FIG. 7, these simulations indicate
that particles of alternate shape still are likely to produce NIM
behavior. In these simulations, there are small differences in
particle volume, which probably account for at least some of the
shift in band position. However, for particles of different shape,
there may not always but frequencies in which low loss (where Im(n)
is low) overlaps with negative index. Therefore, without wishing to
be bound by theory, the use of nanoparticles that are close to
spherical may be preferred in practice of embodiments of the
invention.
[0075] Optical data for MgB.sub.2 slabs were obtained (see Example
5) and were fit to the theoretical model for the negative index of
refraction for SiC nanoparticles discussed above to find effective
refractive index behavior for MgB.sub.2/SiC materials, using both
random and regular distribution of spherical SiC particles and the
complex permittivity of MgB.sub.2. The particle size and volume
fraction was varied in these simulations. FIG. 4 shows the results
of a theoretical MgB.sub.2 host material with 500 nm SiC
nanoparticles (.di-elect cons.=6.8+0.1i) and a fill factor
(loading) of 30%. This results indicate multiple refractive index
bands occurring in the visible spectrum with loss ratios less than
0.5, which suggests that waves will propagate through this material
in the negative index bands.
[0076] Embodiments of the invention are also directed to making
such metamaterials. MgB.sub.2 has been discovered to be a high
temperature superconductor (T.sub.c=39 K), which can be made under
similar conditions by either reacting a mixture of Mg and B or
sintering MgB.sub.2 powder at temperatures between 600 and
1100.degree. C. A chief fabrication challenge may be the high vapor
pressure of magnesium, which may cause loss of mass and result in
Mg-poor phases such as MgB.sub.4. Another challenge may be the
tendency of Mg and B to react with their environment at high
temperature, e.g., Mg may oxidize with any air in the system and
alloy with other metals present. Additionally, fully eliminating
voids and pores may be difficult under these reaction conditions.
Therefore, high pressure and/or careful control of the atmosphere
or heating profile may be important in embodiments of the
invention. For example, typical. superconducting grades of
MgB.sub.2 must be processed under hermetic conditions, and for good
density, high pressure must also be applied.
[0077] For instance, an exemplary method for preparing the
metamaterials of the invention may include powder-in-tube (PIT), in
which MgB.sub.2 (or Mg and B) may be loaded into a metal (e.g., Nb,
Ti, Fe, or Ta) tube under inert conditions and the sealed tube is
then drawn through a die and pressed into a thin ribbon for
production, wires and ribbons, which may be useful for use in
superconductive power transmission lines. The ribbon produced by
such methods can then be annealed ex situ. In other embodiments,
metamaterials such as those described above can be prepared by
methods may include (1) hot isostatic pressing (HIP), which is a
powder consolidation technique that uses a similar encapsulation
technique, but may be used to produce a solid billet instead of a
ribbon, (2) low-temperature electron beam sintering, which may
prevent Mg evaporation and (3) conversion of a sol-gel precursor
under a diborane atmosphere.
[0078] Various embodiments of the invention include methods for
preparing a metamaterial using hot isostatic pressing (HIP) wherein
compressed gas may be used to exert pressure on a metal powder or
mixture of metal powders which are loaded into a ductile metal
container (called a "can") and simultaneously heating the material
in the container to allow sintering to occur. For example, in some
embodiments, such methods may include the steps of combining a host
material having a negative permittivity (.di-elect cons.) at
optical frequency and dielectric nanoparticles structured to cause
negative permeability (.mu.) at optical frequencies to produce a
powder mixture, encapsulating the powder mixture in a container,
and consolidating the powder mixture using hot isostatic pressing
to produce at metamaterial billet. In such embodiments, the step of
consolidating the powder mixture may include the steps of placing
the filled container in a chamber with an inert gas such that the
pressure inside the container is from about 5000 psi to about 15000
psi, and simultaneously heating the container. The temperature to
which the container is heated may vary, and in certain embodiments,
the heating may be carried out to a temperature of from about
600.degree. C. to about 700.degree. C. In particular embodiments,
the method may further include the step of cutting the billet to
produce a metamaterial slab and/or lens, and polishing the billet
or the cut billet to remove rough surfaces and/or surface
impurities. Additionally, in some embodiments, the container which
can may be produced in an inert or evacuated atmosphere such that
air and water are excluded during welding. As described in Examples
1 and 2, HIP has been used to make excellent quality pure MgB.sub.2
and MgB.sub.2/SiC samples.
