U.S. patent application number 16/866391 was filed with the patent office on 2020-11-05 for engineered optical fibers and uses thereof.
The applicant listed for this patent is TRUSTEES OF BOSTON UNIVERSITY. Invention is credited to Aaron G. Peterson-Greenberg, Gautam Prabhakar, Siddharth Ramachandran.
Application Number | 20200348226 16/866391 |
Document ID | / |
Family ID | 1000005162522 |
Filed Date | 2020-11-05 |
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United States Patent
Application |
20200348226 |
Kind Code |
A1 |
Ramachandran; Siddharth ; et
al. |
November 5, 2020 |
ENGINEERED OPTICAL FIBERS AND USES THEREOF
Abstract
A system comprises an electromagnetic radiation source, a
polarizing element, a mode converter, an optical fiber, and a
measurement device. The polarizing element receives electromagnetic
radiation produced by the electromagnetic radiation source and
outputs linearly-polarized electromagnetic radiation having a
linear polarization angle .theta..sub.1. The mode converter
converts the linearly-polarized electromagnetic radiation to an
orbital angular momentum (OAM) mode of linearly-polarized
electromagnetic radiation with topological charge L.sub.i. The OAM
mode of linearly-polarized electromagnetic radiation is a
superposition of first and second OAM modes with topological
charges L.sub.i and opposite circular polarizations. The optical
fiber supports propagation of the first and second OAM modes with
an absolute effective index difference .DELTA.n.sub.eff greater
than or equal to 5.times.10.sup.-3, such that linearly-polarized
electromagnetic radiation with linear polarization angle
.theta..sub.2 is emitted by the optical fiber. The measurement
device is configured to determine a property of the electromagnetic
radiation based on the polarization angle .theta..sub.2.
Inventors: |
Ramachandran; Siddharth;
(Boston, MA) ; Prabhakar; Gautam; (Boston, MA)
; Peterson-Greenberg; Aaron G.; (Cambridge, MA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
TRUSTEES OF BOSTON UNIVERSITY |
Boston |
MA |
US |
|
|
Family ID: |
1000005162522 |
Appl. No.: |
16/866391 |
Filed: |
May 4, 2020 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
62842895 |
May 3, 2019 |
|
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G01N 21/01 20130101;
G01N 21/31 20130101; G01N 21/21 20130101 |
International
Class: |
G01N 21/31 20060101
G01N021/31; G01N 21/01 20060101 G01N021/01; G01N 21/21 20060101
G01N021/21 |
Goverment Interests
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
[0002] This invention was made with government support under the
following grants: Grant No. 354281 awarded by the Department of
Energy; Grant Nos. FA9550-14-1-0165 N00014-13-1-0627 awarded by the
Department of Defense; and Grant No. ECCS-1610190 awarded by the
National Science Foundation. The government has certain rights in
the invention.
Claims
1. A system for measuring a property of electromagnetic radiation,
the system comprising: an electromagnetic radiation source
configured to produce electromagnetic radiation; a polarizing
element configured to receive the electromagnetic radiation
produced by the electromagnetic radiation source and output
linearly-polarized electromagnetic radiation having a linear
polarization angle .theta..sub.1; a mode converter configured to
receive the linearly-polarized electromagnetic radiation and output
an orbital angular momentum (OAM) mode of linearly-polarized
electromagnetic radiation with a topological charge L.sub.i, the
OAM mode of linearly-polarized electromagnetic radiation being a
superposition of (i) a first OAM mode with topological charge
L.sub.i and a first circular polarization, and (ii) a second OAM
mode with topological charge L.sub.i and a second circular
polarization, the first circular polarization being opposite from
the second circular polarization; an optical fiber configured to
receive the first OAM mode and the second OAM mode, and support
propagation to an output of the optical fiber of the first OAM mode
with an effective index n.sub.eff1 and the second OAM mode with an
effective index n.sub.eff2, an absolute difference .DELTA.n.sub.eff
between n.sub.eff1 and n.sub.eff2 being greater than or equal to
5.times.10.sup.-5, such that linearly-polarized electromagnetic
radiation having a topological charge L.sub.i and a linear
polarization angle .theta..sub.2 is emitted at the output of the
optical fiber; and one or more measurement devices configured to
determine the property of the electromagnetic radiation based at
least on the polarization angle .theta..sub.2 of the
electromagnetic radiation emitted at the output of the optical
fiber.
2. The system of claim 1, further comprising: an additional
polarizing element configured to receive the linearly-polarized
electromagnetic radiation from the output of the optical fiber and
convert the linearly-polarized electromagnetic radiation having the
linear polarization angle .theta..sub.2 into a first component have
a linear polarization angle .theta..sub.n and a second component
having a linear polarization angle .theta..sub.n+90.degree.; a
first power meter configured to measure a power of the first
component having the linear polarization angle .theta..sub.n; and a
second power meter configured to measure a power of the second
component having the linear polarization angle
.theta..sub.n+90.degree., wherein the determined property of the
produced electromagnetic radiation is based at least on the
measured power of the first component and the measured power of the
second component.
3. The system of claim 2, wherein the determined property is an
optical activity angle .gamma. determined according to
.gamma.=.theta..sub.2-.theta..sub.1 and .theta. 2 = tan - 1 ( P
.theta. n + 9 0 .smallcircle. P .theta. n ) , ##EQU00012## where
P.sub..theta..sub.1 is the measured power of the first component
having the linear polarization angle .theta..sub.1, and where
P.sub..theta..sub.n+90.degree. is the measured power of the second
component having the linear polarization angle
.theta..sub.n+90.degree..
4. The system of claim 2, wherein the system is configured to
determine an optical activity angle difference .DELTA..gamma.
between (i) a first optical activity angle .gamma..sub.1 of a first
beam of electromagnetic radiation having a first center wavelength
.lamda..sub.1, and (ii) a second optical activity angle
.gamma..sub.2 of a second beam of electromagnetic radiation having
a second center wavelength .lamda..sub.2.
5. The system of claim 4, wherein the system is configured to
determine a wavelength difference .DELTA..lamda. between the first
beam of electromagnetic radiation and the second beam of
electromagnetic radiation, based on the optical activity angle
difference .DELTA..gamma..
6. The system of claim 5, wherein the wavelength .lamda. of the
produced electromagnetic radiation is determined according to
.DELTA. .lamda. = - .pi. z .DELTA. n g .lamda. 2 , ##EQU00013##
where z is a length of the optical fiber, and .DELTA.n.sub.g is a
group index difference between the first OAM mode and the second
OAM mode.
7. The system of claim 1, wherein the optical fiber has a length of
between about 1 centimeter and about 1 kilometer.
8. The system of claim 1, wherein the first OAM mode propagates
with a group index n.sub.g1 and the second OAM mode propagates with
a group index n.sub.g2, and wherein an absolute difference
.DELTA.n.sub.g between a group index n.sub.g1 of the first OAM mode
and the group index n.sub.g2 of the second OAM mode increases with
the topological charge L.sub.i.
9. The system of claim 1, wherein the topological charge L.sub.i is
greater than or equal to 1.
10. The system of claim 9, wherein the topological charge L.sub.i
is between about 1 and about 200.
11. The system of claim 1, wherein the mode converter is further
configured to output additional OAM modes of the linearly-polarized
electromagnetic radiation, the additional OAM modes including a
third OAM mode and a fourth OAM mode, the third OAM mode and the
fourth OAM mode having an identical topological charge that is
different than the topological charge of the first OAM mode and the
second OAM mode, the third OAM mode and the fourth OAM mode having
opposing circular polarizations.
12. The system of claim 11, further comprising a mode sorter
configured to direct (i) the first OAM mode and a second OAM mode
to a first set of the one or more measurement devices, and (ii) the
third OAM mode and a fourth OAM mode to a second set of the one or
more measurement devices.
13. The system of claim 12, wherein the determination of the
property of the produced electromagnetic radiation is determined
based on measurements of the first set of the one or more
measurement devices and the second set of the one or more
measurement devices.
14. The system of claim 13, wherein the determination of the
property of the produced electromagnetic radiation based on the
first OAM mode and the second OAM mode has a first free spectral
range, and wherein a determination of the property of the produced
electromagnetic radiation based on the first OAM mode, the second
OAM mode, the third OAM mode, and the fourth OAM mode has a second
free spectral range greater than the first free spectral range.
15. The system of claim 1, wherein the determined property of the
electromagnetic radiation includes a change in optical activity
angle, a change in wavelength, a visibility, a spectral bandwidth,
a spectral amplitude, a spectral amplitude ratio, a spectral
separation, or any combination thereof, a center wavelength in a
range of wavelengths, a spread of wavelengths in the range of
wavelengths, or any combination thereof.
16. A method for measuring a property of electromagnetic radiation,
the method comprising: emitting electromagnetic radiation from an
electromagnetic radiation source; converting the electromagnetic
radiation to linearly-polarized electromagnetic radiation having a
polarization angle .theta..sub.1; converting the linearly-polarized
electromagnetic radiation into a first orbital angular momentum
(OAM) mode of linearly-polarized electromagnetic radiation with a
topological charge L.sub.1, the OAM mode of linearly-polarized
electromagnetic radiation being a superposition of (i) a first OAM
mode with topological charge L.sub.1 and a first circular
polarization, and (ii) a second OAM mode with topological charge
L.sub.1 and a second circular polarization, the first circular
polarization being opposite from the second circular polarization;
causing (i) the first OAM mode of linearly-polarized
electromagnetic radiation to propagate through an optical fiber
with an effective index n.sub.eff1 and (ii) the second OAM mode of
linearly-polarized electromagnetic radiation to propagate through
the optical fiber with an effective index n.sub.eff2, an absolute
difference .DELTA.n.sub.eff between n.sub.eff1 and n.sub.eff2 being
greater than or equal to 5.times.10.sup.-5, such that
linearly-polarized electromagnetic radiation having a topological
charge L.sub.1 and a linear polarization angle .theta..sub.2 is
emitted at the output of the optical fiber; and determining the
property of the produced electromagnetic radiation based at least
on the linear polarization angle .theta..sub.2.
17. The method of claim 16, further comprising: converting the
linearly-polarized electromagnetic radiation into a second OAM mode
of linearly-polarized electromagnetic radiation with a topological
charge L.sub.2, the additional OAM mode of linearly-polarized
electromagnetic radiation being a superposition of (i) a third OAM
mode with topological charge L.sub.2 and the first circular
polarization, and (ii) a fourth OAM mode with topological charge
L.sub.2 and the second circular polarization; causing the third OAM
mode and the fourth OAM mode to propagate through the optical fiber
with the first OAM mode and the second OAM mode such that the
linearly-polarized electromagnetic radiation emitted at the output
of the optical fiber includes (i) linearly-polarized
electromagnetic radiation having the topological charge L.sub.1 and
the linear polarization angle .theta..sub.2 and (ii)
linearly-polarized electromagnetic radiation having the topological
charge L.sub.2 and the linear polarization angle .theta..sub.3; and
determining the property of the produced electromagnetic radiation
based at least on the linear polarization angle .theta..sub.2 and
the linear polarization angle .theta..sub.3.
18. The method of claim 17, further comprising: converting the
linearly-polarized electromagnetic radiation into a third OAM mode
of linearly-polarized electromagnetic radiation with a topological
charge L.sub.2, the additional OAM mode of linearly-polarized
electromagnetic radiation being a superposition of (i) a fifth OAM
mode with topological charge L.sub.3 and the first circular
polarization, and (ii) a sixth OAM mode with topological charge
L.sub.3 and the second circular polarization; causing the fifth OAM
mode and the sixth OAM mode to propagate through the optical fiber
with the first OAM mode, the second OAM mode, the third OAM mode,
and the fourth OAM mode such that the linearly-polarized
electromagnetic radiation emitted at the output of the optical
fiber includes (i) linearly-polarized electromagnetic radiation
having the topological charge L.sub.1 and the linear polarization
angle .theta..sub.2, (ii) linearly-polarized electromagnetic
radiation having the topological charge L.sub.2 and the linear
polarization angle .theta..sub.3, and (iii) linearly-polarized
electromagnetic radiation having the topological charge L.sub.3 and
the linear polarization angle .theta..sub.4; and determining the
property of the produced electromagnetic radiation based at least
on the linear polarization angle .theta..sub.2, the linear
polarization angle .theta..sub.3, and the linear polarization angle
.theta..sub.4.
19. The method of claim 18, wherein the determination of the
property of the produced electromagnetic radiation based on the
linear polarization angle .theta..sub.2, the linear polarization
angle .theta..sub.3, and the linear polarization angle
.theta..sub.4 has a third free spectral range greater than the
first free spectral range and the second free spectral range.
20. The method of claim 18, further comprising: causing, after
being emitted at the output of the optical fiber, the first OAM
mode of linearly-polarized electromagnetic radiation, the second
OAM mode of linearly-polarized electromagnetic radiation, and the
third OAM mode of linearly-polarized electromagnetic radiation pass
through a rotatable polarizing element as the rotatable polarizing
element rotates; measuring a maximum power and a minimum power of
the first OAM mode of linearly-polarized electromagnetic radiation
passing through the rotatable polarizing element; measuring a
maximum power and a minimum power of the second OAM mode of
linearly-polarized electromagnetic radiation passing through the
rotatable polarizing element; measuring a maximum power and a
minimum power of the third OAM mode of linearly-polarized
electromagnetic radiation passing through the rotatable polarizing
element; determining a visibility for each of the first OAM mode,
the second OAM mode, and the third OAM mode, based at least on the
maximum and minimum power of each of the first OAM mode, the second
OAM mode, and the third OAM mode passing through the rotatable
polarizing element; and determining a spectral bandwidth of the
emitted electromagnetic radiation based at least on the determined
visibility for each of the first OAM mode, the second OAM mode, and
the third OAM mode.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application claims the benefit of and priority to U.S.
Provisional Patent Application Ser. No. 62/842,895, filed on May 3,
2019, entitled "ENGINEERED OPTICAL FIBERS AND USES THEREOF," which
is hereby incorporated by reference herein in its entirety.
