US 11,209,314 B2

11

Cavity buildup dispersion spectrometer 200 and processes
herein unexpectedly provides information on time scales as
short as the round-trip time of the electromagnetic radiation
within the resonator, which for high-Q systems is orders of
magnitude shorter than the decay time of the resonator. This
temporal response makes measurements by the cavity
buildup dispersion spectrometer inherently more rapid than
those performed by conventional cavity enhanced spectros-
copy methods that are rate limited by resonator decay times
or transmittance. Moreover, cavity buildup dispersion spec-
trometer 200 provides accurate, first-principles measure-
ments of refractive index, cavity length, and the like, that are
directly linked to the SI dimensions of time or frequency,
precluding the need for calibration against reference mate-
rials.

The articles and processes herein are illustrated further by
the following Examples, which are non-limiting

EXAMPLES

Example 1. Intermode Cavity Build-Up
Spectroscopy

Intermode cavity buildup spectroscopy (ICBUS) was per-
formed. FIG. 9 shows two half-cycles from a heterodyne-
detected cavity ring-down spectroscopy (HD-CRDS) style
of alternating adjacent cavity mode transmission signal
acquisition. The top panels show the time-domain (left) and
Fourier domain (right) spectrum of a half cycle with the

pumping frequency £3 228 nominally on-resonance (analo- 3

gous to HD-CRDS). The dashed trace in the top right panel
is a Lorentzian fit. The bottom panels show the second half
cycles, with the pumping beam now off-resonance by a
programmed detuning beat frequency 231 of AVj.,,-8.75

kHz (>10 cavity half-widths). The trace in the bottom right 3

panel is the fit within the beat region near vg, to a modified
electric-field ICBUS model (two frequencies plus one cross
term only). Floated in the Fourier domain analysis were
values of ¥,. AVjeqx and the cavity mode decay rate (I’)

FIG. 10 shows fitted parameters from a continuous time
series of pairs of alternating half cycles. ICBUS model
results are shown in the top three panels (I, Vg). and AVjea,)s
and the HD-CRDS results are in the bottom two panels (I,
Voeat)

The Allan deviation of Av,,.,, is plotted versus time in
FIG. 11. The fitted value of Av,,,, hits a flicker noise floor
of ~1 Hz. This is likely limited by the Pound-Drever-Hall
(PDH) phase-locked loop, maybe from 1/f noise in the
electronic circuit. ICBUS should be limited by the linewidth
of the locked laser relative to the cavity, a limit of mutual
coherence in the transient time-domain signals. Also shown
in FIG. 11 is a dashed line for thermal-noise limit for the
optical cavity stability for which measurement of vg, is not
subject to this limitation.

Fitted precision on the ICBUS fitted parameters was
reduced when the PDH lock performance was degraded, but
accuracy was not. This is not present in HD-CRDS, wherein
accuracy in the Fourier domain analysis was degraded by the
PDH lock.

Example 2. Cavity Buildup Dispersion
Spectroscopy

Measurements of ultrahigh-fidelity absorption spectra can
help validate quantum theory, engineer ultracold chemistry,
and remotely sense atmospheres. Recent achievements in
cavity-enhanced spectroscopy using either frequency-based

S

20

40

&

60

12

dispersion or time-based absorption approaches have set
new records for accuracy with uncertainties at the sub-per-
mil level. However, laser scanning or susceptibility to non-
linearities limits their ultimate performance. Here we pres-
ent cavity buildup dispersion spectroscopy (CBDS) in which
the dispersive frequency shift of a cavity resonance is
encoded in the cavity’s transient response to a phase-locked
non-resonant laser excitation. Beating between optical fre-
quencies during buildup exactly localizes detuning from
mode center, and thus enables single-shot dispersion mea-
surements. CBDS can yield an accuracy limited by the
chosen frequency standard and measurement duration and is
currently 50 times less susceptible to detection nonlinearity
compared to intensity-based methods. Moreover, CBDS is

5 significantly faster than previous frequency-based cavity-

enhanced methods. The generality of CBDS shows promise
for improving fundamental research into a variety of light-
matter interactions.

Highly accurate models of light-matter interactions can be
used for fundamental studies of molecular hydrogen, engi-
neering of ultracold chemistry, tests of molecular structure
calculations, modeling of planetary atmospheres, and the
development of advanced spectroscopic databases. The lat-
ter application can provide improvements in remote sensing

s and measurements of variations in greenhouse gas concen

trations at 0.1% uncertainty levels required to better predict
changes in earth’s climate. To develop and test these models
using first-principles approaches, accurate experimental
techniques are required.

Recent achievements in cavity-enhanced spectroscopy
using either frequency-based dispersion or time-based
absorption approaches have set new records for accuracy
with uncertainties at the sub-per-mil level. However, laser
scanning or susceptibility to nonlinearities limits their ulti-
mate performance. Cavity mode-dispersion spectroscopy
(CMDS) is one such technique recently developed to meet
these challenges. While CMDS yields absorption spectra
entirely in terms of measured optical frequency shifts, the
shifts are not read out instantaneously. This is also true for
multiplexed approaches to CMDS performed with a broad-
band optical frequency comb. Consequently, these CMDS
techniques are susceptible to drifts. Although frequency-
agile rapid scanning (FARS) spectroscopy provides single-
shot acquisition of local absorption limited only by the

5 cavity response time, it is an intensity-based technique and

inherently susceptible to nonlinearities in the detection sys-
tem. Therefore, each of these established techniques in
ultrasensitive absorption spectroscopy has a critical weak-
ness.