[0079] In various other embodiments, metamaterials may be prepared
by low-temperature e-beam sintering. For example, in some
embodiments, the metamaterial may be prepared by a method which
includes the steps of combining a host material having a negative
permittivity (.di-elect cons.) at optical frequency and dielectric
nanoparticles structured to cause negative permeability (.mu.) at
optical frequencies to produce a powder mixture, dispersing the
powder mixture in a solvent to form a dispersion, dispensing the
dispersion onto a substrate, allowing the solvent to evaporate such
that a film of the powder mixture may form on the substrate, and
subjecting the powder mixture film to e-beam sintering to produce a
consolidated metamaterial. In such embodiments, the solvent may be
any volatile liquid capable of evaporating at or near room
temperature such as, but not limited to, ethanol, methanol,
acetone, and the like, and combinations thereof. The substrate of
embodiments may be any substrate used in such sintering techniques
known in the art, such as, for example, a silicon wafer. The
parameters such as dose and film thickness may be optimized and
varied depending upon the materials use. For example, in some
embodiments, the dosage interval for the film may be from about
25,000 kGy to about 150,000 kGy, and the sintering may occur at a
temperature of less than about 150.degree. C. In certain
embodiments, the sintering may take place under an inert
environment such as, for example, under nitrogen. In other
embodiments, the method may further including grinding or milling
the starting materials to produce a powder mixture having a smaller
particle size. Without wishing to be bound by theory, reducing the
average particle size may eliminate pores in the final material. In
embodiments in which the metamaterial is formed using e-beam
sintering, the consolidated metamaterial may have a thickness of
from about 100 nm to about 100 .mu.m.
[0080] At the temperatures where MgB.sub.2 sintering occurs
(>600.degree. C.), magnesium has a high vapor pressure, and to
make high quality sintered materials, it may be necessary to either
use careful encapsulation and high pressure processes like HIP or
PIT techniques, or controlled chemical environments (e.g., excess
Mg vapor). In e-beam sintering, the process may be carried out so
rapidly that a stoichiometric imbalance may be less of the problem.
Additionally, SiC may remain intact and well-distributed in the
MgB.sub.2 matrix during the sintering step.
[0081] Additionally, e-beam sintering may be used for processing
thin samples of MgB.sub.2 at low temperature. The accelerated
electrons produced during this process are extremely energetic, but
they are absorbed within the top 100 nm-100 .mu.m of a sample, and
the actual penetration depth depends on the e-beam energy (voltage)
and the material density. Large amounts of energy can be deposited
into a surface coating without a drastic effect on the temperature
of the underlying substrate. Moreover, E-beam sintering is a
cumulative process that occurs gradually with increasing dosage, so
one hour's worth of e-beam irradiation can be delivered
continuously, or in six ten-minute increments, yielding the same
effect. Moreover, there is no heat-up or cool-down time, and with
the use of a water-cooled stage, the sample can be maintained at
room temperature. For example, in some embodiments, no cooling may
be used for the processing metamaterials, and the maximum
temperature of the sample may be maintained at or below 150.degree.
C. Therefore, in the case of MgB.sub.2, the material at atmospheric
pressure may be sintered without the evaporation of magnesium.