TECHNICAL FIELD
[0003] The present disclosure relates to optical fibers used for
measuring the wavelength of an optical signal. Specifically, the
present disclosure relates to optical fibers configured to support
stable propagation of orbital angular momentum modes of an optical
signal over long distances to measure optical activity in the
optical signal.
BACKGROUND
[0004] Wavelength measurement devices, such as wavemeters or
spectrometers with high resolving power R=.lamda./.DELTA..lamda.
(where .lamda. is the general wavelength around which the device is
operating, and .DELTA..lamda. is the resolution of the device), are
of great utility to a variety of fields such as high-precision
spectroscopy, atomic-line measurements etc. Such devices can be
broadly divided into two categories: scanning devices where
different wavelengths are sequentially mapped to a detector (e.g.
grating based spectrometers, Fabry-Perot interferometers), and
"single-shot" devices which project different wavelengths to
different pixels of a sensor array. While scanning devices are
inherently slow and mechanical, they can yield very high resolving
powers R>10.sup.6, whereas single-shot measurements are fast but
are limited in resolving powers to about R>10.sup.4, and don't
operate well at low light levels. Thus, new devices are needed that
are fast, but have high resolutions and operate well at low light
levels.
SUMMARY
[0005] According to some aspects of the present disclosure, a
system for measuring a property of electromagnetic radiation
comprises an electromagnetic radiation source, a polarizing
element, a mode converter, an optical fiber, and one or more
measurement devices. The electromagnetic radiation source is
configured to produce electromagnetic radiation. The polarizing
element is configured to receive the electromagnetic radiation
produced by the electromagnetic radiation source and output
linearly-polarized electromagnetic radiation having a linear
polarization angle .theta..sub.1. The mode converter is configured
to receive the linearly-polarized electromagnetic radiation and
output an orbital angular momentum (OAM) mode of linearly-polarized
electromagnetic radiation with a topological charge L.sub.i. The
OAM mode of linearly-polarized electromagnetic radiation is a
superposition of (i) a first OAM mode with topological charge
L.sub.i and a first circular polarization, and (ii) a second OAM
mode with topological charge L.sub.i and a second circular
polarization. The first circular polarization is opposite from the
second circular polarization. The optical fiber is configured to
receive the first OAM mode and the second OAM mode, and support
propagation to an output of the optical fiber of the first OAM mode
with an effective index n.sub.eff1 and the second OAM mode with an
effective index n.sub.eff2. An absolute difference .DELTA.n.sub.eff
between n.sub.eff1 and n.sub.eff2 is greater than or equal to
5.times.10.sup.-5, such that linearly-polarized electromagnetic
radiation having a topological charge L.sub.i and a linear
polarization angle .theta..sub.2 is emitted at the output of the
optical fiber. The one or more measurement devices are configured
to determine the property of the electromagnetic radiation based at
least on the polarization angle .theta..sub.2 of the
electromagnetic radiation emitted at the output of the optical
fiber.
[0006] According to some aspects of the present disclosure, a
method for measuring a property of electromagnetic radiation
comprises: emitting electromagnetic radiation from an
electromagnetic radiation source; converting the electromagnetic
radiation to linearly-polarized electromagnetic radiation having a
polarization angle .theta..sub.1; converting the linearly-polarized
electromagnetic radiation into a first orbital angular momentum
(OAM) mode of linearly-polarized electromagnetic radiation with a
topological charge L.sub.1, the OAM mode of linearly-polarized
electromagnetic radiation being a superposition of (i) a first OAM
mode with topological charge L.sub.1 and a first circular
polarization, and (ii) a second OAM mode with topological charge
L.sub.1 and a second circular polarization, the first circular
polarization being opposite from the second circular polarization;
causing (i) the first OAM mode of linearly-polarized
electromagnetic radiation to propagate through an optical fiber
with an effective index n.sub.eff1 and (ii) the second OAM mode of
linearly-polarized electromagnetic radiation to propagate through
the optical fiber with an effective index n.sub.eff2, an absolute
difference .DELTA.n.sub.eff between n.sub.eff1 and n.sub.eff2 being
greater than or equal to 5.times.10.sup.-5, such that
linearly-polarized electromagnetic radiation having a topological
charge L.sub.1 and a linear polarization angle .theta..sub.2 is
emitted at the output of the optical fiber; and determining the
property of the produced electromagnetic radiation based at least
on the linear polarization angle .theta..sub.2.
[0007] According to some aspects of the present disclosure, the
method further comprises: converting the linearly-polarized
electromagnetic radiation into a second OAM mode of
linearly-polarized electromagnetic radiation with a topological
charge L.sub.2, the additional OAM mode of linearly-polarized
electromagnetic radiation being a superposition of (i) a third OAM
mode with topological charge L.sub.2 and the first circular
polarization, and (ii) a fourth OAM mode with topological charge
L.sub.2 and the second circular polarization; causing the third OAM
mode and the fourth OAM mode to propagate through the optical fiber
with the first OAM mode and the second OAM mode such that the
linearly-polarized electromagnetic radiation emitted at the output
of the optical fiber includes (i) linearly-polarized
electromagnetic radiation having the topological charge L.sub.1 and
the linear polarization angle .theta..sub.2 and (ii)
linearly-polarized electromagnetic radiation having the topological
charge L.sub.2 and the linear polarization angle .theta..sub.3; and
determining the property of the produced electromagnetic radiation
based at least on the linear polarization angle .theta..sub.2 and
the linear polarization angle .theta..sub.3.
[0008] In some aspects of the present disclosure, the method
further comprises: converting the linearly-polarized
electromagnetic radiation into a third OAM mode of
linearly-polarized electromagnetic radiation with a topological
charge L.sub.2, the additional OAM mode of linearly-polarized
electromagnetic radiation being a superposition of (i) a fifth OAM
mode with topological charge L.sub.3 and the first circular
polarization, and (ii) a sixth OAM mode with topological charge
L.sub.3 and the second circular polarization; causing the fifth OAM
mode and the sixth OAM mode to propagate through the optical fiber
with the first OAM mode, the second OAM mode, the third OAM mode,
and the fourth OAM mode such that the linearly-polarized
electromagnetic radiation emitted at the output of the optical
fiber includes (i) linearly-polarized electromagnetic radiation
having the topological charge L.sub.1 and the linear polarization
angle .theta..sub.2, (ii) linearly-polarized electromagnetic
radiation having the topological charge L.sub.2 and the linear
polarization angle .theta..sub.3, and (iii) linearly-polarized
electromagnetic radiation having the topological charge L.sub.3 and
the linear polarization angle .theta..sub.4; and determining the
property of the produced electromagnetic radiation based at least
on the linear polarization angle .theta..sub.2, the linear
polarization angle .theta..sub.3, and the linear polarization angle
.theta..sub.4.
[0009] According to some aspects of the present disclosure, the
method further comprises: causing, after being emitted at the
output of the optical fiber, the first OAM mode of
linearly-polarized electromagnetic radiation, the second OAM mode
of linearly-polarized electromagnetic radiation, and the third OAM
mode of linearly-polarized electromagnetic radiation pass through a
rotatable polarizing element as the rotatable polarizing element
rotates; measuring a maximum power and a minimum power of the first
OAM mode of linearly-polarized electromagnetic radiation passing
through the rotatable polarizing element; measuring a maximum power
and a minimum power of the second OAM mode of linearly-polarized
electromagnetic radiation passing through the rotatable polarizing
element; measuring a maximum power and a minimum power of the third
OAM mode of linearly-polarized electromagnetic radiation passing
through the rotatable polarizing element; determining a visibility
for each of the first OAM mode, the second OAM mode, and the third
OAM mode, based at least on the maximum and minimum power of each
of the first OAM mode, the second OAM mode, and the third OAM mode
passing through the rotatable polarizing element; and determining a
spectral bandwidth of the emitted electromagnetic radiation based
at least on the determined visibility for each of the first OAM
mode, the second OAM mode, and the third OAM mode.
[0010] According to some aspects of the present disclosure, a
system for measuring a linear polarization angle of electromagnetic
radiation comprises an electromagnetic radiation source, a
polarizing element, a mode converter, an optical fiber, and a
rotatable polarizing element. The electromagnetic radiation source
is configured to produce electromagnetic radiation. The polarizing
element is configured to receive the electromagnetic radiation
produced by the electromagnetic radiation source and output
linearly-polarized electromagnetic radiation having a linear
polarization angle .theta..sub.1. The mode converter is configured
to receive the linearly-polarized electromagnetic radiation and
output an orbital angular momentum (OAM) mode of linearly-polarized
electromagnetic radiation with a topological charge L.sub.i. The
OAM mode of linearly-polarized electromagnetic radiation is a
superposition of (i) a first OAM mode with topological charge
L.sub.i and a first circular polarization, and (ii) a second OAM
mode with topological charge L.sub.i and a second circular
polarization. The first circular polarization is opposite from the
second circular polarization. The optical fiber is configured to
receive the first OAM mode and the second OAM mode, and support
propagation to an output of the optical fiber of the first OAM mode
with an effective index n.sub.eff1 and the second OAM mode with an
effective index n.sub.eff2. An absolute difference .DELTA.n.sub.eff
between n.sub.eff1 and n.sub.eff2 is greater than or equal to
5.times.10.sup.-5, such that linearly-polarized electromagnetic
radiation having a topological charge L.sub.i and a linear
polarization angle .theta..sub.2 is emitted at the output of the
optical fiber. The rotatable polarizing element is configured to
allow a maximum amount of the linearly-polarized electromagnetic
radiation emitted at the output of the optical fiber to pass when a
rotation angle of the rotatable polarizing element matches the
linear polarization angle .theta..sub.2.
[0011] According to some aspects of the present disclosure, a
system for measuring a linear polarization angle of electromagnetic
radiation comprises an electromagnetic radiation source, a
polarizing element, a mode converter, an optical fiber, and a
polarimeter. The electromagnetic radiation source is configured to
produce electromagnetic radiation. The polarizing element is
configured to receive the electromagnetic radiation produced by the
electromagnetic radiation source and output linearly-polarized
electromagnetic radiation having a linear polarization angle
.theta..sub.1. The mode converter is configured to receive the
linearly-polarized electromagnetic radiation and output an orbital
angular momentum (OAM) mode of linearly-polarized electromagnetic
radiation with a topological charge L.sub.i. The OAM mode of
linearly-polarized electromagnetic radiation is a superposition of
(i) a first OAM mode with topological charge L.sub.i and a first
circular polarization, and (ii) a second OAM mode with topological
charge L.sub.i and a second circular polarization. The first
circular polarization is opposite from the second circular
polarization. The optical fiber is configured to receive the first
OAM mode and the second OAM mode, and support propagation to an
output of the optical fiber of the first OAM mode with an effective
index n.sub.eff1 and the second OAM mode with an effective index
n.sub.eff2. An absolute difference .DELTA.n.sub.eff between
n.sub.eff1 and n.sub.eff2 is greater than or equal to 5.times.10-,
such that linearly-polarized electromagnetic radiation having a
topological charge L.sub.i and a linear polarization angle
.theta..sub.2 is emitted at the output of the optical fiber. The
polarimeter is configured to receive the linearly-polarized
electromagnetic radiation emitted at the output of the optical
fiber and measure the linear polarization angle .theta..sub.2.
[0012] The above summary is not intended to represent each
implementation or every aspect of the present disclosure.
Additional features and benefits of the present disclosure are
apparent from the detailed description and figures set forth
below.
BRIEF DESCRIPTION OF THE DRAWINGS
[0013] The disclosure will be better understood from the following
description of example implementations together with reference to
the accompanying drawings.
[0014] FIG. 1 is a first system for measuring a property of
electromagnetic radiation, according to aspects of the present
disclosure;
[0015] FIG. 2A is a cross-section of an optical fiber for use with
the system of FIG. 1, according to aspects of the present
disclosure;
[0016] FIG. 2B is a refractive index profile of the optical fiber
of FIG. 2A, according to aspects of the present disclosure;
[0017] FIG. 3A is a plot of the effective index of spin-orbit
aligned modes and spin-orbit anti-aligned modes, according to
aspects of the present disclosure;
[0018] FIG. 3B is a plot of the effective index difference between
a spin-orbit aligned mode and a spin-orbit anti aligned mode,
according to aspects of the present disclosure;
[0019] FIG. 3C is a plot of the group index difference between a
spin-orbit aligned mode and a spin-orbit anti-aligned mode and the
square of the topological charge of the modes, according to aspects
of the present disclosure;
[0020] FIG. 4 is an image of the rotation of the polarization angle
of a beam of electromagnetic radiation as the beam of
electromagnetic radiation propagates through an optical fiber,
according to aspects of the present disclosure;
[0021] FIG. 5 is a plot of the relationship between a change in
optical activity angle and a change in wavelength, according to
aspects of the present disclosure;
[0022] FIG. 6A is an image of a wavelength difference, according to
aspects of the present disclosure;
[0023] FIG. 6B is an image of an optical activity angle difference
corresponding to the wavelength difference of FIG. 6A, according to
aspects of the present disclosure;
[0024] FIG. 7 is an image of an iris removing one or more
degenerate modes from a beam of electromagnetic radiation,
according to aspects of the present disclosure;
[0025] FIG. 8 is a plot of optical activity angle versus
wavelength, according to aspects of the present disclosure;
[0026] FIG. 9A is a first plot comparing measurements of the
wavelength of electromagnetic radiation using the system of FIG. 1
and using a reference measurement device, according to aspects of
the present disclosure;
[0027] FIG. 9B is a second plot comparing measurements of the
wavelength of electromagnetic radiation using the system of FIG. 1
and using a reference measurement device, according to aspects of
the present disclosure;
[0028] FIG. 9C is a third plot comparing measurements of the
wavelength of electromagnetic radiation using the system of FIG. 1
and using a reference measurement device, according to aspects of
the present disclosure;
[0029] FIG. 10A is a plot of the measured optical activity angle
versus time as an optical fiber of the system of FIG. 1 is
mechanically perturbed, according to aspects of the present
disclosure;
[0030] FIG. 10B is a plot of the measured optical activity angle
versus time as the temperature of an optical fiber of the system of
FIG. 1 is increased, according to aspects of the present
disclosure;
[0031] FIG. 11 is a second system for measuring a property of
electromagnetic radiation, according to aspects of the present
disclosure;
[0032] FIG. 12 is a third system for measuring a property of
electromagnetic radiation, according to aspects of the present
disclosure;
[0033] FIG. 13 is a fourth system for measuring a property of
electromagnetic radiation, according to aspects of the present
disclosure;
[0034] FIG. 14A is a plot of the mapping between optical activity
angle and wavelength for one mode of electromagnetic radiation,
according to aspects of the present disclosure;
[0035] FIG. 14B is a plot of the mapping between optical activity
angle and wavelength for three modes of electromagnetic radiation,
according to aspects of the present disclosure;
[0036] FIG. 14C is a plot of the free spectral range of the system
of FIG. 1 versus the number of modes of electromagnetic radiation,
according to aspects of the present disclosure;
[0037] FIG. 14D is a plot of the resolution of the system of FIG. 1
versus the number of modes of electromagnetic radiation, according
to aspects of the present disclosure;
[0038] FIG. 15 is a representation of a multiplexed version of the
system of FIG. 1, according to aspects of the present
disclosure;
[0039] FIG. 16A is a comparison of a broadband spectrum of
electromagnetic radiation and a narrow spectrum of electromagnetic
radiation, according to aspects of the present disclosure;
[0040] FIG. 16B is a plot of measure power versus polarization
angle, according to aspects of the present disclosure;
[0041] FIG. 16C is a plot of the visibility of the system of FIG. 1
versus the bandwidth of the electromagnetic radiation being
measured, according to aspects of the present disclosure;
[0042] FIG. 17A is plot of the spectral amplitude and the spectral
separation of a complex spectrum being modified, according to
aspects of the present disclosure;
[0043] FIG. 17B is a plot of the visibility of the system of FIG. 1
versus the spectral amplitude ratio of the spectrum of FIG. 17A,
according to aspects of the present disclosure; and
[0044] FIG. 17C is a plot of optical activity angle measured using
the system of FIG. 1 versus the spectral separation of the spectrum
of FIG. 17A, according to aspects of the present disclosure.