Cavity buildup dispersion spectroscopy (CBDS) provides
an accurate measurement of cavity mode frequency that can
be implemented on time scales that are substantially shorter
than the cavity buildup time. In CBDS, a frequency-locked
laser beam is instantaneously injected into a high-finesse

5 cavity followed by observation of the transient transmitted

signal. The net response involves optical interference
between the excitation and the transient cavity fields, with
the latter field occurring at the local cavity resonance
frequency and in opposition to the former field. Thus,
measurement of the resulting heterodyne beat frequency
provides the local cavity mode position. In practice, absorp-
tion-induced dispersion within the resonator leads to
changes in the measured mode-by-mode beat frequencies,
which yield dispersion spectra. CBDS measurements can be

5 made on timescales equal to or significantly less than the

buildup duration and show the method to be highly immune
to nonlinear response in the detection system. This speed


US 11,209,314 B2

Sheet 12 of 12

Dec. 28, 2021

U.S. Patent

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US 11,209,314 B2

19

Sup __ImlL(vy ~0))
AT, moRe{L(oq = @0)}"

(10)

For symmetric line profiles Re{ £(-«,)}, Im{ L(-
,)} is an odd function centered on w,, such that Aw,>0 for
o>, and Aw,<0 for @<w,. This means that ab sorption-
induced dispersion tends to “push” local cavity modes away
from their unperturbed positions. In practice, this result can
be used to disambiguate the signs of measured heterodyne
beat frequencies.

While one or more embodiments have been shown and
described, modifications and substitutions may be made
thereto without departing from the spirit and scope of the
invention. Accordingly, it is to be understood that the present
invention has been described by way of illustrations and not
limitation. Embodiments herein can be used independently
or can be combined.

All ranges disclosed herein are inclusive of the endpoints,
and the endpoints are independently combinable with each
other. The ranges are continuous and thus contain every
value and subset thereof in the range. Unless otherwise
stated or contextually inapplicable, all percentages, when
expressing a quantity, are weight percentages. The suflix
“(s)” as used herein is intended to include both the singular
and the plural of the term that it modifies, thereby including
at least one of that term (¢.g., the colorant(s) includes at least
one colorants). “Optional” or “optionally” means that the

subsequently described event or circumstance can or cannot ;

occur, and that the description includes instances where the
event occurs and instances where it does not. As used herein,
“combination” is inclusive of blends, mixtures, alloys, reac-
tion products, and the like.

As used herein, “a combination thereof” refers to a
combination comprising at least one of the named constitu-
ents, components, compounds, or elements, optionally
together with one or more of the same class of constituents,
components, compounds, or elements.

All references are incorporated herein by reference.

The use of the terms “a” and “an” and “the” and similar
referents in the context of describing the invention (espe-
cially in the context of the following claims) are to be
construed to cover both the singular and the plural, unless
otherwise indicated herein or clearly contradicted by con-
text. “Or” means “and/or.” It should further be noted that the
terms “first,” “second,” “primary.” “secondary,” and the like
herein do not denote any order, quantity, or importance, but
rather are used to distinguish one element from another. The
modifier “about” used in connection with a quantity is
inclusive of the stated value and has the meaning dictated by
the context (e.g., it includes the degree of error associated
with measurement of the particular quantity). The conjunc-
tion “or” is used to link objects of a list or alternatives and
is not disjunctive; rather the elements can be used separately
or can be combined together under appropriate circum-
stances.

What is claimed is:

1. A cavity buildup dispersion spectrometer comprising:

a shutter that receives coherent electromagnetic radiation,

modulates the coherent electromagnetic radiation at a
shutter frequency; and produces modulated electro-
magnetic radiation from the coherent electromagnetic
radiation;

a frequency shifter in communication with the shutter and

that receives the modulated electromagnetic radiation
from the shutter, frequency shifts the modulated elec-

0

2

35

&

0

20

tromagnetic radiation by a shifter frequency; and pro-

duces frequency shifted radiation that is different from

the modulated electromagnetic radiation by the shifter
frequency:

a resonator in communication with the frequency shifter
and comprising:

a plurality of mirrors separated by a distance;

an intracavity space interposed between the mirrors
having the distance as a length; and
plurality of cavity modes comprising: a primary
cavity mode at a primary resonance frequency; and
a secondary cavity mode at a secondary resonance
frequency, such that the resonator:
receives the frequency shifted radiation from the

frequency shifter;
receives coherent electromagnetic radiation;
produces cavity radiation, in the intracavity space,

from the frequency shifted radiation and the
coherent electromagnetic radiation;
receives an analyte in the intracavity space;
subjects the analyte to the cavity radiation
transmits the cavity radiation as transmitted electro-
magnetic radiation; and
a receiver in communication with the resonator and that:
receives the transmitted electromagnetic radiation from
the resonator; and

produces detector signal from the transmitted electro-
magnetic radiation, such that the detector signal
comprises a beat frequency that corresponds to a
change in a motion of resonator that comprises a
change in the distance between the mirrors or a
change of refractive index of the analyte in the
intracavity space.

2. The cavity buildup dispersion spectrometer of claim 1,
further comprising a frequency locking loop in communi-
cation with the resonator and the second coherent electro-
magnetic source and that:

receives second coherent radiation from the resonator;

produces a coherent electromagnetic radiation from the
second coherent radiation; and

communicates the coherent electromagnetic radiation to
the second coherent electromagnetic source.

3. The cavity buildup dispersion spectrometer of claim 2.
wherein the resonator produces the second coherent radia-
tion from the cavity radiation, and the resonator communi-
cates the second coherent radiation to the frequency locking
loop.

4. The cavity buildup dispersion spectrometer of claim 3,
wherein the frequency locking loop comprises:

a receiver in communication with the resonator and
receives the second coherent radiation from the reso-
nator and produces an electronic error signal from the
second coherent radiation;

a loop filter in communication with the receiver and that
receives the electronic error signal from the receiver
and produces a feedback control signal from the elec-
tronic error signal; and

an electromagnetic source in communication with the
loop filter and that: receives the feedback control signal
from the loop filter, produces a coherent electromag-
netic radiation from the feedback control signal, and
communicates the coherent electromagnetic radiation
to a second coherent electromagnetic source and the
resonator.

5. The cavity buildup dispersion spectrometer of claim 4,

further comprising the second coherent electromagnetic

.


U.S. Patent Dec. 28, 2021 Sheet 3 of 12 US 11,209,314 B2

4 * 233
227~ 78 228~| |
i2 A
zB
A
c
8 i2
=

Frequency

FIG. 3


US 11,209,314 B2

13

makes possible entirely new studies in dynamic cavity
response for physical sensing, as well as time-resolved
spectroscopy of transient free radicals and other short-lived
species in both thermal and non-thermal gases.