[0082] In still other embodiments, the metamaterial may be produced
using a sol-gel technique, and without wishing to be bound by
theory, this technique may be used to produce thin films that are
substantially optically smooth. Recently, MgB.sub.2 nanotubes have
been produced using a sol-gel technique, see Nath and Parkinson,
Adv. Mater., 18:1865 (2006), using following scheme:
[overall]
MgBr.sub.2.6H.sub.2O+2NaBH.sub.4.fwdarw.MgB.sub.2+2NaBr+2H.sub.2O+8H.sub.-
2+2O.sub.2, (5)
in which step 1 is the reaction with borohydride, performed in
solution:
[step 1]
MgBr.sub.2.6H.sub.2O+2NaBH.sub.4MgO.H.sub.2O+(B.sub.2O.sub.3)+2-
NaBr+H.sub.2O+8H.sub.2 (6)
and step 2 is conversion to boride, which occurs in a tube furnace
under diborane gas:
[step 2] MgO+(B.sub.2O.sub.3)MgB.sub.2+2O.sub.2. (7)
[0083] In such embodiments, magnesium bromide or magnesium chloride
may be reacted in ethanol with sodium borohydride to from a
solution in which an oxide precursor is produced, which forms a
gel-like precipitant in the ethanol. Precipitation occurs in the
presence of water creating, a smooth gel-like phase may develop. In
some embodiments, water may be added to the reaction solution to
form a second solution, and in other embodiments, atmospheric water
or water vapor may cause precipitation of magnesium dibromide from
the second solution. In embodiments in which water is added, the
rate of addition may affect the characteristics of the material
produced. For example, if water is added more quickly, the texture
of the precipitate may be grainier having about 0.1 to about 1
.mu.M particles. Additionally, the addition of water at an early
stage may allow for the removal of all or substantially all of the
NaBr from the reaction mixture, although borate may also be removed
by such addition as well. Precursor solutions of suspensions may be
used to make spin cast films with controllable thickness of up to
about 1 .mu.m. In some embodiments, precursors may be evolved from
solution as a white precipitate.
[0084] In some embodiments, the collected precipitate or film may
be reacted under an atmosphere of diborane. For example, in certain
embodiments, the precipitate may be reacted in a tube furnace under
diborane. In such embodiments, diborane, B.sub.2H.sub.6, may be
generated in situ by dripping a diglyme solution of iodine into
NaBH.sub.4 and entraining the gaseous products in an argon
stream.
[0085] Any of the methods described above may further include the
step of milling the starting materials, i.e., host material and the
nanoparticles, either individually or as a mixture to produce
milled powders. In such embodiments, any method for milling may be
used. For example, in some embodiments, SiC particles and MgB.sub.2
powder may be milled in a dry ball mill using beads, which are
harder than MgB.sub.2 but not as hard as SiC such as ziconia, to
break down the MgB.sub.2 particles. In other embodiments, harder
beads which can break down both starting materials may be used to
mill the starting materials.
[0086] In any of the methods described above, embodiments of the
methods of the invention may include the steps of suspending and/or
precipitating the nanoparticles in a solvent and fractionating the
nanoparticles using, for example, gravity or centrifugation.
Without wishing to be bound by theory, the size distribution of the
nanoparticles can be narrowed slightly using such techniques.
However, these steps may be more effective at removing the smallest
particles than it is at separating the large and/or irregular
nanoparticles.
[0087] In some embodiments, commercially available starting
materials may be used, and in other embodiments, one or more of the
starting materials may be produced in situ. For example, the
sol-gel method described above represents an in situ method for
producing MgB.sub.2. Other methods for producing MgB.sub.2 are
available in the art and may be incorporated into various
embodiments of the invention. In certain embodiments, SiC
nanoparticles may be made by carbothermal reduction, that is,
SiO.sub.2 may be reacted with carbon at high temperatures to
produce SiC. Silica microspheres are available down to submicron
sizes, with excellent size and shape distribution, which can, in
some embodiments, be converted to SiC spheres.
[0088] The metamaterials described herein can be used for any
purpose generally applicable to metamaterials. For example, in some
embodiments, the metamaterials may be used as lenses.
[0089] In other embodiments, the metamaterials of embodiments may
be used to prepare a spray coatable optical filter. In such
embodiments, the matrix material of metal nanoparticles alone in
free space or in a polymeric binder that provides the electric
response may be used to form a nanocomposite with a random or
regular assembly of larger polaritonic nanoparticles such as SiC
that supplies a magnetic response. Such materials may be capable of
being deposited rapidly over large areas as thin films without
vacuum processing and can function as a transmission or reflection
filter at visible wavelengths. In other embodiments, these types of
materials can be specifically designed for use at ultraviolet,
visible, or infrared wavelengths.