[0045] While the present disclosure is susceptible to various
modifications and alternative forms, specific implementations have
been shown by way of example in the drawings and will be described
in detail herein. It should be understood, however, that the
present disclosure is not intended to be limited to the particular
forms disclosed. Rather, the present disclosure is to cover all
modifications, equivalents, and alternatives falling within the
spirit and scope of the present disclosure as defined by the
appended claims.
DETAILED DESCRIPTION
[0046] While the present disclosure is susceptible of many
different forms, there is shown in the drawings and will herein be
described in detail example implementations of the present
disclosure, with the understanding that the present disclosure is
to be considered as an example of the principles of the present
disclosure and is not intended to limit the broad aspect of the
present disclosure to the illustrated implementations.
[0047] Disclosed herein are techniques for measuring properties of
electromagnetic radiation that rely on optical activity undergone
by the electromagnetic radiation as it propagates through a system.
Optical activity is an inherent property of chiral materials (such
as sugar water), where the polarization angle of linearly-polarized
light input into the material rotates as it propagates down the
material. The amount of rotation is based at least in part on the
wavelength of the electromagnetic radiation. Thus, by measuring
this rotation, properties of the material (such as the material's
concentration or the wavelength of the electromagnetic radiation)
can be determined.
[0048] FIG. 1 shows a system 100 for measuring a property of
electromagnetic radiation that relies on the optical activity of
the electromagnetic radiation. However, instead of using a chiral
material, system 100 relies on the optical activity exhibited by
orbital angular momentum (OAM) modes of the electromagnetic
radiation in optical fibers. By measuring the polarization angle of
the electromagnetic radiation that is emitted by the optical fiber
and comparing that to the polarization angle of the electromagnetic
radiation when entering the optical fiber, the amount of rotation
imparted to the electromagnetic radiation can be measured. In turn,
a variety of different properties of the electromagnetic radiation
can be determined based on this measurement.
[0049] System 100 includes a variety of different optical
components through which electromagnetic radiation propagates.
Generally, the components can be coupled via any suitable
mechanism, such as via optical fibers; a tabletop setup of lenses,
mirrors, etc.; or any suitable device, technique, etc. Components
that are coupled together are arranged so that electromagnetic
radiation that is emitted from one component is received at the
other component.
[0050] System 100 includes an electromagnetic radiation source 102
that produces electromagnetic radiation. In use, the
electromagnetic radiation source 102 can be any object or component
that produces the electromagnetic radiation that is being measured,
based on the specific application for which system 100 is being
used. For example, the electromagnetic radiation source 102 could
be a tissue sample, one or more components reacting to produce
electromagnetic radiation (such as visible light infrared light,
ultraviolet light, etc.), an optical component designed to produce
electromagnetic radiation, etc. In applications designed to test
and/or characterize the performance of system 100, the
electromagnetic radiation source 102 can be a tunable laser, or a
narrow linewidth laser source, such as an external cavity
laser.
[0051] System 100 further includes a polarizing element 104
configured to receive the electromagnetic radiation from the
electromagnetic radiation source 102. The polarizing element 104 is
configured to convert the electromagnetic radiation emitted by the
electromagnetic radiation source 102 to a single linear
polarization having a polarization angle .theta..sub.1. In some
implementations, .theta..sub.1 is 0.degree., e.g., the
electromagnetic radiation emitted from the polarizing element 104
is linearly polarized along the x direction. Generally however, any
angle can be used for .theta..sub.1, as this polarization angle
will be used as a reference to compare to after the electromagnetic
radiation propagates through the optical fiber. The polarizing
element 104 can be any suitable device or mechanism that creates
linearly polarized light, such as an absorptive polarizer, a
beam-splitting polarizer (which could include polarization by
Fresnel reflection, birefringent polarizers, thin film polarizers,
wire-grid polarizer, etc.), or any linear polarizer.
[0052] System 100 can optionally include a variety of components
optically coupled between the electromagnetic radiation source 102
and the polarizing element 104, depending on the application of
system 100. These components can include an optical isolator 103A,
a polarization controller 103B, a 3 dB coupler 103C, an optical
spectrum analyzer 103D, a Fabry-Perot interferometer 103E, and a
lens 103F. The optical isolator 103A is used to prevent
back-reflections of electromagnetic radiation back into the
electromagnetic radiation source 102. The polarization controller
103B can be used to control the amount of input power that the
electromagnetic radiation emitted from the polarizing element 104
has. In some implementations, the polarization controller 103B
receives unpolarized electromagnetic radiation from the
electromagnetic radiation source 102, and converts the unpolarized
electromagnetic radiation to linearly-polarized electromagnetic
radiation at an arbitrary angle.
[0053] The 3 dB coupler 103C is used to couple the output of the
polarization controller 103B to each of the optical spectrum
analyzer 103D, the Fabry-Perot interferometer 103E, and the lens
103F. The 3 dB coupler 103C thus splits the electromagnetic
radiation into three separate channels. While a 3 dB coupler is
shown, any type of coupler could be used. In applications where the
system 100 (or any component of system 100) is being tested, the
optical spectrum analyzer 103D and the Fabry-Perot interferometer
103E can be used to independently measure the wavelength of the
electromagnetic radiation. These results can be compared to the
output of the system 100, in order to validate the system 100. In
some implementations, the optical spectrum analyzer 103D can be
used to provide a lower-resolution absolute measurement of the
electromagnetic radiation from the electromagnetic radiation source
102. In some implementations, the Fabry-Perot interferometer 103E
can be used to provide a higher-resolution relative measurement of
the electromagnetic radiation from the electromagnetic radiation
source 102 relative to a reference wavelength. Finally, the lens
103F is used to focus the electromagnetic radiation onto the
polarizing element 104.
[0054] The linearly-polarized electromagnetic radiation emitted
from the polarizing element 104 propagates to a mode converter 106
that is coupled to the polarizing element 104. A beam trap 105A can
be optically coupled to the polarizing element 104 to absorb all of
the other polarizations of the electromagnetic radiation emitted by
the electromagnetic radiation source 102. A number of optical
components, such as mirror 105B, can be used to direct the
linearly-polarized electromagnetic radiation to the mode converter
106.
[0055] The mode converter 106 converts the linearly-polarized
electromagnetic radiation from the polarizing element 104 into an
orbital angular momentum (OAM) mode. The mode converter 106 can be
any suitable component that can create the OAM mode, such as a
spatial light modulator, a q-plate, a fiber grating, a spiral phase
plate, a metasurface, or any combination thereof. In some
implementations, the mode converter 106 has a fork-pattern
hologram. An OAM mode is any mode where the electromagnetic
radiation has an angular momentum component that is dependent on
the field spatial distribution of the electromagnetic radiation.
The OAM modes of electromagnetic radiation can also have a
component of angular momentum that is dependent on the polarization
of the electromagnetic radiation.
[0056] Generally, OAM modes of electromagnetic radiation are
characterized by helical wavefronts with an optical vortex at the
center. The amount of OAM possessed by the electromagnetic
radiation can be described by its topological charge L, which is a
positive or negative integer. The topological charge of an OAM mode
is a discretized representation of the spatial field distribution
of that OAM mode. Electromagnetic radiation with a topological
charge L=0 has no OAM. The electromagnetic radiation in this mode
is not helical, and the wavefronts are simply a series of
continuously phase-constant surfaces. The wavefronts of
electromagnetic radiation with a topological charge L=.+-.1 are
shaped as a single helical surface, with a step length equal to the
wavelength .lamda. of the electromagnetic radiation. The wavefronts
of electromagnetic radiation with a topological charge L=.+-.2 are
shaped as a |L| distinct but intertwined helices, with the step
length of each helical surface equal to |L|.times..lamda.. The OAM
mode of linearly-polarized electromagnetic radiation emitted from
the mode converter 106 can have a topological charge L.sub.i, which
can generally be any positive integer greater than zero, or
negative integer less than zero.
[0057] The mode converter 106 outputs the OAM mode of the
linearly-polarized electromagnetic radiation to an optical fiber
108. As the electromagnetic radiation propagates through the
optical fiber 108, the polarization angle of the electromagnetic
radiation rotates. The optical fiber 108 causes the polarization
angle to rotate, because the electromagnetic radiation with
topological charge L.sub.i and with linear polarization is a
superposition of two different non-degenerate OAM modes. Each of
these two OAM modes have the same topological charge L.sub.i (which
is also the same as the linearly-polarized electromagnetic
radiation), but have opposing circular polarizations. Thus, one of
the two OAM modes is left-handed circular polarized, while the
other OAM mode is right-handed circular polarized. The optical
fiber 108 thus receives the two different circularly-polarized OAM
modes and supports propagation of the circularly-polarized OAM
modes to the output of the optical fiber 108. The superposition of
these two OAM modes is linearly-polarized electromagnetic radiation
which enters the optical fiber 108 with a polarization angle of
.theta..sub.1 and a topological charge L.sub.i. Because this
electromagnetic radiation is the superposition of (i) left-handed
circularly polarized electromagnetic radiation having topological
charge L.sub.i and (ii) right-handed circularly polarized
electromagnetic radiation having topological charge L.sub.i, the
polarization angle of the electromagnetic radiation in the optical
fiber 108 will rotate.
[0058] Referring to FIGS. 2A and 2B, in one implementation, the
optical fiber 108 is a ring-core fiber that is formed from a
ring-core 203, and an outer cladding layer 206 that surrounds the
ring-core 203. The ring-core 203 has an annular body 204 and a
hollow (e.g., air-filled) center 202. The ring-core 203 guides the
two circularly-polarized OAM modes through the optical fiber 108.
In one implementation, the ring-core 203 is formed from
germanium-doped silicon dioxide, and the cladding layer 206 is
formed from silicon dioxide (also referred to as silica). The
refractive index profile 208 of the optical fiber 108 is shown in
FIG. 2B. The vertical axis measures .DELTA.n, which is the
difference between the refractive index of the material relative to
the refractive index of standard silicon dioxide/silica. The
horizontal axis measures the radial distance through the center of
the optical fiber 108. As is shown, the refractive index of the
annular body 204 of ring-core 203 is generally higher than the
refractive indices of both the hollow center 202 of the ring-core
203, and the cladding layer 206. Other implementations can use
other designs for the optical fiber 108, such as by using different
materials or by having different refractive index profiles. For
example, in some implementations, the optical fiber 108 can have a
low index center layer instead of the hollow center. Generally, any
design can be used for the optical fiber 108, so long as the
optical fiber 108 supports propagation of the circularly-polarized
OAM modes.
[0059] Referring now to FIGS. 3A, 3B, and 3C, the optical fiber 108
imparts rotation to the polarization of the propagating
electromagnetic radiation, because the two circularly-polarized OAM
modes have different effective indices n.sub.eff within the optical
fiber 108. The effective index n.sub.eff of any given mode is a
measure of how fast the phase of the electromagnetic radiation
within that mode propagate within the optical fiber 108. The
effective index n.sub.eff generally describes the phase velocity of
the OAM mode in the optical fiber 108. However, system 100 is
generally a dispersive system, and thus generally has some amount
of wavelength-dependent chromatic dispersion, e.g., the effective
index of a mode changes with wavelength. As such, pulses of
electromagnetic radiation traveling in OAM modes in the optical
fiber 108 generally form envelopes that propagate through the
optical fiber 108 at a velocity described by a group index n.sub.g.
The group index n.sub.g is generally related to the effective index
n.sub.eff according to
n g = n eff - .lamda. d n eff d .lamda. . ##EQU00001##
[0060] FIG. 3A shows a plot 301 illustrating the different
effective indices n.sub.eff for four different OAM modes of
electromagnetic radiation. The vertical axis shows the effective
index n.sub.eff, while the horizontal measure shows the topological
charge L, which is a measure of how much OAM each mode carries. The
four OAM modes are categorized by their topological charge L, as
well as by whether the OAM mode is left-handed circularly polarized
(.sigma..sup.+) or right-handed circularly polarized
(.sigma..sup.-). OAM mode 302A has a topological charge -L and a
circular polarization .sigma..sup.+. OAM mode 302B has a
topological charge -L and a circular polarization .sigma..sup.-.