Techniques in condensed-phase sensing can use micro-
resonators with optical quality factors of Q<10* to readout
dispersive signals on nanosecond timescales. Those
approaches leverage heterodyne and rapidly swept laser
cavity ring-down readout concepts developed decades ago to
reduce technical noise and improve sensitivity. Dispersive
sensing uses decaying signals which occur after the cavity
driving field is effectively extinguished. Unlike this
Example, dispersive micro-resonator sensors do not probe
the temporal region associated with cavity buildup—a
regime which includes two synchronous fields of interest
here: a non-resonant laser-driven field with rapidly changing
amplitude and the cavity’s transient response to this field
which always occurs at the cavity resonance frequency.

Here, dispersion spectroscopy was performed in the tran-
sient buildup regime. The CBDS approach requires the
sequential injection of discrete and arbitrarily detuned laser
fields that are optically phase-coherent with the resonant
cavity field. The use of high-Q, macroscopic-length resona-
tors allows one to set acquisition times in the microsecond
range. Therefore, the measurement paradigm does not sac-
rifice ability to study a wide range of dynamic phenomena.
In addition, the cavity buildup dispersion spectrometer
establishes immunity of CBDS to common nonlinearities
and biases that can occur with conventional intensity-based

cavity-enhanced spectroscopy methods. Interrogation of 3

consecutive cavity modes via buildup signals to measure
broadband phenomena such as molecular absorption spectra
is unavailable in conventional devices and methods.

With respect to transient cavity response to single-mode,

non-resonant excitation, a conventional, linear optical cavity 3

formed by two mirrors has intensity reflectivity R and
separated by a distance L. The cavity is filled with an
intracavity gas medium described by an absorption coefli-
cient a. Assuming lossless mirrors, we define an effective
mirror reflectivity and round-trip time of the empty cell as
R,g-Re and t,=2 nL/e=1/Svpsq, respectively, where c is
the speed of light in vacuum, n is the refractive index of the
absorptive medium and 8vzsp is the cavity free spectral
range (FSR). Consider the single excitation of cavity lon-
gitudinal mode order q of angular frequency «, by an optical
electric field of angular frequency ,, and amplitude € given
by E,()=€e, which is instantaneously switched on at time
t=0. The net time response of the field transmitted by the
cavity E,,,,(t) can be calculated by summing contributions
over a finite number of M passes in the cavity realized from
t,/2 to t and leads to the following form

Ell) Eu lee TE, a

wherein

and P=-1,-! In(R,,) describes the width (HWHM) of q-th
cavity mode. The resulting field involves the sum of two
fields: the excitation term proportional to e“’* and the
transient response of the cavity (Green’s function) given by
ete", It can be easily shown that (21',)~! is the conven-
tional intensity-based time constant, t, of a light decay
measured in cavity ring-down spectroscopy (CRDS). The

S

3

40

&

3!

60

14

structure of Eq. (1) illustrates how the induced transient field
of the cavity tends to oppose the driving field and causes
interference which is manifest as a decaying beat signal at
angular frequency S0=0,-0,.

In order to compute the intensity, we square the real-
valued part of the complex-analytic field from Eq. (1). To
account for the finite detector bandwidth, we ignore the
resulting optical frequency terms in the beat signal. These
operations yield the detected intensity exiting the cavity as

Togeht) Tout 40 21426 F# cos(Soor)], Q)
where 1,,,°=IEo4¢17/2. Equation (2) describes the time-
dependent buildup signal in the CBDS method. Note the
occurrence of two characteristic rates, one at 21’, equal to the
familiar ring-down intensity decay rate, and the other at half
of this value, which corresponds to the decay rate of the
induced transient cavity field.

Representative simulations of detector signal 220 are
plotted in FIG. 5 using the model presented in Eq. (2) and
a familiar ring-down intensity decay rate of 20,,=33 kHz. In
the left panel, detector signal 220 includes information about
a beat frequency 231 [5v=80/(27)] that is equal to 0 kHz. In
the central panel, detector signal 220 includes information
about a beat frequency 231 that is equal to 100 kHz. In the
right panel, detector signal 220 includes information about
a beat frequency 231 that is equal to 1000 kHz.

For reasons discussed below, it is useful to analyze CBDS
signals in the frequency domain. Taking the Fourier trans-
form of I,,,(t) and neglecting the DC term gives the function

)

1 1 1
Tw=P, - _._ 1
Fo be ae T) ford) ioieran)

which is the sum of three complex Lorentzian resonances.
The first resonance is centered at w=0, and corresponds to
decay of intensity in the transient field. The other two
resonances are at =+d and describe the slower decay of
the intensity in the beat signal caused by interference
between the two fields. In practice, we can use Eq. (3) to

calculate the real-valued quantity, | F (@)I?, to model the
power spectral density of the measured CBDS signal. Evalu-

ation of | F (@)I? leads to three symmetric Lorentzian com-
ponents and three asymmetric, dispersive components asso-
ciated with the off-diagonal terms.

Representative simulations of the square of the Fourier
transform of the time-domain signals in FIG. 5 are plotted in
FIG. 6. Peaks in the Fourier power spectra in FIG. 6 identify
each beat frequency 231. The left panel includes information
about a beat frequency 231 [5v=5«/(2x)] that is equal to 0
kHz. The central panel includes information about a beat
frequency 231 that is equal to 100 kHz. The right panel
includes information about a beat frequency 231 that is
equal to 1000 kHz.

The parameters used to simulate several detector signal
220 in FIG. 5 and calculate their respective Fourier power
spectra in FIG. 6 which contain several beat frequency 231
correspond to our experimental conditions. The time-depen-
dent buildup signal in the right panel of FIG. 5 exhibits large
damped oscillations with a peak signal that is four times
greater than the asymptotic value reached at long times
These strong oscillations occur when the frequency detuning
is greater than the cavity linewidth, (i.e. d0/I>1). For
smaller frequency detuning values, the period of oscillation
is longer than the cavity decay time so that I,,,(Ql,,,.°[1-
eT, which as expected for on-resonance excitation of the


US 11,209,314 B2

17

time-domain is readily achieved because of the tight fre-
quency-locking scheme. The Fourier spectrum of the beat-
ing signal appearing in the transmitted light allows deter-
mination of the frequency detuning 5v,,,.,, of the cavity
resonance with respect to the probe beam frequency v,. The
relation kK3Vpse—(Vagnt5Vmeas) Yields the dispersive shift
Sv, of the cavity resonance relative to the locking point
frequency v,. Here, 5v;sp is the FSR corresponding to
cavity conditions outside the molecular resonance with
potential contribution from the broadband intracavity dis-
persion, and k is the integer number of modes between the
locking point and the measured cavity mode.