[0090] In still other embodiments, thin films of the metamaterials
of embodiments may be useful in the preparation of negative index
materials (NIMs) and may be capable of being used to achieve
high-resolution reproductions of features in the near-field, which
may be particularly useful for lithographic applications. In such
embodiments, the super-resolution phenomena of NIMs can be
leveraged, and random structures of particles in a matrix of some
embodiments may lend themselves to solution processes such as, for
example, spin coating, which may be especially compatible with
photolithographic applications.
[0091] In yet other embodiments, the metamaterials of embodiments
described herein may be tailored to provide a refractive index with
positive n values. For example, when a sphere or ball lens has a
refractive index equal to two, it focuses light to its back
surface, and when that surface is reflective, light is
retroreflected, i.e., returned in the same direction from which it
came. Spherical retroreflectors are very advantageous to enhance
visibility of objects to humans. Thus, in some embodiments, the
metamaterials described herein may be used in the preparation of
road signs or other instruments that are observed by humans. There
are currently few infrared transparent materials that can be used
for transmissive optics, and transparent n=2 metamaterials are not
readily available.
[0092] In further embodiments, the metamaterials described herein
may be prepared as infrared metamaterials for emissivity control
and enhancement of thermophotovoltaic devices where the ability to
control the spectral emissivity of a surface can have applications
in thermal signature control. For example, the efficiency of
thermophotovoltaics can be improved by tuning the thermal emission
wavelength to the bandgap of the semiconductor in the photovoltaic
(PV) module. In thermophovoltaics, radiation from a blackbody is
absorbed by the PV module, which does not typically absorb the full
spectrum of radiation. If the emissivity of the radiator is
modified so that the radiation all falls in a narrow band, then it
can be absorbed by a single-junction solar cell far more
efficiently. In such embodiments, a metamaterial coating such as
those described herein can be designed that changes the spectral
emissivity of a thermal radiator so that it no longer emits in a
broad spectrum, like a blackbody, but instead emits preferentially
in the high absorbance bands, such as the extinction bands as shown
in FIG. 24. The emissivity can be tuned to the absorption bands of
known semiconductors active in the visible and infrared spectrum
such as, for example SiC (434 nm), Si (1107 nm), or Ge (1851 nm),
and in such embodiments, absorption losses of the metamaterials are
not a disadvantage, and robust materials such as borides and
carbides may also be used. Theoretical efficiencies of
thermovoltaic structures using single-junction solar cells have
been estimated at 50% to 60% using metamaterials for emissivity
control.
EXAMPLES
[0093] Although the present invention has been described in
considerable detail with reference to certain preferred embodiments
thereof, other versions are possible. Therefore the spirit and
scope of the appended claims should not be limited to the
description and the preferred versions contained within this
specification. Various aspects of the present invention will be
illustrated with reference to the following non-limiting
examples.
Example 1
Hot Isostatic Pressing
Pure MgB.sub.2
[0094] HIP on MgB.sub.2 powders was performed in a custom fabricate
niobium HIP container having green (i.e., before compression)
dimensions of approximately one cubic inch. The `cans` were
fabricated using an Exo TIG inert atmosphere glove box welder
facility to get clean ductile welds that survive the demands of
high temperature HIP. The can was filled with MgB.sub.2 powder
(Alfa Aesar) and fully off-gassed with a vacuum to remove adsorbed
species on the powder surfaces. The integrity of the filled can was
checked with a residual gas analyzer and helium leak detector
connected to the pump-off tube, after which it was sealed. The
sealed can was placed in a HIP unit and treated at 600.degree.
C.
[0095] The completed MgB.sub.2 billet is shown in FIG. 11. The
MgB.sub.2 billet is very hard and robust with a measured density is
2.63 g/cm.sup.3, which is close to the theoretical value. It can be
cut with a low-speed diamond blade, and samples of about 1 mm were
removed for ellipsometric, normal incidence reflection, and surface
plasmon resonance measurements. The surface of MgB.sub.2 is subject
to slow oxidation, which can affect the optical properties over
time. The color of MgB.sub.2 is either golden or black, depending
on the polarization of the incoming light relative to the
orientation of the crystal grains as can be seen in the optical
micrograph in FIG. 11. The surface of MgB.sub.2 can be polished
effectively with diamond grit.