OAM mode 302C has a topological charge +L and a circular
polarization .sigma..sup.-. OAM mode 302D has a topological charge
+L and a circular polarization .sigma..sup.+. The expression of the
electric fields of these four OAM modes has the following form:
E .fwdarw. ( r , .phi. ) = F ( r ) { e .+-. iL .phi. .sigma. .+-. e
.-+. iL .phi. .sigma. .+-. } ##EQU00002##
[0061] F(r) is the radial field, which can be the same for each
mode. The e.sup..+-.iL.PHI. and e.sup..-+.iL.PHI. terms refer to
the azimuthal component of the field distribution of the modes due
to OAM. The of terms refer to the circular polarization and
respective handedness of the OAM modes. The two OAM modes with the
same sign or handedness of topological charge L and polarization
.sigma. (the top branch of the above equation) are referred to as
spin-orbit aligned modes. The two OAM modes with the opposite sign
or handedness of topological charge L and polarization .sigma. (the
bottom branch of the above equation) are referred to as spin-orbit
anti-aligned modes. As can be seen, the two spin-orbit aligned
modes (OAM modes 302B and 302D) have the same effective index
n.sub.eff, which is different than the effective index of the two
spin-orbit anti-aligned modes (OAM modes 302A and 302C). Thus, by
simultaneously exciting one spin-orbit aligned mode and one
spin-orbit anti-aligned modes in the optical fiber 108 (whose
polarizations add to become linear polarization), the optical fiber
108 will have two modes with different effective indices
propagating therein.
[0062] FIG. 3B shows a plot 303 of the effective index n.sub.eff of
two different example OAM modes versus the wavelength .lamda.. In
the example, OAM mode 304A has a topological charge L=11 and a
polarization .sigma..sup.-, while OAM mode 304B has a topological
charge L=11 and a polarization .sigma..sup.-. As is shown, the
effective indices n.sub.eff of the two example OAM modes 304A, 304B
are different from each other, and are dependent on the wavelength
.lamda.. This difference in effective indices between the two OAM
modes corresponds to a difference in the group indices between the
two OAM modes, which in turn causes the linearly-polarized
electromagnetic radiation formed from the superposition of the two
OAM modes to rotate as it propagates through the optical fiber
108.
[0063] In some implementations, the minimum absolute difference
between the effective indices of the two OAM modes for use with
system 100 is
.DELTA.n.sub.eff=|n.sub.eff1-n.sub.eff2|=5.times.10.sup.-5.
Generally, if the non-degeneracy condition of the effective indices
of the two OAM modes is met, the system 100 is minimally
dispersive, then the minimum difference .DELTA.n.sub.g in the group
indices is also about 5.times.10.sup.-5. By exciting two OAM modes
with at least this absolute difference in effective indices, the
group index difference .DELTA.n.sub.g between the two modes is
sufficient to impart a detectable amount of rotation to the
electromagnetic radiation. This minimum value for .DELTA.n.sub.eff
also substantially prohibits any coupling between the two OAM modes
due to external perturbations, such as via temperature or
mechanical fluctuations. By increasing the effective index
difference .DELTA.n.sub.eff, the group index difference
.DELTA.n.sub.g is increased, which enables system 100 to achieve
higher wavelength resolutions, e.g., the smallest detectable
wavelength different between two beams of electromagnetic radiation
is lower. Generally, any optical fiber that can achieve an
effective index difference that is greater than or equal
5.times.10.sup.-5 can stably guide the two different OAM modes.
[0064] In the illustrated implementation, the effective index
n.sub.eff of the two spin-orbit anti-aligned OAM modes is greater
than the effective index n.sub.eff of the two spin-orbit aligned
OAM modes. However, in other implementations, the optical fiber 108
can be designed so that the effective index n.sub.eff of the two
spin-orbit anti-aligned OAM modes is less than the effective index
n.sub.eff of the two spin-orbit aligned OAM modes. Generally, so
long as the spin-orbit aligned OAM modes and the spin-orbit
anti-aligned OAM modes have different values for their respective
effective indices n.sub.eff, the spin-orbit aligned and spin-orbit
anti-aligned modes can be used with system 100.
[0065] FIG. 3C shows a plot 305 of .DELTA.n.sub.g versus the square
of the topological charge L, for two OAM modes with different
effective indices in an exemplary ring-core optical fiber, such as
optical fiber 108. As is shown, .DELTA.n.sub.g scales as L.sup.2 in
the exemplary ring-core optical fiber. In other implementations of
the optical fiber that support stable propagation of the OAM modes,
.DELTA.n.sub.g may scale as L.sup.3. In general, the exact
dependence of .DELTA.n.sub.g on L can vary. For example,
.DELTA.n.sub.g could scale as L.sup.n (L to the n.sup.th power), or
with other dependences on L. Generally however, .DELTA.n.sub.g
always increases monotonically with L. Thus, .DELTA.n.sub.g can be
increased by increasing the topological charge L of the OAM modes
that are propagating through the optical fiber 108, which in turn
increases the wavelength resolution of the system 100. The mode
converter 106 can be used to convert the electromagnetic radiation
output from the electromagnetic radiation source 102 to higher OAM
modes, which in turn increases the group index difference
.DELTA.n.sub.g between the two OAM modes.
[0066] Generally, optical fiber 108 is cylindrically symmetric and
isotropic, and is designed to mirror the field profile of the OAM
modes. In turn, this mirroring maximizes the effective index
difference .DELTA.n.sub.eff between the spin-orbit aligned mode and
the spin-orbit anti-aligned mode. The effective index difference
.DELTA.n.sub.eff can be due at least in part to the inhomogeneity
of the ring-core, which introduces polarization-dependent
perturbations based on the polarization of the OAM modes. The
perturbations are enhanced by the OAM of the electromagnetic
radiation.
[0067] Referring back to FIG. 1, in some implementations, system
100 includes mirrors 107A and 107B to direct the OAM mode of the
linearly-polarized electromagnetic radiation to a lens 107C mounted
on a six-axis stage 107D. The lens 107C and the six-axis stage 107D
is used to precisely couple the two OAM modes output by the mode
converter 106 to an input of the optical fiber 108, in order to
reduce modal cross-talk. In some implementations, walk-the-beam
methods are used for optical alignment. In some implementations, a
>20 dB mode purity is obtained between the two desired OAM modes
and any other modes that may have inadvertently been excited in the
optical fiber 108.
[0068] As the two OAM modes travel through the optical fiber 108,
the two modes propagate at different speeds due to their effective
index difference. Because a single linearly-polarized OAM mode is
the superposition of the two circularly-polarized OAM modes, the
result is that the polarization angle of the linearly-polarized
electromagnetic radiation rotates as the electromagnetic radiation
travels through the optical fiber 108. This rotation is shown in
FIG. 4, which is a graphical representation of the orientation of
polarization of the linearly-polarized electromagnetic radiation as
it propagates through a section of the optical fiber 108. In the
illustrated implementation, the electromagnetic radiation begins
having a generally vertical polarization angle, shown by arrow
402A. However, the initial polarization angle of the
electromagnetic radiation can generally be at any angle, so long as
the electromagnetic radiation is linearly polarized. As the
electromagnetic radiation propagates through optical fiber 108, the
polarization angle begins to rotate. For example, arrow 402B shows
that the polarization of the electromagnetic radiation is nearly
horizontal, while arrow 402C shows that the polarization of the
electromagnetic radiation has rotated back to vertical. The
propagating beam of electromagnetic radiation is described as
{right arrow over
(E)}(r,.PHI.)=F(r)exp(iL.PHI.)exp(i.beta.z)[.sigma..sup.+
exp(i.gamma.)+.sigma..sup.- exp(-i.gamma.)]
.fwdarw.{right arrow over
(E)}(r,.PHI.)=F(r)exp(iL.PHI.)exp(i.beta.z)[{circumflex over (x)}
cos(.gamma.)-y sin(.gamma.)].
Here, .beta.=.pi.(n.sub.eff,so.sub.a+n.sub.eff,so.sub.aa)/.lamda.
is the average propagation constant between the two OAM modes;
.gamma. is the optical activity angle of the electromagnetic
radiation; z is the length of the optical fiber 108; and .PHI. is
the azimuthal angle
.gamma. = z .times. .DELTA. .beta. 2 = .pi. z .DELTA. n eff .lamda.
, ##EQU00003##
.DELTA..beta. is the difference in the propagation constant between
the two OAM modes, and .DELTA.n.sub.eff is the difference in the
effective index of the two OAM modes. Thus, it can be observed that
the combination of the oppositely circularly-polarized OAM modes
(e.g., left-handed and right-handed) of electromagnetic radiation
propagating through optical fiber 108 is a linear polarization, and
that this linearly-polarized electromagnetic radiation rotates as a
function of the distance z of the optical fiber 108, the wavelength
.lamda. of the electromagnetic radiation, and the effective index
separation .DELTA.n.sub.eff between the two OAM modes.
[0069] Referring back to FIG. 1, the linearly-polarized
electromagnetic radiation emitted at the output of the optical
fiber 108 (which is a superposition of the two circularly-polarized
OAM modes) has a polarization angle .theta..sub.2. The difference
between the polarization angles .theta..sub.1 and .theta..sub.2 is
equal to the optical activity angle .gamma., which in turn is
dependent on the wavelength .lamda. of the electromagnetic
radiation. The linearly-polarized electromagnetic radiation at the
output of the optical fiber 108 can be focused and/or collimated by
lens 109A onto a beam splitter 109B. The beam splitter 109B can
split the output beam of electromagnetic radiation into two
different portions. One portion can propagate to an imaging device,
such as a camera 109C, which can be used for validation or testing
purposes. The other portion can propagate to a polarizing element
110.
[0070] Camera 109C can also be used to capture an image of the
output electromagnetic radiation's intensity profile, in order to
determine the modal purity of the output electromagnetic radiation.
Modal purity refers to the amount of unwanted non-degenerate mode
coupling (to OAM modes of different topological charges L) or
degenerate mode coupling (from an OAM mode of topological charge L
to its corresponding -L OAM mode equivalent). Power from the input
OAM modes can couple to these non-degenerate and degenerate modes,
reducing the accuracy of system 100. Different types of analyses
can be performed to determine the amount of modal purity in system
100. In one implementation, an interferometric analysis can be
performed to detect interference effects between different modes,
to test the modal purity.
[0071] In other implementations, a time-of-flight method can be
used to test modal purity. In these implementations, system 100
includes an additional electromagnetic radiation source that shares
an optical path with the electromagnetic radiation source 102. The
additional electromagnetic radiation source could be, for example,
a picosecond pulsed laser. The addition electromagnetic radiation
source is configured to emit pulses that propagate through the mode
converter 106 and the optical fiber 108. The pulses excite modes
that travel at different speeds, similar to the electromagnetic
radiation source 102. After the pulses are emitted from the optical
fiber 108, these pulses propagate to a high speed detector coupled
to an oscilloscope. The oscilloscope displays the different pulses
received from the additional electromagnetic radiation source.
Because the different modes that are being excited in the optical
fiber 108 are viewable on the oscilloscope, any changes that need
to be made to the system 100 can be made, in order to achieve modal
purity between the two OAM modes. In some implementations, this
time-of-flight method can also be used to measure the group index
difference .DELTA.n.sub.g between the two OAM modes, because the
group index n.sub.g of the two OAM modes determines the speed at
which the electromagnetic radiation propagates. Generally, any
number of suitable methods or techniques can be used to test the
modal purity.
[0072] Polarizing element 110 is configured to receive the
linearly-polarized electromagnetic radiation, and convert this
electromagnetic radiation into two orthogonal linearly-polarized
components. The first component has a polarization angle equal to
.theta..sub.n, while the second component has a polarization angle
equal to .theta..sub.n+90.degree.. In some implementations, the
first component has a polarization angle identical to the
polarization angle of the electromagnetic radiation that entered
the optical fiber 108, and thus .theta..sub.n=.theta..sub.1, and
.theta..sub.n+90.degree.=.theta..sub.1+90.degree.. In some of these
implementations, where the initial beam of electromagnetic
radiation is linearly-polarized along the x-axis, the first
component of electromagnetic radiation from the polarizing element
110 is the {circumflex over (x)} component of the electromagnetic
radiation output from the optical fiber 108, while the second
component of electromagnetic radiation from the polarizing element
110 is the y component of the electromagnetic radiation output from
the optical fiber 108. Generally, so long as the polarizing element
110 outputs two orthogonal components of electromagnetic radiation,
the polarization angle .theta..sub.2 of the electromagnetic
radiation that exits the optical fiber 108 can be measured with
simplicity. In some implementations however, the electromagnetic
radiation output from the optical fiber 108 can be split into
components that are not orthogonal. The polarizing element 110 can
be any suitable optical component, such as a polarization beam
splitter, a rotatable linear polarizer, a polarimeter, etc.
[0073] The first component of the electromagnetic radiation is
directed to a power meter 114A, while the second component of the
electromagnetic radiation is directed to a power meter 114B. Power
meter 114A measures the power P.sub..theta..sub.n of the first
component, while power meter 114B measures the power
P.sub..theta..sub.n.sub.+90.degree. of the second component. In
some implementations, the power meters 114A, 114B are
germanium-based photodetectors. The ratio of the two powers is
equal to the square of the tangent of the second polarization angle
.theta..sub.2, and thus
.theta. 2 = tan - 1 ( P .theta. n + 9 0 .smallcircle. P .theta. n )
. ##EQU00004##
The optical activity angle .gamma. is the difference between
.theta..sub.1 and .theta..sub.2, can thus be read out
instantaneously, with minimal or no post-processing.