Frequency detuning and intracavity gas sample.

Frequency agile rapid scanning for fast spectral acquisi-
tion was achieved by adjusting the detuning frequency Vjyy
using a high-bandwidth (~20 GHz) electro-optic modulator.
We ensure that only a single sideband of EOM; excites the
cavity mode and all other sidebands as well as the carrier are
fully reflected from the cavity. Using a macroscopic-length
(0.75 m) resonator containing a sample of carbon dioxide
(CO.,) in air and tuning our laser frequency to the probe the
peak absorption, we observe signals comprising a complex
valued molecular spectrum.

Molecular spectra retrieval.

For each cavity resonance, a buildup signal was recorded
at a new value of Vy,» Corresponding fits of the buildup
model to the time-domain detector signal 220 at each
frequency step show absorptive and dispersive changes in
the width and position of cavity modes within the frequency

range of the measured molecular line. Measured dispersive 3

shifts 5v,(v-v,), determined for each cavity mode, were
used to reconstruct the purely frequency-based complex-
valued (absorption and dispersion) line shape of a CO,
transition. The absorption was calculated from the measured
dispersion using a Voigt model of line shape £(«).

CBDS achieves high accuracy through precise measure-
ment of the cavity resonance frequencies resulting from
accurate modeling and fitting of the buildup signals in the
frequency domain. The generality of our field-based method
enables applications to dynamic cavity-enhanced sensing
throughout the electromagnetic spectrum, making the
method amenable to the analysis of intermode (Example 1)
and multiplexed buildup signals with detuned local excita-
tion fields. The tightly frequency-locked optical scheme
allows for coherent time-domain averaging of CBDS sig-
nals, and therefore ultrahigh precision with minimal data
storage. We see CBDS for improving the accuracy of
fundamental and atmospheric absorption spectroscopy stud-
ies as well as metrological applications which to date have
depended exclusively on intensity-based experiments. The
rapidity and sensitivity of CBDS should also render it useful
in fast biological processes and single-particle spectroscopy.
Moreover, CBDS methods are expected to be readily
extendable to broadband spectroscopic techniques using an
optical frequency comb, which could open new possibilities
for high-accuracy measurements in this field. In classical
dual-comb spectroscopy, information about the absorptive
and dispersive components of the sample spectrum is
encoded in the amplitude and phase shift of the detected beat
notes, respectively, whereas in CBDS this information
would be encoded directly in the measured mode widths and
mode frequencies,

The digital nature and resulting noise immunity of fre-
quency measurements provides properties making fre-
quency the quantity in nature that can be determined with the
highest precision and accuracy. Given this perspective, the
CBDS technique also aligns well with general efforts to

2

40

&

18

express physical quantities in terms of frequency. Atomic
and molecular spectra entirely measured in terms of cavity
resonance frequencies can be easily referenced to the atomic
frequency standard. CBDS provides robust Sl-referenced
uncertainties and will greatly facilitate interlaboratory com-
parisons of data. In this context, CBDS can be used for to
Doppler and ro-vibrational thermometry as well as to a new
gas pressure standard currently being developed that are
based on precisely measuring the dispersive shifts of optical
cavity modes. Nondestructive detection of Rydberg atoms
based on cavity dispersion and chemical kinetic study of
may be performed by CBDS for speed and accuracy of
determination of atomic and molecular populations.

In the context of saturation-free CRDS, the relation
between absorption in the cavity medium and concomitant
perturbations on the cavity mode frequencies can be derived
so that the frequency-dependence of the real and imaginary
parts of the index of refraction n(w)=n)+x%(w)/(2n,) of the
absorbing cavity gas can be expressed in terms of the
absorptive and dispersive components of the complex-val-
ued resonant susceptibility «(w)=(w)-iz"(w). The real and
imaginary components of x are tied by causality consider-
ations that ensure zero impulse response for t<0. Absorption
and dispersion are thus given by

6)

and

tig” (@)

x) ©

wy

wo,
la

nh”

respectively. Here Aw,=w,-0, is the absorption-induced
shift of the unperturbed mode position, w,. The ratio of
mode shift Aw, to absorption coeflicient, 0, reduces to

Ay @

%y

‘(w)
Bg V"()"

where c is the speed of light and ng is non-resonant refractive
index of the sample.

Substituting o.,=(1/c)(1/t,-1/%,,0)- with t,, equal to the
cavity time constant in the absence of absorption, and the
uncertainty relation 2P.t,=1 into Eq. (6) gives the ratio of
the frequency shift to the increase in decay rate, AV-T,-
Dy» 8

Avy _ x) @)

By nO"

For measurements of isolated line shapes, one can write
the resonant susceptibility for a line located at «, as

M0) = ~ity Lew, oS 2)

Here * denotes complex conjugate, S, is the line intensity
given by 2ncS,, in which S,, is the intensity in standard
dimensions of line areaxwave number per molecule, n,, is
the number density of the absorber and £() is the com-
plex-valued line profile function normalized so that [£(«)
dw=1. Equation (8) can be rewritten using complex line
shape function £(w)



US 11,209,314 B2

7

some embodiments, discriminator 208 is interposed between
resonator 205 and receiver 209, wherein receiver 209
receives transmitted electromagnetic radiation 218 from
resonator 205 and discriminator signal gender 19 from
discriminator 208. It should be appreciated that when
receiver 209 receives a plurality of different frequencies,
e.g., that of frequency shifted radiation 214 and that of
coherent electromagnetic radiation 211, receiver 209 pro-
duces detector signal 220 that has a beat frequency corre-
sponding to an interference between frequency shifted radia-
tion 214 and coherent electromagnetic radiation 211. It is
contemplated that a change in the beat frequency of detector
signal 220 corresponds to a change in refractive index of
analyte 225 in resonator 205 or a change in distance D
between mirrors 223.