Example 2
Hot Isostatic Pressing
MgB.sub.2/SiC Metamaterials
[0096] MgB.sub.2 (Alfa Aesar) and 30 vol % SiC nominally, 130 nm
powder (Nanostructured and Amorphous Materials) or 0.5 .mu.m BF-17
powder (H. C. Starck) were mixed and milled in a ball mill using
zirconia beads. The BF-17 powder was first suspended in THF, and
the first fraction was removed after 10 minutes for use in the
composite. For milling, zirconia beads were used because they are
harder than MgB.sub.2, but it is not as hard as SiC. Milling for 80
hours produced powders that were no bigger than a half micron in
size, and which were very well distributed.
[0097] These materials were then encapsulated in a metal can and
HIPped at a temperature of 700.degree. C. to ensure that the
MgB.sub.2 consolidated well, but remained well below the sintering
temperature of SiC. A thin slice, about 1 mm, was cut from the
resulting billets with a diamond blade, and polished with diamond
grit as before. SEM images of the polished cross section of the
BF-17 composite are shown in FIG. 12. The large inclusions of
MgB.sub.2 remain in the sample, which probably arise from
insufficiently ground starting material. The composition of the
large inclusions was verified in the SEM by energy dispersive x-ray
(EDX) spectroscopy. However, most of the area is of a composite
nature, and higher magnification reveals that in the majority of
the material is a continuous MgB.sub.2 phase surrounding submicron
inclusions of SiC (also verified by EDX), as per the metamaterial
design.
Example 3
E-beam Sintering
[0098] Electron beam (e-beam) sintering of composites of
MgB.sub.2/SiC was accomplished using a technique that delivers
small (1 cm2 to large 30.times.30 cm) sintering to ultra thin (200
nm) to thicknesses of 6.5 microns in ambient conditions. Samples
for e-beam sintering were made by milling the nominally 130 nm SiC
particles with 325 mesh (about 45 .mu.m) MgB.sub.2 powder for 80 h
in a dry ball mill. The volume fraction (assuming full density) was
30% SiC. Zirconia beads were used for the milling, which are harder
than MgB.sub.2 but not as hard as SiC, which were effective in
breaking down the boride particles.
[0099] To make films, 0.05 g of the powder was mixed with 5 g of
acetone in a test tube, and shaken. The fast-settling particles
were removed after 30 minutes, and the remaining supernatant, in
which the particles were settled out more slowly, was used to cast
the films. Silicon chips were placed in 4 mL (a depth of about
3/8'') of the remaining suspension and the acetone allowed to
slowly evaporate.
[0100] The resulting films were 6.5 .mu.m thick. A series of them
was then subjected to an e-beam sintering, under a nitrogen
atmosphere (<10 ppm oxygen). Samples were removed at dosage
intervals of 25,000 kGy, up to 150,000 kGy for the longest sample.
The results are shown in FIG. 13. During the course of the
experiment, the MgB.sub.2 is clearly consolidating, and the
remaining identifiable particles (with material melted around
them), is likely the MgB.sub.2 surrounding the SiC. After a dose of
150,000 kGy, the MgB.sub.2 seems completely melted, but not yet
completely coalesced.
Example 4
Optical Characterization of MgB.sub.2
Ellipsometry
[0101] Complimentary ellipsometric measurements were made using a
spectroscopic ellipsometer (J. A. Woollam) on the pure MgB.sub.2
slab made by HIP and polished using 0.5 .mu.m diamond powder. The
surface oxidized only slowly, and scans did not produce different
results over the course of at least 30 hours.
[0102] The data is best fit using a 2-term Lorentzian, i.e., one
Drude oscillator and one Lorentzian oscillator. Including
additional oscillators does not improve the fit. The experimental
reflectance curve is shown in FIG. 14, and the complex refractive
index (n+ik) is shown in FIG. 15. The plasma energy, visible on the
graphs either where n and k cross, is about 600 nm, or 2.1 eV.