[0074] Once the optical activity angle .gamma. is determined, a
wavelength measurement can be performed. As shown above, there the
optical activity angle .gamma. is explicitly related to the
wavelength .lamda. by
.gamma. = .pi. z .DELTA. n e f f .lamda. . ##EQU00005##
However, .DELTA.n.sub.eff is also wavelength-dependent, which must
be accounted for. A first-order Taylor expansion of the above
equation reveals how the optical activity angle .gamma. changes in
response to a change in wavelength of the electromagnetic radiation
source 102, yielding the linear spectroscopic mapping:
.DELTA. .gamma. = - { .pi. z .DELTA. n g .lamda. 2 } .DELTA.
.lamda. = .alpha. .lamda. . ##EQU00006##
[0075] Here, .DELTA..gamma. is the change in optical activity
angle, .DELTA.n.sub.g is the group index difference between the two
OAM modes, .DELTA..lamda. is a change in wavelength (which could be
a change between a first center wavelength and a second center
wavelength), and .alpha. is a calibration factor defining the
strength of the rotation imparted by the optical fiber 108. In some
implementations, .alpha. can be generally be deduced
experimentally. Additionally or alternatively, accurate theoretical
modeling of the OAM modes of the optical fiber 108 would yield
.DELTA.n.sub.g, and thus .DELTA..gamma. also.
[0076] FIG. 5 shows a plot 502 of the relationship between
.DELTA..lamda. and .DELTA..gamma., obtained using an experimental
characterization of the system 100 (or any of the other systems
disclosed herein). The calibration factor .alpha. can be determined
from plot 502. First, a beam of reference electromagnetic radiation
having a reference wavelength .lamda..sub.0 is input to system 100.
System 100 then determines a reference optical activity angle
.gamma..sub.0, which measures how much the reference
electromagnetic radiation rotated within the optical fiber. The
reference wavelength .lamda..sub.0 can be determined by an external
component, such as the optical spectrum analyzer 103C, a gas
absorption-based reference, cell, or any other suitable component.
Second, a plurality of beams of electromagnetic radiation, each
having a wavelength .lamda., are input into system 100. For each
beam of electromagnetic radiation, the corresponding optical
activity angle .gamma. is determined by system 100, and the
wavelength .lamda. is determined by the reference component. Then,
for each of the plurality of beams of electromagnetic radiation,
the difference in optical activity angles
.DELTA..gamma.=.gamma.-.gamma..sub.0 is plotted against the change
in wavelength .DELTA..lamda.=.lamda.-.lamda..sub.0. A fit is
performed on the data, so that
.gamma.-.gamma..sub.0=-.alpha.(.lamda.-.lamda.0), and the
calibration factor .alpha. is obtained. Thus, any change in
wavelength .DELTA..lamda. linearly maps to a change in optical
activity angle .DELTA..gamma..
[0077] Once the calibration factor .alpha. is obtained, system 100
can subsequently be used to measure wavelength change or wavelength
drift .DELTA..lamda.. The smallest detectable wavelength
change/drift is the resolution of the system 100. System 100 can be
used for a variety of different applications. For example, system
100 could be used in coherent laser beam combining applications, to
identify and measure wavelength drift in any of the laser beams. In
another example, system 100 could be used with optical clocks, to
identify and measure drift in an electromagnetic radiation source
relative to a reference atomic resonance wavelength. In yet another
implementation, system 100 can be used to measure over time how the
wavelength of electromagnetic radiation emitted by the biological
sample changes. Generally, system 100 is stable, and the
calibration factor .alpha. remains substantially constant over time
and is robust to perturbations (such as mechanical or thermal
changes). However, system 100 can be periodically re-characterized
to determine an updated value of the calibration factor .alpha. as
needed. Indeed, system 100 can be used in any application where
spectrometers, wavemeters, and/or spectrum analyzers are currently
used, in order to provide higher resolutions and/or higher
acquisition speeds.
[0078] FIGS. 6A and 6B illustrate the linear mapping between a
change in wavelength .DELTA..lamda. and a change in optical
activity angle .DELTA..gamma.. As shown in FIG. 6A, two beams of
electromagnetic radiation 602A and 602B can have some wavelength
difference .DELTA..lamda.. As shown in FIG. 6B, beam of
electromagnetic radiation 602A results in an optical activity angle
604A, while beam of electromagnetic radiation 602B results in an
optical activity angle 604B. Thus, the change in wavelength .lamda.
introduces a change in the optical activity angle .DELTA..gamma.
that is measured by system 100 for the beams of electromagnetic
radiation 602A, 602B. Thus, because of the wavelength dependence on
the group index difference .DELTA.n.sub.g between the two OAM
modes, wavelength differences .DELTA..lamda. can be measured.
[0079] Other properties can also be measured using system 100. For
example, system 100 can be used to measure the center wavelength in
the range of wavelengths, and/or the spread of the wavelengths in
the range wavelengths, e.g., the bandwidth of the electromagnetic
radiation. Other properties of complex spectra can also be
measured, such as spectral separation, spectral amplitude ratio,
etc.
[0080] System 100 can be implemented using a variety of different
parameters for the different components. Generally, the parameters
can be changed, depending on a number of factors for a given
application, including resolution requirements, space concerns,
cost, etc. Because the .DELTA..lamda. is proportional to both the
length of the optical fiber z and the group index difference
.DELTA.n.sub.g, and because the group index difference
.DELTA.n.sub.g increases with topological charge L, the resolution
of the system 100 (e.g., minimum detectable .DELTA..lamda.) can be
increased by increasing the length of the optical fiber z and/or
the topological charge L, e.g., by increasing the calibration
factor .alpha..
[0081] For example, the optical fiber 108 can range in length
between the centimeter scale (e.g., a length of about 1 centimeter
or greater) up to the kilometer range. In still other
implementations, the length of the optical fiber 108 can be less
than 1 centimeter. In another example, the magnitude of the
topological charge L of the OAM modes can generally be any integer
between 1 and about 200 in many implementations. However,
topological charges greater than 200 are also contemplated. The
type of fiber used for the optical fiber 108 can also be modified
as needed. For example, one implementation of system 100 includes a
ring-core optical fiber 108 formed from a germanium-doped silicon
dioxide ring and silicon dioxide cladding, as discussed above.
However, the optical fiber 108 can have any suitable design or be
made from any suitable material, so long as the optical fiber 108
supports propagation of a spin-orbit aligned OAM mode and a
spin-orbit anti-aligned OAM mode have a minimum refractive index
different .DELTA.n.sub.eff of greater than or equal to about
5.times.10.sup.-5.
[0082] As discussed herein, system 100 has a resolution that is the
minimum wavelength difference detectable by measuring changes in
optical activity. The resolution is generally dependent on the
length of the optical fiber 108, the wavelength ranges which the
system 100 is configured to operate at, and other factors. In one
implementation, system 100 operates at a wavelength of about 1000
nanometers and has an optical fiber length of greater than or equal
to 1 centimeter, and achieves a resolution of about 1.2 nanometers.
In still another implementation, the system 100 operates at a
wavelength of about 1000 nanometers and has an optical fiber length
of greater than or equal to 6.0 centimeters, and achieves a
resolution of about 0.2 nanometers. In yet another implementation,
the system 100 has a resolution of about 0.3 picometers, with a
resolving power (general wavelength at which the system 100 is
operating divided by the resolution) of
R.gtoreq.3.4.times.10.sup.6. In still other implementations, the
system 100 operates around another center wavelength, e.g., less
than 1000 nanometers or greater than 1000 nanometers. Typical
wavelength ranges in which the system 100 may operate covers the
transparency range of optical fibers, which extends from the blue
wavelengths of 400 nanometers through the mid-infrared wavelengths
of 10,000 nanometers. The system 100 is capable of operating in all
these wavelength ranges provided that the material with which the
optical fiber is primarily constructed is sufficiently transparent
to electromagnetic radiation at these wavelengths.
[0083] System 100 includes a number of components positioned
between the polarizing element 110 and the power meters 114A, 114B.
For example, both the orthogonal components of the electromagnetic
radiation output from the optical fiber 108 can be directed to an
additional mode converter 112. In some implementations, it can be
difficult to only measure the two OAM modes from the optical fiber
108, because the input electromagnetic radiation can include
additional OAM modes with different topological charges. In
particular, if the desired OAM modes inadvertently couple to OAM
modes that are degenerate in relation to the desired OAM modes
(e.g., OAM modes having the opposite topological charge -L). the
corresponding rotation of the degenerate OAM modes would be
opposite direction to that of the desired OAM modes, but with the
same magnitude of rotation. Thus, the presence of the unwanted OAM
modes can lead to errors when calculating the optical activity
angle .gamma..
[0084] The additional mode converter 112 is used to convert the two
orthogonal components of the output linearly-polarized
electromagnetic radiation (which is a superposition of the two OAM
modes) into a topological charge L.sub.f=0 state (e.g., no OAM
mode), while any degenerate modes are converted to a topological
charge L.sub.degenerate=2L.sub.i state. A first iris 113A can be
placed between the mode converter 112 and the first power meter
114A, while a second iris 113B can be placed between the mode
converter 112 and the second power meter 114B. Because the optical
power in the L.sub.degenerate=2L.sub.i state of the degenerate
modes is a ring that diffracts faster than power in the Gaussian
spot-like L.sub.f=0 state of the electromagnetic radiation being
measured, the first and second irises 113A, 113B prevent any of the
degenerate modes from reaching the respective power meters 114A,
114B. Flip mirror 113C can be placed between iris 113A and power
meter 114A, and is used to direct a portion of the first component
of the output linearly-polarized electromagnetic radiation (the
component having a polarization angle .theta..sub.n) to camera
113E.
[0085] Similarly, flip mirror 113D can be placed between iris 113B
and power meter 114B, and is used to direct a portion of the second
component of the output linearly-polarized electromagnetic
radiation to camera 113E. Camera 113E can then be used to check to
ensure that the degenerate modes are not reaching the power meters
114A, 114B. In some implementations, mirror 111A can direct the
second component of the output linearly-polarized electromagnetic
radiation (the component having a polarization angle
.theta..sub.n+90.degree.) to a half-wave plate 111B, which can
shift the polarization angle 90.degree., so that the second
component has the same polarization angle .theta..sub.n as the
first component. Mirror 111C can then direct the second component
to the additional mode converter 112. Despite now having the same
polarization angle .theta..sub.1, the two components are
distinguished by system 100 because the two components are measured
by the two different power meters 114A, 114B. Converting the second
component to have the same polarization angle as the first
component eliminates any possible measurement errors that could be
introduced by the different polarization angles.
[0086] FIG. 7 shows images 702A and 702B that are representations
of the output electromagnetic radiation with and without the
degenerate modes. Image 702A shows the output electromagnetic
radiation after having been modified by the additional mode
converter 112. Image 702B shows the electromagnetic radiation after
passing through an iris 704 (which could be either iris 113A or
iris 113B). As shown, the halo from the 2L.sub.i degenerate mode
has been eliminated, and the remaining electromagnetic radiation
propagates to detector 706 (which can be power meter 114A or power
meter 114B.
[0087] FIG. 8 illustrates a plot 801 showing the optical activity
angle .gamma. as a function of the wavelength of the
electromagnetic radiation. Data points 802A-802G plot the optical
activity angle .gamma. of electromagnetic radiation having a
topological charge L=10, while data 804A-804G plot the optical
activity angle .gamma. of electromagnetic radiation having a
topological charge L=12. Plot 801 also includes a linear fit 803 of
the data points for the topological charge L=10 electromagnetic
radiation, and a linear fit 805 of the data points for the
topological charge L=12 electromagnetic radiation. As is shown,
system 100 demonstrates that the optical activity angle .gamma.
changes with the wavelength of the electromagnetic radiation being
measured, and the rate of this change increases with the
topological charge L of the OAM modes used.
[0088] FIGS. 9A and 9B show the results of a series of measurements
conducted to evaluate the performance of system 100 (or any of the
other systems disclosed herein). Plot 902A in FIG. 9A shows a
comparison between the wavelength obtained using system 100 and the
wavelength measured using a reference system (such as Fabry-Perot
interferometer 103E) for electromagnetic radiation centered around
1028.55 nanometers. Plot 902B in FIG. 9B shows a comparison between
the wavelength obtained using system 100 and the wavelength
measured using a reference system (such as Fabry-Perot
interferometer 103D) for electromagnetic radiation centered around
1028.7 nanometers. A residual error analysis around the slope=1
line reveals that system 100 is able to predict the wavelength of
the electromagnetic radiation with an accuracy of approximately 1
picometer.
[0089] FIG. 9C shows the results of a similar analysis as those of
FIGS. 9A and 9B. For the analysis of FIG. 9C, the wavelength of the
electromagnetic radiation source 102 was finely tuned using a
thermoelectric cooler, and then the analysis of FIGS. 9A and 9B was
performed. The results are shown in plot 902C, which plots the
wavelength measured by the reference system (such as Fabry-Perot
interferometer 103E) on the vertical axis, and the wavelength
measured by system 100 on the horizontal axis. As is shown, the
individual data points 904A-904G generally align with the inset
intensity traces 906A-906G from the Fabry-Perot interferometer
103E. System 100 (or any of the other systems disclosed herein) can
thus be capable of measuring wavelength differences of about 0.3
picometers for electromagnetic radiation generally centered around
1028 nanometers, which corresponds to a resolving power of about
R=3.4.times.10.sup.6.
[0090] FIG. 10A shows a plot 1002 that compares optical activity
angle measurements obtained using system 100 (or any of the other
systems disclosed herein) and polarization state measurements
obtained using a conventional birefringent polarization-maintaining
fiber spectrometer, as the optical fiber is mechanically perturbed
over time. The measurement 1004A from system 100 (or any of the
other systems disclosed herein) is generally constant over time,
while the measurement 1004B from the conventional
polarization-maintaining fiber spectrometer is sensitive to the
mechanical perturbations, such that any spectroscopic mapping (such
as between .DELTA..gamma. and .DELTA..lamda.) formed using the
conventional polarization-maintaining fiber spectrometer is
unstable, and thus incapable of serving as a stable wavelength
measurement device. As such, system 100 is, in some
implementations, robust enough to be insensitive to mechanically
perturbed surroundings. In contrast, other systems are too
sensitive to small mechanical perturbations, and thus are not
suitable for applications involving a mechanically perturbed
environment.