Detector signal 220 is received by analyzer 210 that
produces analyzer signal 221 from detector signal 220.
Exemplary analyzers 210 include field programmable gate
arrays, digital computers, oscilloscopes, and the like. Ana-
lyzer signal 221 includes information with regard to the
refractive index of analyte 225 in resonator 205 and distance
D between mirrors 223.

Cavity buildup dispersion spectrometer 200 can be made
in various ways. It should be appreciated that cavity buildup
dispersion spectrometer 200 includes a number of optical
and electrical components, wherein such components can be
interconnected and placed in communication (e.g., optical
communication, electrical communication, and the like) by
physical or free-space interconnects. The components can be

disposed on mounts that can be disposed on a bulkhead for 3

alignment and physical compartmentalization. As a result,
cavity buildup dispersion spectrometer 200 can be disposed
in a terrestrial environment or space environment.

In an embodiment, a process for making cavity buildup

dispersion spectrometer 200 includes: optically connecting 3

second coherent electromagnetic source 202 to electromag-
netic source 201 by extracting a portion of coherent elec-
tromagnetic radiation 211 from first coherent electromag-
netic source 201 using partially reflective or transmissive
elements, or by frequency locking the coherent electromag-
netic radiation 211 and the coherent electromagnetic radia-
tion 212 to a frequency locked electromagnetic source or to
a resonator; optically connecting shutter 203 to second
coherent electromagnetic source 202 by waveguides, optical
fibers or free space coupling; optically connecting frequency
shifter 204 to shutter 203 by waveguides, optical fibers or
free space coupling; optically connecting resonator 205 to
receiver 206 by polarization controlling, polarization select-
ing, or polarization discriminating elements: electrically
connecting receiver 206 to loop filter 207 by coaxial cabling
or a wireless connection; electrically connecting loop filter
207 to electromagnetic source 201 by coaxial cabling or a
wireless connection; optically connecting resonator 205 to
discriminator 208 by a waveguide, optical fiber or free space
coupling; optically connecting discriminator 208 to receiver
209 by a waveguide, optical fiber or free space coupling; and
electrically connecting receiver 209 to analyzer 210 by
coaxial cabling, waveguide or a wireless connection.
Cavity buildup dispersion spectrometer 200 and processes
disclosed herein have numerous beneficial uses. In an
embodiment, a process for performing cavity buildup dis-
persion spectroscopy with cavity buildup dispersion spec-
trometer 200 includes: receiving, by shutter 203, coherent
electromagnetic radiation 212 by coupling through a wave-
guide, optical fiber or free space; modulating, by shutter 203,
coherent electromagnetic radiation 212 at shutter frequency;
producing, by shutter 203, modulated electromagnetic radia-

S

2

40

8

tion 213 from coherent electromagnetic radiation 212 by
electro-optic or acousto-optic phase or frequency modula-
tion or a physical or mechanical shuttering device; receiv
ing, by frequency shifter 204, modulated electromagnetic
radiation 213 from shutter 203 by coupling through a
waveguide, optical fiber or free space: frequency shifting, by
frequency shifter 204, modulated electromagnetic radiation
213 by shifter frequency by electro-optic or acousto-optic
phase or frequency modulation; receiving, by resonator 205,
frequency shifted radiation 214 from frequency shifter 204
by waveguide, optical fiber or free space coupling; receiv-
ing, by resonator 205, coherent electromagnetic radiation
211 by waveguide, optical fiber or free space coupling;
producing, by resonator 205, cavity radiation 224, in intra-

5 cavity space 232, from frequency shifted radiation 214 and

coherent electromagnetic radiation 211 by excitation of a
cavity mode; receiving, by resonator 205, analyte 225 in
intracavity space 232 by the analyte occupying the mode
volume of resonator; subjecting analyte 225 to cavity radia-
tion 224 by the analyte being present in the mode volume
during the shutter 203 on time (OT); transmitting cavity
radiation 224 as transmitted electromagnetic radiation 218
from resonator 205 by waveguide, optical fiber or free space
coupling; receiving, by receiver 209, transmitted electro-

5 magnetic radiation 218 from resonator 205 by waveguide,

optical fiber or free space coupling; and producing, by
receiver 209, detector signal 220 from transmitted electro-
magnetic radiation 218 to perform cavity buildup dispersion
spectroscopy by RF detector, antenna, optical diode or other
transducer, wherein detector signal 220 includes beat fre-
quency 231 that corresponds to a change in a motion of
resonator 205 that includes a change in the distance between
mirrors 223 or a change of refractive index of analyte 225 in
intracavity space 232. According to an embodiment, deter-
mining the change in the distance or refractive index from
detector signal 220.

In an embodiment, performing cavity buildup dispersion
spectroscopy includes receiving, by frequency locking loop
222, second coherent radiation 215 from resonator 205 by
waveguide, optical fiber or free space coupling; producing,
by frequency locking loop 222, coherent electromagnetic
radiation 211 from second coherent radiation 215 by phase
sensitive feedback to first coherent electromagnetic source
201; and communicating coherent electromagnetic radiation

5 211 to second coherent electromagnetic source 202 from

frequency locking loop 222 by measuring the beat frequency
between coherent electromagnetic radiation 211 and coher-
ent electromagnetic radiation 212, and performing a phase
locking loop, or by extracting a portion of radiation from
first coherent electromagnetic source 201 using partially
reflective or transmissive elements, or by frequency locking
the coherent electromagnetic radiation 211 and the coherent
electromagnetic radiation 212 to a frequency locked elec-
tromagnetic source or to a resonator.

In an embodiment, performing cavity buildup dispersion
spectroscopy includes producing, by resonator 205, second
coherent radiation 215 from cavity radiation 224 by receiv-
ing cavity radiation reflected by mirror 223.1 and cavity
radiation 224 transmitted by mirror 223.1; and communi-
cating, by resonator 205, second coherent radiation 215 to
frequency locking loop 222 by waveguide, optical fiber or
free space coupling and electrically connecting to receiver
206,

In an embodiment, with reference to FIG. 12, performing

5 cavity buildup dispersion spectroscopy includes producing

by resonator 205, second coherent radiation 215 from cavity
radiation 224 by receiving cavity radiation reflected by


U.S. Patent Dec. 28, 2021 Sheet 8 of 12 US 11,209,314 B2

4

x10° x10

8k 42.8

: ie \"
Onl xe)
5° Psa 424 £
2 ' ©
8 ? 492 8
Bat | :

42
2 i i i i

1.8
6359.8 6359.9 6360 6360.1 63602 63603
Wave number (cm’')

FIG. 8


U.S. Patent Dec. 28, 2021 Sheet 5 of 12 US 11,209,314 B2

—— dv =O khz moon du = 100 khz dv = 1000 khz

221

Intensity (arb. units.)
2 = _
7 " . :
ee
8
ho ae

ao

0 8 100 150 0 50 100 150 0 50 100 150
Time (us) Time (us) Time (i:s)

FIG. 5


US.