Example 5
Optical Characterization of MgB.sub.2
Specular Reflection of MgB.sub.2
[0103] To verify the results above, these results were compared to
normal incidence reflection measurements using a UV-Vis
spectrometer fit with a reflection accessory. For comparison, the
ellipsometer data was used in an analytic formulation for the
normal incidence off a slab and this analytical solution was
compared to the experimental data from the spectrometer. As can be
seen below in FIG. 16, the blue curve (experimental data) compares
very well in its functional form to the data obtained from
analytical solutions using the ellipsometer data (yellow line). The
reflectance data was shifted by a constant value of 0.3 to account
for differences associated with the reference mirror of the
spectrometer.
Example 6
Optical Characterization of MgB.sub.2
Surface Plasmon Spectroscopy (SPR) and Negative Index Behavior
[0104] A test bed for the measurement of surface plasmon resonances
in metamaterials by surface plasmon coupling via a measurement of
reflection vs. angle, and as a function of polarization was used.
Surface plasmons, which are oscillations of free conductors
confined to an interface, are excited in a conductor when light
impinges on the surface at the correct angle, frequency and
polarization. Typically, monochromatic light is directed through a
prism, and the intensity of the recovered beam is monitored as a
function of angle. Usually, it will reflect from the conductor
surface, but at the surface plasmon resonance, energy will be
absorbed. In the case of the SPR experiment, this is indicated by a
minimum (a "dip") in the curve above the critical angle of the
prism.
[0105] For a normal conductor, only light polarized in the plane of
the surface (p-polarized) can excite a surface plasmon when the
permittivity is negative. For s-polarized light, only the magnetic
field of the radiation can interact with the light beam, and a
surface plasmon can be excited in this case only when the magnetic
permeability is negative. For a normal conductor, which has
.di-elect cons.<0 but .mu.>0, surface plasmon excitation can
only occur with p-polarized light. In a NIM, however, surface
plasmons can be excited for both s- and p-polarized light, and dips
for both polarizations should be observed. The reflection geometry
allows measurement of opaque samples, and validates .di-elect cons.
and .mu. independently.
[0106] FIG. 17 shows the experimental configuration of the test
bed. Experiments were performed in the Otto configuration, where a
small air gap exists between the prism and the material under test.
This introduces another variable into the analysis, as the shape of
the curves will depend on the width of the gap as well as on the
material properties. FIG. 18 shows exemplary data from a typical
conductor.
Example 7
Optical Characterization of MgB.sub.2
SPR
[0107] FIG. 19 and FIG. 20 show the results for MgB.sub.2 for
varying air gap in both p- and s-polarization using an HeNe laser
light source at 632 nm. In both cases, the data match the predicted
curves well, and as expected, a dip occurs only in p-polarization.
The MgB.sub.2 behaves like a negative permittivity material, but
still has a positive permeability. For both results, the angle at
which the surface plasmon coupling occurs shifts to smaller angles
with larger air gaps, which is also predicted in simulations.
Example 8
Optical Characterization of MgB.sub.2
SPR Measurements of Negative Refractive Index Behavior
[0108] For MgB.sub.2/SiC samples prepared by e-beam sintering and
HIP, we expect to see surface plasmon coupling for both p- and
s-polarization when the SiC is of the proper size and fill
fraction. According to modeling results, the expected size range
that will produce NIM behavior will be for particles that are about
500 nm in diameter. Particles with a median diameter of 500 nm were
used in composite metamaterials made by HIP.
[0109] FIG. 21 shows typical curves taken for these MgB.sub.2/SiC
samples. In these cases, there is a clear dip visible for both s-
and p-polarizations, indicative of negative values for both
.di-elect cons. and .mu. and, by inference, a negative index of
refraction. Therefore, SEM analysis shows that we have obtained a
microstructure close to that which was desired to test the theory,
and materials based on random arrangements of spheres can be made
for negative index materials in the visible spectrum.