[0091] FIG. 10B shows a plot 1006 of optical activity angle
measurements obtained using system 100 (or any of the other systems
disclosed herein) as a function of the temperature of the system
100. The optical fiber 108 of system 100 was heated from 22.degree.
C. to 60.degree. C. while the optical activity angle was being
measured. The resulting thermal expansion of the optical fiber 108
(e.g., increases in the fiber length z) causes the optical activity
angle measurements to vary in a strictly periodic fashion, as the
earlier equation showed, thus demonstrating the resiliency of
system 100 to thermal perturbations. Thus, as shown in FIGS. 10A
and 10B, the superposition of the two OAM modes in the optical
fiber 108 maintains both amplitude and phase differences under
nearly all conditions, because of spin-orbit interaction stability
in the optical fiber 108. This inherent stability allows for the
length z of the optical fiber 108 to be increased up to the
kilometer scale.
[0092] FIG. 11 shows a system 1100 that can be used to measure
properties of electromagnetic radiation. System 1100 is similar to
system 100, and includes components such as the electromagnetic
radiation source 102, the polarizing element 104, the mode
converter 106, the optical fiber 108, the polarizing element 110,
the additional mode converter 112, and the power meters 114A, 114B.
However, instead of having irises 113A and 113B to remove the
degenerate modes coupled to the electromagnetic radiation output
from the optical fiber 108, system 1100 includes two lenses 1113A,
1113B, and two single-mode fibers 1115A and 1115B. Single-mode
fiber 1115A is positioned between mode converter 112 and power
meter 114A, and single-mode fiber 1115B is positioned between mode
converter 112 and power meter 114B. Lens 1113A directs one of the
outputs of the additional mode converter 112 to single-mode fiber
1115A. Lens 1113B directs the other output of the additional mode
converter 112 to single-mode fiber 1115B. The single-mode fibers
1115A, 1115B are designed to only support propagation of the
L.sub.f=0 modes that are output from the mode converter 112, e.g.,
the electromagnetic radiation that was formerly the two OAM modes
propagating through the optical fiber 108. Thus, single-mode fiber
1115A ensures that only the L.sub.f=0 mode of the first component
of the output electromagnetic radiation reaches power meter 114A,
while single-mode fiber 1115B ensures that only the L.sub.f=0 mode
of the second component of the output electromagnetic radiation
reaches power meter 114B.
[0093] FIG. 12 shows a system 1200 that can be used to measure
properties of electromagnetic radiation. System 1200 is similar to
system 100 and system 1100, and includes the electromagnetic
radiation source 102, the polarizing element 104, the mode
converter 106, the optical fiber 108, and the polarizing element
110. However, system 1200 includes a polarizing beam splitter 1207A
and a quarter wave plate 1207B positioned between the mode
converter 106 and the optical fiber 108. The polarizing beam
splitter 1207A and a quarter wave plate 1207B can be used to
convert linearly-polarized electromagnetic radiation directly into
left-handed circularly polarized electromagnetic radiation and
right-handed circularly polarized electromagnetic radiation, before
being input into the optical fiber 108. The quarter wave plate
1207B could also in some implementations be used to pass
linearly-polarized electromagnetic radiation.
[0094] Further, the polarizing element 110 of system 1200 does not
split the electromagnetic radiation output from the optical fiber
108 into two orthogonal components, and system 1200 does not
include separate power meters 114A, 114B to measure the power of
the orthogonal component. Instead, the polarizing element 110 is a
linear polarizer that is configured to rotate. The polarizing
element 110 rotates until the rotation angle of the linear
polarizer matches the polarization angle .theta..sub.2 of the
electromagnetic radiation output from the optical fiber 108. When
this match occurs, the power of the electromagnetic radiation
passing through the polarizing element 110 as measured by a power
meter 1214 is at a maximum. By determining the rotation angle of
the polarizing element 110 when the power meter 1214 detects the
maximum power passing through the polarizing element 110, the
polarization angle .theta..sub.2 of the electromagnetic radiation
can be determined, from which the optical activity angle .gamma.
can then be determined.
[0095] FIG. 13 shows a system 1300 that can be used to measure
properties of electromagnetic radiation. System 1300 is similar to
system 1200, except that system 1200 does not include a polarizing
element that the electromagnetic radiation output from the optical
fiber 108 is incident on. Instead, the rotated electromagnetic
radiation that is output from the optical fiber 108 is directed to
a polarimeter 1314. The polarimeter 1314 is configured to receive
the electromagnetic radiation from the optical fiber 108 and
measure the polarization angle .theta..sub.2, from which the
optical activity angle .gamma. can then be determined.
[0096] Referring to FIGS. 14A-14D, in some implementations, the
systems disclosed herein (including system 100, 1100, 1200, and
1300) can benefit from multiplexing multiple OAM modes of differing
topological charge L that are supported by the optical fiber 108.
Here, a plurality of linearly polarized OAM modes can be introduced
into the optical fiber 108, and each OAM mode is separately
measured at the output. The free spectral range (FSR) of any system
describes the range of wavelengths over which measurements by the
disclosed systems are distinguishable, or unique. In the disclosed
systems, the relation between the optical activity angle and the
powers of the orthogonal components of the output electromagnetic
radiation from the optical fiber 108 limits the FSR, because the
range of measurable optical activity angles .gamma. is limited to a
range of between about 0.degree. and about 90.degree.. This means
that when optical activity measurements are performed using a
single set of OAM modes with topological charge L, the wavelength
range over which the systems provide unique wavelength mapping is
limited.
[0097] FIG. 14A shows a plot 1402 of the optical activity angle
versus wavelength for a single pair of OAM modes. As shown, the
pair of OAM modes has unique measurements only in a range of
between 0.degree. and 90.degree.. That is, there is only a small
wavelength range within which there is a unique mapping between
optical activity angle and wavelength, and thus the usable range of
a unique change in optical angle .DELTA..gamma. is limited.
Moreover, if the detectors (such as power meters 114A, 114B) that
measure each polarization component are noisy in nature (e.g., they
measure a finite amount of power even in the absence of
illumination with electromagnetic radiation), this range uniquely
measurable optical activity angles is further reduced. Since the
usable range of unique .DELTA..gamma. is limited, the measurable
range of .DELTA..lamda. is also limited. This limited measurable
range of .DELTA..lamda. is the FSR of the system. The measurable
range of .DELTA..lamda. is shown in plot 1402 with a solid line,
while the non-measurable range of wavelengths is shown in plot 1402
with a dashed line
[0098] FIG. 14B shows a plot 1406 with three pairs of OAM modes
(six modes total) excited in the optical fiber 108 at the same
time. The measurements 1408A from the first pair of OAM modes are
shown with a solid line. The measurements 1408B from the second
pair of OAM modes are shown with a dashed line. The measurements
1408C from the first pair of OAM modes are shown with a bold line
of repeating dashes and dots. With three different pairs of OAM
modes, there are three different optical activity angle
measurements for any given wavelength. The range over which there
is a unique mapping between the three optical activity angle
measurements and the wavelength is much greater, as compared to
when only using one OAM mode. By utilizing additional pairs of OAM
modes in some implementations, the free spectral range of the
disclosed systems can be increased from about 46 picometers to
about 365 nanometers. The new FSR of the systems is determined by
the composite spectral repetition range of all the pairs of OAM
modes used in taking measurements, allowing for a large degree of
enhancement. This FSR enhancement will also critically depend on
the parameters that determine each mode's optical activity
response, such as fiber length, wavelength, .DELTA.n.sub.g (between
each distinct pair of OAM modes), etc. This improvement occurs
without any sacrifice in system resolution. In some
implementations, the system resolution can even improve.
[0099] FIG. 14C shows an example plot 1412 of the system FSR versus
the number of modes. With only one mode, the system FSR 1414A is
less than 10.sup.-1 nanometers. With two modes, the system FSR
1414B increases to around 10.sup.1 nanometers. And with three
modes, the system FSR 1414C increases to above 10.sup.2 nanometers.
FIG. 14D shows a plot 1416 of the system resolution, plotted
against the number of modes. The value of the system resolution is
the smallest measurable change in wavelength .DELTA..lamda.. With
only one mode, the resolution 1418A is about 0.28 picometers. With
two modes, the resolution 1418B of the system has increased, with a
value of about 0.24 picometers. And with three modes, the
resolution 1418C has further increased, with a value of about 0.18
picometers. Thus, plots 1412 and 1416 demonstrate that as the
number of modes that are simultaneously excited in the fiber
increase, the range of measurable changes in wavelength .lamda.
increases, causing the system FSR to increase. Simultaneously, the
system resolution also increases.
[0100] FIG. 15 shows a representation of a multiplexed version of
any of the systems disclosed herein. As is shown, three different
OAM modes 1502A, 1502B, 1502C are excited in an optical fiber 108,
having length z. In the example, the three different OAM modes
correspond to L=10, L=11, and L=12. However, any number of OAM
modes having any topological charge value can be used. In FIG. 15,
the graphical representations the OAM modes 1502A, 1502B, 1502C are
intensity patterns in spiral shapes that result from interfering
the OAM modes with a Gaussian beam. However, these spiral intensity
patterns are shown for illustrative purposes only. The value of the
wavelength 1504 of the OAM modes can range from .lamda..sub.1 to
.lamda..sub.n.
[0101] Plot 1506 shows an illustrative example of the change in the
output angle of each of the three different modes (on polarization
axes where x polarization represents 0.degree. and y polarization
represents 90.degree.). As shown, the output angle 1508A of the
L=10 OAM mode (light dashed line) is less than the output angle
1508B of the L=11 OAM mode (dotted and dashed line), which is less
than the output angle 1508C of the L=12 OAM mode (heavy dashed
line). Plot 1510 shows the results of the wavelength measurements
using the multiplexed system. As is shown, each OAM mode results in
a distinct set of measurements 1512A (L=10), 1512B (L=11), 1512C
(L=12). Thus, distinct calibration factors .alpha. and resolving
powers R.sub.10, R.sub.111, and R.sub.12 can be identified. Thus,
by multiplexing, the system FSR can be increased, and high system
resolutions can be maintained, as described above. In these
multiplexing implementations, the systems can include a mode sorter
to separate the modes (e.g., sorting via the mode's topological
charge), and additional power detectors to measure the power of the
additional modes and/or the orthogonal components of the additional
modes. For example, if three pairs of OAM modes are used, a first
set of power detectors can be used to measure the first pair of OAM
modes or the components thereof, a second set of power detectors
can be used to measure the second pair of OAM modes or the
components thereof, and a third set of power detectors can be used
to measure the third pair of OAM modes or the components
thereof.
[0102] Thus, the disclosed systems can support the propagation of
multiple different pairs of circularly-polarized OAM modes all
having different topological charges. These different OAM modes can
all initially have a polarization angle .theta..sub.1 when entering
the optical fiber 108. Due to the different topological charges,
the different OAM modes generally all rotate a different amount in
the optical fiber, and thus are emitted from the optical fiber at
different polarization angles .theta..sub.2, .theta..sub.3,
.theta..sub.4, etc. These polarization angles can be used to
measure various properties of the electromagnetic radiation, as
discussed herein. In some implementations, OAM modes with different
topological charges could rotate the same amount in the optical
fiber, and thus have the same polarization angle when emitted from
the optical fiber.
[0103] Referring now to FIGS. 16A-16C, in some implementations, the
systems disclosed herein (including system 100, 1100, 1200, and
1300) can be used to measure the spectral bandwidth of the
electromagnetic radiation source. FIG. 16A shows a broadband
spectrum 1602 of electromagnetic radiation and a narrow spectrum
1604 of electromagnetic radiation. The broadband spectrum 1602
contains more wavelength components than the narrow spectrum 1604.
As the electromagnetic radiation with the broadband spectrum 1602
propagates in the optical fiber 108, the multiple wavelength
components all experience various degrees of rotation. The
superposition of all these optical activity rotations results in
elliptical polarization at the output of the optical fiber 108.
This ellipticity is deduced by measuring the visibility of the
electromagnetic radiation at the output of the fiber, as shown in
plot 1606 of FIG. 16B. The visibility of the system is
V=(P.sub.max-P.sub.min)/(P.sub.max+P.sub.min). Here, P.sub.max and
P.sub.min refer to the maximum and minimum power measured in the
two polarization arms of the output of the fiber. To perform this
measurement, power meter 114A is used to measure P.sub.max, while
power meter 114B is used to measure P.sub.min. In some
implementations, this is achieved by appropriately biasing
polarizing element 110 at a desired angle. In other
implementations, the system sweeps through the wavelengths of the
spectrum until the condition (P.sub.max on power meter 114A and
P.sub.min on power meter 114B) is met. If the functional form of
the spectrum is known (e.g., Lorentzian, Gaussian, Voigt, etc.),
then visibility measurements can be uniquely mapped to different
bandwidths, allowing for direct measurement of the spread of
wavelengths emitting from the electromagnetic radiation source.
[0104] FIG. 16C shows a plot 1608 of the experimental visibility of
one of the disclosed systems, versus the bandwidth of the
electromagnetic radiation being measured. In an example, the
spectral bandwidth of the electromagnetic radiation source is
controlled using an electro-optic phase modulator and arbitrary
waveform generator. As plot 1608 in FIG. 16C shows, as the
bandwidth of the source is progressively increased, the visibility
of the output decreases monotonically. This provides for a one to
one mapping between visibility and the bandwidth of the
electromagnetic radiation source, which is the parameter that can
be measured.
[0105] With only one optically activity pair of OAM modes,
implementation of the spectral bandwidth measurement technique
requires biasing either polarizing angle or wavelength. However, by
using the multiplexing principles described herein with respect to
at least FIGS. 14A-14D and 15, the measurement of complex spectra
generally does not require any biasing or a priori tuning of the
angles of the polarizing element 110, or of the wavelength of the
electromagnetic radiation source.