Intensity ——————_>

aw

Patent

Dec. 28, 2021 Sheet 4 of 12 US 11,209,314 B2

tl t2 8 t4
. ” , _

RT oT FT OT

. senna
time

FIG. 4


US 11,209,314 B2

9

antenna 223.3 and cavity radiation transmitted by antenna
223.3, and communicating, by resonator 205, second coher-
ent radiation 215 to frequency locking loop 222 by coaxial
cable connecting to receiver 206.

In an embodiment, performing cavity buildup dispersion
spectroscopy includes receiving, by receiver 206 of fre-
quency locking loop 222, second coherent radiation 215
from resonator 205 by receiving cavity radiation reflected by
mirror 223.1 and cavity radiation 224 transmitted by mirror
223.1; producing, by receiver 206, electronic error signal
216 from second coherent radiation 215 by phase sensitive
discrimination of coherent radiation 215; receiving, by loop
filter 207 of frequency locking loop 222, electronic error
signal 216 from receiver 206 by coaxial cabling, waveguide,
or a wireless connection; producing, by loop filter 207 of
frequency locking loop 222, feedback control signal 217
from electronic error signal 216 by measurement, filtering
and amplification of electronic error signal; receiving, by
electromagnetic source 201, feedback control signal 217
from loop filter 207 by electrically connecting using coaxial
cabling, waveguide, or wireless connection; producing, by
electromagnetic source 201, coherent electromagnetic radia-
tion 211 by voltage or current actuation driven by electronic
feedback signal 201; and communicating coherent electro-
magnetic radiation 211 to second coherent electromagnetic
source 202 and resonator 205 from electromagnetic source
201 by waveguide, optical fiber or free space coupling.

In an embodiment, performing cavity buildup dispersion
spectroscopy includes receiving, by second coherent elec-

tromagnetic source 202, coherent electromagnetic radiation 3

211 from the electromagnetic source 201 by waveguide,
optical fiber or free space coupling or by extracting a portion
of radiation of radiation from first coherent electromagnetic
source 201 using partially reflective or transmissive ele-

ments; producing, by second coherent electromagnetic 3

source 202, coherent electromagnetic radiation 212 from
coherent electromagnetic radiation 211; and communicating
coherent electromagnetic radiation 212 to frequency locking
loop 222 from second coherent electromagnetic source 202
and first coherent electromagnetic source 201.

In an embodiment, performing cavity buildup dispersion
spectroscopy includes receiving, by resonator 205, coherent
electromagnetic radiation 211 from electromagnetic source
201 by waveguide, optical fiber or free space coupling,

In an embodiment, performing cavity buildup dispersion
spectroscopy includes receiving, by discriminator 208,
transmitted electromagnetic radiation 218 from resonator
205; producing, by discriminator 208, discriminator signal
219 from transmitted electromagnetic radiation 218 by
polarization discriminating elements or frequency depen-
dent delay line; communicating discriminator signal 219 to
receiver 209 from discriminator 208 by waveguide, optical
fiber or free space coupling, and producing, by receiver 209,
detector signal 220 from discriminator signal 219 by RF
power detector or optical diode.

In an embodiment, performing cavity buildup dispersion
spectroscopy includes receiving, by analyzer 210, detector
signal 220 from receiver 209 by electrically connecting
receiver 209 to analyzer 210 by coaxial cabling or a wireless
connection; and producing, by analyzer 210, analyzer signal
221 from detector signal 220 by use of an electronic spec-
trum analyzer.

It should be appreciated that cavity buildup dispersion
spectrometer 200 and performing cavity buildup dispersion
spectroscopy herein described provide frequency-domain
optical read-out of an instantaneous electric field of laser
light transmitted through an optical resonator under hetero-

3

&

3!

10

dyne buildup or repumping conditions at an arbitrary time
delay relative to an initial cavity ring-down event. Moreover,
cavity buildup dispersion spectrometer 200 and performing
cavity buildup dispersion spectroscopy provides simultane-
ous measurement of optical resonator round-trip light
attenuation, referred to as loss, or round-trip phase shifts,
referred to as dispersion, in the frequency domain by iso-
lating optical beating of the transmitted electric fields on a
photodetector. Conventional methods can include multiple
measurement schemes, laser scanning, or additional local
oscillator beams. Advantageously, cavity buildup dispersion
spectrometer 200 and performing cavity buildup dispersion
spectroscopy can include a single probe laser beam. By
control of the probe beam laser frequency relative to the
cavity resonance and power during cavity ring-down events,
cavity repumping occurs at arbitrary delays for controlling a
selected beat signal in transmission and providing fre-
quency-domain absorption and dispersion spectroscopy
simultaneously in an absence of a separate optical local
oscillator.

Cavity buildup dispersion spectrometer 200 and perform-
ing cavity buildup dispersion spectroscopy solves an accu-
racy measurement problem of complex refractive index of
materials such as pure gases, trace gases and aerosols, as

5 well as optical coatings, atomic and molecular monolayers

and condensed-phase large molecules, e.g., proteins and the
like. By performing read-out of an optical beat signal such
as an alternating current or AC signal, cavity buildup dis-
persion spectrometer 200 and performing cavity buildup
dispersion spectroscopy overcomes limitations of conven-
tional read-outs operating at direct current (DC) and over-
comes flicker noise limitations and digitizer nonlinearity
biases.