Example 9
MgB.sub.2/SiC
[0110] Polycrystalline magnesium diboride (MgB.sub.2 in a normal
state, at room temperature) as the host, providing negative
permittivity, and silicon carbide (SiC) nanoparticles embedded
randomly within the host, to provide negative permeability was
fabricated using hot isostatic pressing to produce a fully dense
solid with a well-dispersed SiC nanoparticle phase. The properties
of the resulting bulk metamaterial were evaluated using surface
plasmon coupling, which showed coupling of both magnetic and
electric plasmons, signifying both negative permeability and
permittivity at 632 nm. The volume fraction, f, and the radius of
the SiC spheres, r.sub.SiC, were adjusted to make the regions of
.di-elect cons..sub.eff<0 and .mu..sub.eff<0 overlap to
obtain negative refraction index within the visible region. The
main advantages of this design are the intrinsically low electron
scattering losses of MgB.sub.2 and optical isotropy. Moreover, the
random (as opposed to regular) arrangement of SiC enables simpler
fabrication approaches.
[0111] The effective permeability appears to be negative at some
frequency range due to a Mie resonance associated with the SiC
inclusions, and the effective permittivity appears to be negative
below the plasma frequency of the MgB.sub.2 host material. The SPR
results obtained from the MgB.sub.2/SiC sample are shown in FIG. 22
for varying values of the air gap. The experimental and theoretical
reflectivity plots show good correlation for both p- and
s-polarizations. As expected, for a large air gap, the reflectivity
reaches nearly unity above the critical angle. For smaller air
gaps, a reflectivity dip occurs above the critical angle for both
polarization states at angles of incidence within the
45.degree.-60.degree. degree window, as predicted by the dispersion
curves. As this occurs for both polarizations, it indicates both
.di-elect cons.<0 and .mu.<0 at this wavelength.
Example 10
Preparation of Au/SiC Material
[0112] Gold spheres having an average particle size of 13 nm (close
to the 10 nm required in the simulation) were prepared using known
techniques. These gold particles were functionalized with
dodecanethiol in the course of the synthesis, and suspend in
nonpolar organic solvents. The volume fraction taken up by
particles in the theoretical experiments is 76%, which is very
close to the maximum fill factor that can be achieved with randomly
packed spheres of this size ratio. In order for these spheres to
have a modest chance of remaining separated in a condensed film, a
surfactant layer between the spheres is likely to take up most of
the remaining volume. This means that the composite won't be
Au/SiC/Air, but will contain some organic material between the gold
and silicon carbide spheres, as suggested in FIG. 23. Effective
medium calculations suggest that this is acceptable, and that
negative index will still be observed when the binder has a
refractive index greater than 1. (1.2 was the value in the
simulation.) The losses increase only modestly.
[0113] The dodecanethiol layer on the gold, as well as any
surfactant on the SiC and any added binder material take up the 24%
of "free space" in the condensed phase. To make films, both
materials were suspended in toluene. The SiC was functionalized
with Triton X-100 or polycarbonate to make up a volume fraction of
24% relative to all the solids. In some cases it was suspended with
no stabilizer, using the volume fraction of solids for Au and SiC
for the condensed phase. All suspensions were then sonicated and
spin cast onto glass slides to form thin layers or slowly
evaporated to form thicker layers. The resulting films, even the
one with no stabilizer, were extremely soft, probably resulting
from a significant volume fraction of the dodecanethiol compared to
the Au or SiC solids. Profilometry measurements were not possible
on these soft films.
Example 11
Au/SiC Metamaterial Spray Coatable Optical Filter
[0114] An Au and SiC nanoparticles metamaterial can function as a
transmission or reflection filter at visible wavelengths, and these
types of materials can be specifically designed for ultraviolet,
visible, or infrared wavelengths. For modeling, a sample of a
mixture of two isotropic dielectric-magnetic media was
prepared.