[0106] Referring to FIGS. 17A-17C, with multiple simultaneous
measurements using multiple OAM modes, more complex spectra
features could also be resolved. For example, changes in the
spectral amplitude and the spectral separation can be measured.
FIG. 17A shows a Gaussian double hump spectrum. The upper plot
1701A shows an example change in the spectral amplitude, while the
lower plot 1701B shows an example change in the spectral
separation. In the spectral amplitude plot 1701A, the initial
spectrum contains peaks 1702A and 1702B, which is lower than peak
1702B. The Gaussian double hump spectrum can be modified so that
peak 1702B transforms into peak 1703B. Plot 1708 in FIG. 17B shows
a plot of the system visibility versus the spectral amplitude
ratio. As can be seen, as the spectral amplitude ratio changes (for
example as shown in plot 1701A), the system visibility can be
measured for each of three different OAM modes, which allows for a
larger unique mapping of visibility to spectral amplitude
ratio.
[0107] Similarly, in the spectral separation plot 1701B, the
initial spectrum contains peaks 1704A, 1704B. The spectral
separation of the Gaussian double hump spectrum can be changed, so
that the spectrum consists of peaks 1706A, 170B, which have a
smaller spectral separation. Plot 1710 in FIG. 17C shows a plot of
the measured optical activity angle versus the spectral separation.
As can be seen, as the spectral separation changes (for example as
shown in plot 1701B), the optical activity angle can be measured
for each of three different OAM modes, which allows for a larger
unique mapping of visibility to spectral separation. Generally, by
multiplexing multiple OAM modes, any number of different features
of complex spectra can more accurately be measured. Therefore, with
enough modes available for multiplexing, the disclosed systems can
be used to measure spectral bandwidth, as well as additional and
more complex spectral parameters (such as spectral amplitude,
spectral separations, etc.), all while remaining in a single-shot
configuration.
[0108] While systems 100, 1100, 1200, and 1300 are shown with a
variety of different components, certain implementations require
fewer components than what is illustrated. For example, in some
implementations, these systems include only the electromagnetic
radiation source 102, the polarizing element 104, the mode
converter 106, the optical fiber 108, and the components necessary
to determine the final polarization angle. In systems 100 and 1100,
those additional components include at least the polarizing element
110, the mode converter 112, and the power meters 114A, 114B. In
system 1200, those additional components include at least the
polarizing element 110 that is a rotating linear polarizer, and the
power meter 1214. In system 1300, those additional components
include at least the polarimeter 1314. Thus, the disclosed systems
can include any number of different measurement devices that aid in
determining the angle of the electromagnetic radiation after it is
emitted from the optical fiber 108, and/or any further properties,
such as optical activity, wavelength, spectral bandwidth, spectral
amplitude, etc. These measurement devices can include any required
power meters, polarizing components, polarimeters, and/or
processing devices to analyze the data. Moreover, the use of any
mirrors, lenses, and other optical components used to direct the
electromagnetic radiation can be dependent on the specific set up
of the system and spatial concerns. For example, mirrors can be
used to make the systems more compact if needed.
[0109] Additionally, the disclosed systems can include any number
of processing devices to control any one or more of the components
of the systems, and/or to perform any of the analysis or
calculations discussed herein. For example, the systems may include
a processing device (such as a desktop computer, a laptop computer,
etc.) coupled to the power meters 114A, 114B, power meter 1214, or
polarimeter 1314. The processing device can be configured to
receive data indicative of the measurements performed by those
devices, and process that data to generate the polarization angle
of the electromagnetic radiation emitted by the optical fiber 108.
The processing device can then perform any necessary analysis or
calculations needed to determine the change in optical activity
angle, and map that change in optical activity angle to a change in
wavelength. The processing device(s) can also perform any necessary
analysis or calculations needed to determine the system's
visibility, and map that visibility to a specific or change in
spectral bandwidth. The processing device(s) can also perform any
necessary analysis or calculations needed to manipulate the power
detector measurements and map the power meter measurements to some
spectral property or properties.
[0110] While the present disclosure has been described with
reference to one or more particular implementations, those skilled
in the art will recognize that many changes may be made thereto
without departing from the spirit and scope of the present
disclosure. Each of these implementations and obvious variations
thereof is contemplated as falling within the spirit and scope of
the present disclosure. It is also contemplated that additional
implementations according to aspects of the present disclosure may
combine any number of features from any of the implementations
described herein.
ALTERNATIVE IMPLEMENTATIONS
[0111] Alternative Implementation 1.
[0112] A system for measuring a property of electromagnetic
radiation, the system comprising: an electromagnetic radiation
source configured to produce electromagnetic radiation; a
polarizing element configured to receive the electromagnetic
radiation produced by the electromagnetic radiation source and
output linearly-polarized electromagnetic radiation having a linear
polarization angle .theta..sub.1; a mode converter configured to
receive the linearly-polarized electromagnetic radiation and output
an orbital angular momentum (OAM) mode of linearly-polarized
electromagnetic radiation with a topological charge L.sub.i, the
OAM mode of linearly-polarized electromagnetic radiation being a
superposition of (i) a first OAM mode with topological charge
L.sub.i and a first circular polarization, and (ii) a second OAM
mode with topological charge L.sub.i and a second circular
polarization, the first circular polarization being opposite from
the second circular polarization; an optical fiber configured to
receive the first OAM mode and the second OAM mode, and support
propagation to an output of the optical fiber of the first OAM mode
with an effective index n.sub.eff1 and the second OAM mode with an
effective index n.sub.eff2, an absolute difference .DELTA.n.sub.eff
between n.sub.eff1 and n.sub.eff2 being greater than or equal to
5.times.10.sup.-5, such that linearly-polarized electromagnetic
radiation having a topological charge L.sub.i and a linear
polarization angle .theta..sub.2 is emitted at the output of the
optical fiber; and one or more measurement devices configured to
determine the property of the electromagnetic radiation based at
least on the polarization angle .theta..sub.2 of the
electromagnetic radiation emitted at the output of the optical
fiber.
[0113] Alternative Implementation 2.
[0114] The system of Alternative Implementation 1, wherein the
first OAM mode is left circularly-polarized and the second OAM mode
is right circularly-polarized, or the first OAM mode is right
circularly-polarized and the second OAM mode is left
circularly-polarized.
[0115] Alternative Implementation 3.
[0116] The system of Alternative Implementation 1, wherein the
optical fiber is a ring-core optical fiber formed from a ring-core
and a cladding layer surrounding the ring-core, the ring-core
guiding the first OAM mode and the second OAM mode within the
fiber.
[0117] Alternative Implementation 4.
[0118] The system of Alternative Implementation 3, wherein the
ring-core includes an annular body and a hollow center.
[0119] Alternative Implementation 5.
[0120] The system of Alternative Implementation 4, wherein the
annular body of the ring-core is formed from germanium-doped
silicon dioxide, and the cladding is formed from silicon
dioxide.
[0121] Alternative Implementation 6.
[0122] The system of Alternative Implementation 4, wherein the
annular body of the ring-core has a higher refractive index than
both the hollow center of the ring-core and the cladding layer.
[0123] Alternative Implementation 7.
[0124] The system of Alternative Implementation 3, wherein the
ring-core has a higher refractive index than the cladding
layer.
[0125] Alternative Implementation 8.
[0126] The system of Alternative Implementation 1, further
comprising: an additional polarizing element configured to receive
the linearly-polarized electromagnetic radiation from the output of
the optical fiber and convert the linearly-polarized
electromagnetic radiation having the linear polarization angle
.theta..sub.2 into a first component have a linear polarization
angle .theta..sub.n and a second component having a linear
polarization angle .theta..sub.n+90.degree.; a first power meter
configured to measure a power of the first component having the
linear polarization angle .theta..sub.n; and a second power meter
configured to measure a power of the second component having the
linear polarization angle .theta..sub.n+90.degree., wherein the
determined property of the produced electromagnetic radiation is
based at least on the measured power of the first component and the
measured power of the second component.
[0127] Alternative Implementation 9.
[0128] The system of Alternative Implementation 8, wherein the
determined property is an optical activity angle .gamma. determined
according to .gamma.=.theta..sub.2-.theta..sub.1 and
.theta. 2 = tan - 1 ( P .theta. n + 9 0 .smallcircle. P .theta. n )
, ##EQU00007##
where P.sub..theta..sub.1 is the measured power of the first
component having the linear polarization angle .theta..sub.1, and
where P.sub..theta..sub.n+90.degree. is the measured power of the
second component having the linear polarization angle
.theta..sub.n+90.degree..
[0129] Alternative Implementation 10.
[0130] The system of Alternative Implementation 8, wherein the
system is configured to determine an optical activity angle
difference .DELTA..gamma. between (i) a first optical activity
angle .gamma..sub.1 of a first beam of electromagnetic radiation
having a first center wavelength .lamda..sub.1, and (ii) a second
optical activity angle .gamma..sub.2 of a second beam of
electromagnetic radiation having a second center wavelength
.lamda..sub.2.
[0131] Alternative Implementation 11.
[0132] The system of Alternative Implementation 10, wherein the
system is configured to determine a wavelength difference
.DELTA..lamda. between the first beam of electromagnetic radiation
and the second beam of electromagnetic radiation, based on the
optical activity angle difference .DELTA..gamma..
[0133] Alternative Implementation 12.
[0134] The system of Alternative Implementation 13, wherein the
wavelength .lamda. of the produced electromagnetic radiation is
determined according to
.DELTA. .lamda. = - .pi. z .DELTA. n g .lamda. 2 , ##EQU00008##
where z is a length of the optical fiber, and .DELTA.n.sub.g is a
group index difference between the first OAM mode and the second
OAM mode.
[0135] Alternative Implementation 13.
[0136] The system of Alternative Implementation 12, wherein
- .pi. z .DELTA. n g .lamda. 2 ##EQU00009##
is determined experimentally prior to determining the first optical
activity angle .gamma..sub.1 of the first beam of electromagnetic
radiation and the second optical activity angle .gamma..sub.2 of
the second beam of electromagnetic radiation.
[0137] Alternative Implementation 14.
[0138] The system of Alternative Implementation 8, wherein the
additional polarizing element is a polarization beam splitter, a
rotatable linear polarizer, or a polarimeter.
[0139] Alternative Implementation 15.
[0140] The system of Alternative Implementation 1, wherein the
determined property is a wavelength of the produced electromagnetic
radiation.
[0141] Alternative Implementation 16.
[0142] The system of Alternative Implementation 1, wherein the
produced electromagnetic radiation includes electromagnetic
radiation in a range of wavelengths, and wherein the determined
property is (i) a center wavelength of the range of wavelengths,
(ii) a spread of wavelengths in the range of wavelengths, or (iii)
both (i) and (ii).
[0143] Alternative Implementation 17.
[0144] The system of Alternative Implementation 1, wherein the
optical fiber has a length of between about 1 centimeter and about
1 kilometer.
[0145] Alternative Implementation 18.
[0146] The system of Alternative Implementation 1, wherein the
first OAM mode propagates with a group index
n g 1 = n eff 1 - .lamda. d n e f f 1 d .lamda. , ##EQU00010##
and wherein the second OAM mode propagates with group index
n g 2 = n e f f 2 - .lamda. d n e f f 2 d .lamda. .
##EQU00011##
[0147] Alternative Implementation 19.
[0148] The system of Alternative Implementation 18, wherein an
absolute difference .DELTA.n.sub.g between the group index n.sub.g1
of the first OAM mode and the group index n.sub.g2 of the second
OAM mode increases with the topological charge L.sub.i.
[0149] Alternative Implementation 20.
[0150] The system of Alternative Implementation 1, wherein the
topological charge L.sub.i is greater than or equal to 1.
[0151] Alternative Implementation 21.
[0152] The system of Alternative Implementation 20, wherein the
topological charge L.sub.i is between about 1 and about 200.
[0153] Alternative Implementation 22.
[0154] The system of Alternative Implementation 1, wherein the
property of the produced electromagnetic radiation is a wavelength
of the produced electromagnetic radiation, and wherein the system
has a wavelength resolution based at least in part on a length of
the optical fiber, the wavelength resolution of the system being a
smallest detectable wavelength difference between electromagnetic
radiation having two different wavelengths.
[0155] Alternative Implementation 23.
[0156] The system of Alternative Implementation 22, wherein the
wavelength resolution is about 2.1 nanometers, and wherein the
length of the optical fiber is equal to or greater than 1.0
centimeters.
[0157] Alternative Implementation 24.
[0158] The system of Alternative Implementation 22, wherein the
wavelength resolution is about 0.2 nanometers, and wherein the
length of the optical fiber is equal to or greater than 6.0
centimeters.
[0159] Alternative Implementation 25.
[0160] The system of Alternative Implementation 22, wherein the
length of the optical fiber is greater than or equal to 1
centimeter.
[0161] Alternative Implementation 26.
[0162] The system of Alternative Implementation 22, wherein the
wavelength resolution is less than or equal to 1.2 nanometers.
[0163] Alternative Implementation 27.
[0164] The system of Alternative Implementation 1, wherein the
electromagnetic radiation emitted at the output optical fiber
includes one or more additional modes.
[0165] Alternative Implementation 28.
[0166] The system of Alternative Implementation 27, further
comprising an additional mode converter configured to (i) cause the
electromagnetic radiation emitted at the output of the fiber to
have a topological charge L.sub.f=0, and (ii) cause the one or more
additional modes to have a topological charge L.sub.d .noteq.0,
[0167] Alternative Implementation 29.
[0168] The system of Alternative Implementation 28, further
comprising at least one iris positioned between the additional mode
converter and the least one measurement devices, the at least one
iris being configured to prevent the one or more additional modes
from reaching the one or more measurement devices.
[0169] Alternative Implementation 30.