Cavity buildup dispersion spectrometer 200 and perform-
ing cavity buildup dispersion spectroscopy can perform
refractive index sensing for atomic and molecular absorp-
tion, bulk material properties, resonant and non-resonant
complex susceptibilities, and the like. Additionally, cavity
buildup dispersion spectrometer 200 and performing cavity
buildup dispersion spectroscopy can perform physical sens-
ing of length displacement, velocity, acceleration, pressure,
force, acoustics, electric fields, magnetic fields, and the like.
Moreover, cavity buildup dispersion spectrometer 200 and
performing cavity buildup dispersion spectroscopy can inte-
grate with conventional frequency counters for read-out of
complex refractive index and length displacement. Further,
Cavity buildup dispersion spectrometer 200 and performing
cavity buildup dispersion spectroscopy operates in an
absence of advanced software approaches to line shape
fitting and laser scanning so that information is condensed
into a single number of the beat frequency, which is recorded
with high precision and traceability to the international
system of units (SI) definition of the second for accuracy
with simplicity that is highly desirable.

Advantageously, cavity buildup dispersion spectrometer
200 overcomes limitations of technical deficiencies of con-
ventional devices such as conventional absorption spectrom-
eters or cavity-enhanced spectrometers based on resonator
decay rates or transmission of radiation, which do not
measure complex refractive index of the analyte. Further,
cavity buildup dispersion spectrometer overcomes limita-
tions of measurements speed and detector nonlinearity that
occur with other cavity-enhanced methods. Cavity buildup
dispersion spectroscopy as an AC technique that encodes the
relevant information in the pattern of zero crossings of the
oscillating signal, is inherently immune to high order har-
monics produced by the nonlinear response of the analyzer.


U.S. Patent Dec. 28, 2021 Sheet 7 of 12 US 11,209,314 B2

Tir
g
5 0.1 1 10
107 T T a a a es ¥ POPP ELT
—— CRDS, % = 30 us
~--~- CBDS, dv = 100 kHz
10° -- CBDS, dv = 200 kHz

CBDS, dv = 1000 kHz

107

a

o (om!)

10°

10°

49'¢

FIG.7


US 11,209,314 B2

21

source in communication with the shutter and the electro-
magnetic source of the frequency locking loop and that:
receives the coherent electromagnetic radiation from the
electromagnetic source;
produces the coherent electromagnetic radiation from the
coherent electromagnetic radiation; and
communicates the coherent electromagnetic radiation to
the frequency locking loop.

6. The cavity buildup dispersion spectrometer of claim 5,
wherein the resonator receives the coherent electromagnetic
radiation from the electromagnetic source.

7. The cavity buildup dispersion spectrometer of claim 6,
further comprising a discriminator in communication with
the resonator and the receiver and that:

receives the transmitted electromagnetic radiation from

the resonator,

produces discriminator signal from the transmitted elec-

tromagnetic radiation; and

communicates the discriminator signal to the receiver,

such that the receiver produces the detector signal from
the discriminator signal.

8. The cavity buildup dispersion spectrometer of claim 1,
further comprising an analyzer in communication with the
receiver and that:

receives the detector signal from the receiver; and

produces analyzer signal from the detector signal.

9. A process for performing cavity buildup dispersion
spectroscopy with a cavity buildup dispersion spectrometer,
the process comprising:

receiving, by a shutter, coherent electromagnetic radia- 3

tion;

modulating, by the shutter, the coherent electromagnetic
radiation at a shutter frequency;

producing, by the shutter, modulated electromagnetic

radiation from the coherent electromagnetic radiation; 3

receiving, by a frequency shifter, the modulated electro-
magnetic radiation from the shutter;
frequency shifting, by the frequency shifter, the modu-
lated electromagnetic radiation by a shifter frequency;
producing, by the frequency shifter, frequency shifted
radiation shifted by the shifter frequency from the
modulated electromagnetic radiation;
receiving, by a resonator, the frequency shifted radiation
from the frequency shifter, the resonator comprising:
a plurality of mirrors separated by a distance;
an intracavity space interposed between the mirrors
having the distance as a length; and
a plurality of cavity modes comprising: a primary
cavity mode at a primary resonance frequency; and
a secondary cavity mode at a secondary resonance
frequency, such that the resonator;
receiving, by the resonator, coherent electromagnetic
radiation;
producing, by the resonator, cavity radiation, in the intra-
cavity space, from the frequency shifted radiation and
the coherent electromagnetic radiation;
receiving, by the resonator, an analyte in the intracavity
space;
subjecting the analyte to the cavity radiation;
transmitting the cavity radiation as transmitted electro-
magnetic radiation from the resonator;
receiving, by a receiver, the transmitted electromagnetic
radiation from the resonator; and
producing, by the receiver, a detector signal from the
transmitted electromagnetic radiation to perform cavity
buildup dispersion spectroscopy,

2

40

45

22

wherein the detector signal comprises a beat frequency
that corresponds to a change in a motion of resonator
that comprises a change in the distance between the
mirrors or a change of refractive index of the analyte in
the intracavity space.

10. The process of claim 9, further comprising:

receiving, by a frequency locking loop, the second coher-
ent radiation from the resonator;

producing, by the frequency locking loop, a coherent
electromagnetic radiation from the second coherent
radiation; and

communicating the coherent electromagnetic radiation to
the second coherent electromagnetic source from the
frequency locking loop

11. The process of claim 10, further comprising:

producing, by the resonator, the second coherent radiation
from the cavity radiation; and

communicating, by the resonator, the second coherent
radiation to the frequency locking loop.

12. The process of claim 11, further comprising:

receiving, by a receiver of the frequency locking loop, the
second coherent radiation from the resonator;

producing, by the receiver, an electronic error signal from
the second coherent radiation;

receiving, by a loop filter of the frequency locking loop,
the electronic error signal from the receiver;

producing, by the loop filter of the frequency locking
loop, a feedback control signal from the electronic error
signal;

receiving, by an electromagnetic source, the feedback
control signal from the loop filter;

producing, by the electromagnetic source, a coherent
electromagnetic radiation from the feedback control
signal; and

communicating the coherent electromagnetic radiation to
asecond coherent electromagnetic source and the reso-
nator from the electromagnetic source.

13. The process of claim 12, farther comprising:

receiving, by the second coherent electromagnetic source,
the coherent electromagnetic radiation from the elec-
tromagnetic source:

producing, by the second coherent electromagnetic
source, the coherent electromagnetic radiation from the
coherent electromagnetic radiation; and

communicating the coherent electromagnetic radiation to
the frequency locking loop from the second coherent
electromagnetic source.