[0115] The first host medium included a free space (or dielectric
material with known index) doped with small metallic gold spherical
inclusions with a radius, r.sub.Au, and fill factor, f.sub.Au. The
gold particles were 12 nm in diameter, and the volume fractions for
gold particles was varied from 34 to 46%. The permittivity of gold
particles (with losses) can be described by the extended Drude
model. For the small Au particles, the scattering of conduction
electrons from the particle surface is not negligible, and the
plasmon losses include an experimentally measured mean free path of
.LAMBDA..about.20-30 nm for free electrons in gold due to
scattering with photons, and intraband transitions between initial
and final states. This is of the same order of magnitude as the
radius r of a sphere. Consequently, the standard approach for
describing the size dependence of the dielectric function which
assumes that the total rate of scattering of conduction electrons
is the sum of two rates, i.e. the rate of scattering due to bulk
and the rate of scattering due to the surface, was employed.
[0116] The guest material is a polaritonic material, spherical
particles with radius R>r.sub.Au but less than the wavelength of
light in the host medium SiC with a permittivity for the SiC
material, at optical frequencies, of .di-elect cons.=6.7+0.01i. The
spherical inclusions were embedded into the host with the fill
factor f.sub.SiC in two designs either randomly (Maxwell-Garnett
model), or as a regular simple-cubic lattice (Lewin's model), and
the fraction of 120 nm in diameter SiC spheres in the metamaterial
was 30%. Scattering of high permittivity SiC inclusions embedded in
the host provides negative effective permeability in a frequency
bands that depends on the size and volume fraction of the
inclusions.
[0117] FIG. 24 shows the effective refractive index dispersion
calculated for these materials, and the corresponding transmission
and reflection spectra.
Example 12
Tailored-Index (n=2) Metamaterial for MWIR Tagging, Tracking and
Locating
[0118] The composite metamaterials can be designed for MWIR
wavelengths, and as demonstrated in Example 22, is capable of
producing bulk structures. FIG. 25 shows the calculated refractive
index of a gold/SiC metamaterial at the MWIR wavelength of 5950 nm
(5.95 .mu.m) which is close to two, and the losses are very
low.
Example 13
Ag/SiC Metamaterial for High-Resolution Lithography
[0119] For negative index materials (NIMs), thin films have special
uses such as being used to achieve high-resolution reproductions of
features in the near-field, which may be particularly useful for
lithographic applications where the super-resolution phenomena of
NIMs can be leveraged. Since these are random structures of
particles in a matrix, metal/SiC metamaterials lend themselves to
solution processes such as, for example, spin coating, which may be
compatible with photolithographic applications.
[0120] An isotropic low-loss metamaterial NIM was prepared that can
act as a lens at UV wavelengths (193 nm) for use in
sub-diffraction-limited high-resolution photolithography. A
refractive index of -1 and a resolution of .lamda./20 may be
possible at 193 nm using silver/SiC metamaterial.
[0121] FIG. 26 shows the first part of this calculation. For a
silver and SiC particles metamaterial, the refractive index can be
very close to -1 at 193 nm (n.sub.eff=-1 is index-matched to free
space and is an ideal value). In this same region, the imaginary
part of the index is close to zero, which implies that the material
may be transmissive at least for thin samples. The figure of merit
(the magnitude of the real part of the index divided by the
imaginary part) is greater than one, which indicates that light
propagation through the sample is allowed.
[0122] The second part of the calculation is an analysis of the
resolution. Super-resolution can be observed in the near field,
which for lithography applications may be feasible, and a
photoresist has been used as a medium to measure super-resolution
in some laboratories. Published results have documented the
resolution enhancement that a n.sub.eff=-1 metamaterial could
achieve in an application like this, based on distance, which in
these experiments would be controlled by a thin spacer layer of
transparent polymer, as well as losses in the metamaterial slab.
FIG. 27 shows the resolution that is attainable in these
configurations, in terms of the resolution enhancement over a
normal diffraction limited (.lamda./2) optic. For a relatively
low-loss material like the one described in FIG. 26
(Im(n.sub.eff).about.0.2), .lamda./20 resolution can be achieved at
experimentally feasible spacer thicknesses (>10 nm). Any
improvements in the FOM, which will be pursued mathematically and
experimentally in this program, will further ease the spacer
thickness requirement.
* * * * *