[0170] The system of Alternative Implementation 29, further
comprising a single-mode fiber being positioned between the
additional mode converter and the at least one measurement device,
the single-mode fiber supporting propagation of the first OAM mode
and the second OAM mode, thereby preventing the one or more
degenerate modes from reaching the at least one measuring
devices.
[0171] Alternative Implementation 31.
[0172] The system of Alternative Implementation 27, wherein at
least one of the one or more additional modes is a degenerate
mode.
[0173] Alternative Implementation 32.
[0174] The system of Alternative Implementation 1, wherein the mode
converter is further configured to output additional OAM modes of
the linearly-polarized electromagnetic radiation.
[0175] Alternative Implementation 33.
[0176] The system of Alternative Implementation 32, wherein the
additional OAM modes include a third OAM mode and a fourth OAM
mode, the third OAM mode and the fourth OAM mode having an
identical topological charge that is different than the topological
charge of the first OAM mode and the second OAM mode, the third OAM
mode and the fourth OAM mode having opposing circular
polarizations.
[0177] Alternative Implementation 34.
[0178] The system of Alternative Implementation 33, wherein the
additional OAM modes further include a fifth OAM mode and a sixth
OAM mode, the fifth OAM mode and the sixth OAM mode having an
identical topological charge that is different than (i) the
topological charge of the first OAM mode and the second OAM mode,
and (i) the topological charge of the third OAM mode and the fourth
OAM mode, the fifth OAM mode and the sixth OAM mode having opposing
circular polarizations.
[0179] Alternative Implementation 35.
[0180] The system of Alternative Implementation 34, further
comprising a mode sorter configured to direct (i) the first OAM
mode and a second OAM mode to a first set of the one or more
measurement devices, (ii) the third OAM mode and a fourth OAM mode
to a second set of the one or more measurement devices, and (iii)
the fifth OAM mode and a sixth OAM mode to a third set of the one
or more measurement devices.
[0181] Alternative Implementation 36.
[0182] The system of Alternative Implementation 35, wherein the
determination of the property of the produced electromagnetic
radiation is determined based on measurements of the first set of
the one or more measurement devices, and at least one of the second
set of the one or more measurement devices or the third set of one
or more measurement devices.
[0183] Alternative Implementation 37.
[0184] The system of Alternative Implementation 36, wherein the
determination of the property of the produced electromagnetic
radiation based on the first OAM mode and the second OAM mode has a
first free spectral range, and wherein a determination of the
property of the produced electromagnetic radiation based on the
first OAM mode, the second OAM mode, the third OAM mode, and the
fourth OAM mode has a second free spectral range greater than the
first free spectral range.
[0185] Alternative Implementation 38.
[0186] The system of Alternative Implementation 37, wherein a
determination of the property of the produced electromagnetic
radiation based on the first OAM mode, the second OAM mode, the
third OAM mode, the fourth OAM mode, the fifth OAM mode, and the
sixth OAM mode has a third free spectral range greater than the
first free spectral range and the second free spectral range.
[0187] Alternative Implementation 39.
[0188] The system of Alternative Implementation 1, wherein the
determined property of the electromagnetic radiation includes a
change in optical activity angle, a change in wavelength, a
visibility, a spectral bandwidth, a spectral amplitude, a spectral
amplitude ratio, a spectral separation, or any combination thereof,
a center wavelength in a range of wavelengths, a spread of
wavelengths in the range of wavelengths, or any combination
thereof.
[0189] Alternative Implementation 40.
[0190] The system of Alternative Implementation 1, wherein the one
or more measurement devices include: a rotatable polarizing element
configured to receive the linearly-polarized electromagnetic
radiation emitted at the output of the optical fiber; and a power
meter configured to measure a power of electromagnetic radiation
passing through the rotatable polarizing element, wherein the
rotatable polarizing element is configured to allow a maximum
amount of the linearly-polarized electromagnetic radiation emitted
at the output of the optical fiber to pass when a rotation angle of
the rotatable polarizing element matches the linear polarization
angle .theta..sub.2.
[0191] Alternative Implementation 41.
[0192] The system of Alternative Implementation 1, wherein the one
or more measurement devices include a polarimeter configured to
receive the linearly-polarized electromagnetic radiation emitted at
the output of the optical fiber and measure the linear polarization
angle .theta..sub.2.
[0193] Alternative Implementation 42.
[0194] A method for measuring a property of electromagnetic
radiation, the method comprising: emitting electromagnetic
radiation from an electromagnetic radiation source; converting the
electromagnetic radiation to linearly-polarized electromagnetic
radiation having a polarization angle .theta..sub.1; converting the
linearly-polarized electromagnetic radiation into a first orbital
angular momentum (OAM) mode of linearly-polarized electromagnetic
radiation with a topological charge L.sub.1, the OAM mode of
linearly-polarized electromagnetic radiation being a superposition
of (i) a first OAM mode with topological charge L.sub.1 and a first
circular polarization, and (ii) a second OAM mode with topological
charge L.sub.1 and a second circular polarization, the first
circular polarization being opposite from the second circular
polarization; causing (i) the first OAM mode of linearly-polarized
electromagnetic radiation to propagate through an optical fiber
with an effective index n.sub.eff1 and (ii) the second OAM mode of
linearly-polarized electromagnetic radiation to propagate through
the optical fiber with an effective index n.sub.eff2, an absolute
difference .DELTA.n.sub.eff between n.sub.eff1 and n.sub.eff2 being
greater than or equal to 5.times.10.sup.-5, such that
linearly-polarized electromagnetic radiation having a topological
charge L.sub.1 and a linear polarization angle .theta..sub.2 is
emitted at the output of the optical fiber; determining the
property of the produced electromagnetic radiation based at least
on the linear polarization angle .theta..sub.2.
[0195] Alternative Implementation 43.
[0196] The method of Alternative Implementation 42, further
comprising: converting the linearly-polarized electromagnetic
radiation emitted at the output of the optical fiber into a first
component have a linear polarization angle .theta..sub.n and a
second component having a linear polarization angle
.theta..sub.n+90.degree.; measuring a power of the first component
having the linear polarization angle .theta..sub.n; measuring a
power of the second component having the linear polarization angle
.theta..sub.n+90.degree.; and determining the property of the
produced electromagnetic radiation based at least on the measured
power of the first component and the measured power of the second
component.
[0197] Alternative Implementation 44.
[0198] The method of Alternative Implementation 42, further
comprising: converting the linearly-polarized electromagnetic
radiation into a second OAM mode of linearly-polarized
electromagnetic radiation with a topological charge L.sub.2, the
additional OAM mode of linearly-polarized electromagnetic radiation
being a superposition of (i) a third OAM mode with topological
charge L.sub.2 and the first circular polarization, and (ii) a
fourth OAM mode with topological charge L.sub.2 and the second
circular polarization; causing the third OAM mode and the fourth
OAM mode to propagate through the optical fiber with the first OAM
mode and the second OAM mode such that the linearly-polarized
electromagnetic radiation emitted at the output of the optical
fiber includes (i) linearly-polarized electromagnetic radiation
having the topological charge L.sub.1 and the linear polarization
angle .theta..sub.2 and (ii) linearly-polarized electromagnetic
radiation having the topological charge L.sub.2 and the linear
polarization angle .theta..sub.3; determining the property of the
produced electromagnetic radiation based at least on the linear
polarization angle .theta..sub.2 and the linear polarization angle
.theta..sub.3.
[0199] Alternative Implementation 45.
[0200] The method of Alternative Implementation 44, wherein the
determination of the property of the produced electromagnetic
radiation based on the linear polarization angle .theta..sub.2 has
a first free spectral range, and wherein the determination of the
property of the produced electromagnetic radiation based on the
linear polarization angle .theta..sub.2 and the linear polarization
angle .theta..sub.3 has a second free spectral range greater than
the first free spectral range.
[0201] Alternative Implementation 46.
[0202] The method of Alternative Implementation 44, further
comprising: converting the linearly-polarized electromagnetic
radiation into a third OAM mode of linearly-polarized
electromagnetic radiation with a topological charge L.sub.2, the
additional OAM mode of linearly-polarized electromagnetic radiation
being a superposition of (i) a fifth OAM mode with topological
charge L.sub.3 and the first circular polarization, and (ii) a
sixth OAM mode with topological charge L.sub.3 and the second
circular polarization; causing the fifth OAM mode and the sixth OAM
mode to propagate through the optical fiber with the first OAM
mode, the second OAM mode, the third OAM mode, and the fourth OAM
mode such that the linearly-polarized electromagnetic radiation
emitted at the output of the optical fiber includes (i)
linearly-polarized electromagnetic radiation having the topological
charge L.sub.1 and the linear polarization angle .theta..sub.2,
(ii) linearly-polarized electromagnetic radiation having the
topological charge L.sub.2 and the linear polarization angle
.theta..sub.3, and (iii) linearly-polarized electromagnetic
radiation having the topological charge L.sub.3 and the linear
polarization angle .theta..sub.4; determining the property of the
produced electromagnetic radiation based at least on the linear
polarization angle .theta..sub.2, the linear polarization angle
.theta..sub.3, and the linear polarization angle .theta..sub.4.
[0203] Alternative Implementation 47.
[0204] The method of Alternative Implementation 46, wherein the
determination of the property of the produced electromagnetic
radiation based on the linear polarization angle .theta..sub.2, the
linear polarization angle .theta..sub.3, and the linear
polarization angle .theta..sub.4 has a third free spectral range
greater than the first free spectral range and the second free
spectral range.
[0205] Alternative Implementation 48.
[0206] The method of Alternative Implementation 46, further
comprising: causing, after being emitted at the output of the
optical fiber, the first OAM mode of linearly-polarized
electromagnetic radiation, the second OAM mode of
linearly-polarized electromagnetic radiation, and the third OAM
mode of linearly-polarized electromagnetic radiation pass through a
rotatable polarizing element as the rotatable polarizing element
rotates; measuring a maximum power and a minimum power of the first
OAM mode of linearly-polarized electromagnetic radiation passing
through the rotatable polarizing element; measuring a maximum power
and a minimum power of the second OAM mode of linearly-polarized
electromagnetic radiation passing through the rotatable polarizing
element; measuring a maximum power and a minimum power of the third
OAM mode of linearly-polarized electromagnetic radiation passing
through the rotatable polarizing element; determining a visibility
for each of the first OAM mode, the second OAM mode, and the third
OAM mode, based at least on the maximum and minimum power of each
of the first OAM mode, the second OAM mode, and the third OAM mode
passing through the rotatable polarizing element; and determining a
spectral bandwidth of the emitted electromagnetic radiation based
at least on the determined visibility for each of the first OAM
mode, the second OAM mode, and the third OAM mode.
[0207] Alternative Implementation 49.
[0208] A system for measuring a linear polarization angle of
electromagnetic radiation, the system comprising: an
electromagnetic radiation source configured to produce
electromagnetic radiation; a polarizing element configured to
receive the electromagnetic radiation produced by the
electromagnetic radiation source and output linearly-polarized
electromagnetic radiation having a linear polarization angle
.theta..sub.1; a mode converter configured to receive the
linearly-polarized electromagnetic radiation and output an orbital
angular momentum (OAM) mode of linearly-polarized electromagnetic
radiation with a topological charge L.sub.i, the OAM mode of
linearly-polarized electromagnetic radiation being a superposition
of (i) a first OAM mode with topological charge L.sub.i and a first
circular polarization, and (ii) a second OAM mode with topological
charge L.sub.i and a second circular polarization, the first
circular polarization being opposite from the second circular
polarization; an optical fiber configured to receive the first OAM
mode and the second OAM mode, and support propagation to an output
of the optical fiber of the first OAM mode with an effective index
n.sub.eff1 and the second OAM mode with an effective index
n.sub.eff2, an absolute difference .DELTA.n.sub.eff between
n.sub.eff1 and n.sub.eff2 being greater than or equal to
5.times.10.sup.-5, such that linearly-polarized electromagnetic
radiation having a topological charge L.sub.i and a linear
polarization angle .theta..sub.2 is emitted at the output of the
optical fiber; and a rotatable polarizing element configured to
allow a maximum amount of the linearly-polarized electromagnetic
radiation emitted at the output of the optical fiber to pass when a
rotation angle of the rotatable polarizing element matches the
linear polarization angle .theta..sub.2.
[0209] Alternative Implementation 50.
[0210] A system for measuring a linear polarization angle of
electromagnetic radiation, the system comprising: an
electromagnetic radiation source configured to produce
electromagnetic radiation; a polarizing element configured to
receive the electromagnetic radiation produced by the
electromagnetic radiation source and output linearly-polarized
electromagnetic radiation having a linear polarization angle
.theta..sub.1; a mode converter configured to receive the
linearly-polarized electromagnetic radiation and output an orbital
angular momentum (OAM) mode of linearly-polarized electromagnetic
radiation with a topological charge L.sub.i, the OAM mode of
linearly-polarized electromagnetic radiation being a superposition
of (i) a first OAM mode with topological charge L.sub.i and a first
circular polarization, and (ii) a second OAM mode with topological
charge L.sub.i and a second circular polarization, the first
circular polarization being opposite from the second circular
polarization; an optical fiber configured to receive the first OAM
mode and the second OAM mode, and support propagation to an output
of the optical fiber of the first OAM mode with an effective index
n.sub.eff1 and the second OAM mode with an effective index
n.sub.eff2, an absolute difference .DELTA.n.sub.eff between
n.sub.eff1 and n.sub.eff2 being greater than or equal to
5.times.10.sup.-5, such that linearly-polarized electromagnetic
radiation having a topological charge L.sub.i and a linear
polarization angle .theta..sub.2 is emitted at the output of the
optical fiber; and a polarimeter configured to receive the
linearly-polarized electromagnetic radiation emitted at the output
of the optical fiber and measure the linear polarization angle
.theta..sub.2.
[0211] It is expressly contemplated that one or more elements or
any portion(s) thereof from any of the Alternative Implementations
1-50 above can be combined with one or more elements or any
portion(s) thereof from any of the other ones of the Alternative
Implementations 1-50 to form one or more additional alternative
implementations of the present disclosure.
* * * * *