14. The process of claim 13, further comprising, receiv-

» ing, by the resonator, the coherent electromagnetic radiation

from the electromagnetic source.

15. The process of claim 14, farther comprising:

receiving, by a discriminator, the transmitted electromag-
netic radiation from the resonator;

producing, by the discriminator, the discriminator signal
from the transmitted electromagnetic radiation;

communicating the discriminator signal to the receiver
from the discriminator; and

producing, by the receiver, the detector signal from the
discriminator signal.

16. The process of claim 9, further comprising:

receiving, by an analyzer, the detector signal from the
receiver; and

producing, by the analyzer, an analyzer signal from the
detector signal


a2 United States Patent

Fleisher et al.

US011209314B2

(10) Patent No.: US 11,209,314 B2

(54)

(71)

(72)

(73)

(21)

(22)

(65)

(60)

(51)

CAVITY BUILDUP DISPERSION
SPECTROMETER AND PERFORMING
CAVITY BUILDUP DISPERSION
SPECTROSCOPY

Applicant: Government of the United States of
America, as represented by the
Secretary of Commerce, Gaithersburg,
MD (US)

Inventors: Adam Joseph Fleisher, Gaithersburg,

MD (US); Keith Alan Gillis,

Washington Grove, MD (US); Joseph

Terence Hodges, Washington Grove,

MD (US)

GOVERNMENT OF THE UNITED
STATES OF AMERICA, AS
REPRESENTED BY THE
SECRETARY OF COMMERCE,
Gaithersburg, MD (US)

Assignee:

Notice: Subject to any disclaimer, the term of this

patent is extended or adjusted under 35
U.S.C, 154(b) by 0 days

Appl. No.: 17/126,118
Filed: Dee. 18, 2020

Prior Publication Data
US 2021/0190589 Al Jun. 24, 2021

Related U.S. Application Data

Provisional application No. 62/951,200, filed on Dec
20, 2019.

Int. Cl.
GOIN 21/00 (2006.01)
GOLS 3/433 (2006.01)

(Continued)

(45) Date of Patent: Dec. 28, 2021
(52) US. Cl.
CPC vescseeeee GOLF 3/4338 (2013.01); GOLT 3/021

(2013.01); GOLF 30232 (2013.01); GOLF 3/10
(2013.01); GOLJ 3/12 (2013.01)
(58) Field of Classification Search
CPC . GOIN 21/00; GOIN 21/17; GO1J 3/02; GOI
3/4338; GOLJ 3/12; GO1J 3/10; GOII
3/021; GOLJ 3/0232
See application file for complete search history.

(56) References Cited
U.S. PATENT DOCUMENTS
6,094,267 A 7/2000 Levenson et al.
6,727,492 BL 4/2004 Ye et al,

(Continued)

OTHER PUBLICATIONS

Cygan, A., et al., “Cavity buildup dispersion spectroscopy”, Maga-
zine Title, 2020.

(Continued)

Primary Examiner — Abdullahi Nur
(74) Attorney, Agent, or Firm — Office of Chief Counsel
for National Institute of Standards and Technology

(57) ABSTRACT

A cavity buildup dispersion spectrometer includes a shutter
that modulates coherent electromagnetic radiation at a shut-
ter frequency; and produces modulated electromagnetic
radiation; a frequency shifter that frequency shifts the modu-
lated electromagnetic radiation to a shifter frequency and
produces frequency shifted radiation; a resonator that pro-
duces cavity radiation from the frequency shifted radiation
and the coherent electromagnetic radiation, receives an
analyte; subjects the analyte to cavity radiation, and trans-
mits the cavity radiation as transmitted electromagnetic
radiation; and a receiver that: produces a detector signal
from the transmitted electromagnetic radiation, such that the
detector signal includes a beat frequency that corresponds to
a change in a motion of resonator that includes a change in
(Continued)



US 11,209,314 B2

Sheet 10 of 12

e
BORZSTIS

Dec. 28, 2021

$9RT SE

U.S. Patent

tae



U.S. Patent Dec. 28, 2021 Sheet 9 of 12 US 11,209,314 B2
(A) (B)
0.06 0.025
§
0.02 :
oC e
> =
Ss 0.015 z
BI 0.01 n
£ u
0.005 if
$4
-0.04 : - - 0
0 Of 02 03 04 05 95.22 95.24 95.26 95.28
Time (ms) Frequency (MHz)
(C) (D)
0.2 0.06 i
9
ol :
> 0.04 :
> 2:
@ 0 non
¢ aoa
E 0.02 ye
is , 16
Ou iV:
ne
02 . i]
0 O04 062 O03 O04 95.22 95.24 95.26 95.28

Time (ms)

Frequency (MHz)
FIG. 9


U.S. Patent Dec. 28, 2021 Sheet 6 of 12 US 11,209,314 B2

— iv= 00h]
Y 49° or or
c 231 i 234
F 10 2 231 hi (
2 wo |
2
é ‘0

0 { 2 0 { 2 0 { 2
Frequency (MHz) Frequency (MHz) Frequency (MHz)

FIG. 6


US 11,209,314 B2

15

ring-down cavity (left panel of FIG. 5), reduces to a mono-
tonically increasing field amplitude described by the
complement of the exponential decay function. In FIG. 6, we
compare the power spectral density obtained from the Fou-
rier transform (FT) of the time domain signal and the
analytical Fourier transform is given in Eq. (3). Two of the
resonances (one at DC and the other at the positive value of
the beat frequency) are evident, whereas the other resonance
at negative frequencies contributes via its wing. In contrast,

ignoring the three dispersive terms in | F (w)I? and using a "

simplified three-component symmetric Lorentzian model for
this quantity leads to systematic residuals at the 1% level.

With regard to sensitivity of CBDS to absorption coefli-
cient and measurement speed, the CBDS buildup signal,
I,,,{t), depends on the sample absorption coefficient, o,,
through the mode width, I, as well as the beat frequency
term dw which encodes information about the position of
mode «,, The change of mode width AT, caused by absorp-
tion @, in the cavity medium is

and is linked to the corresponding dispersive cavity mode
shift, d0,,, by the complex-valued refractive index n(w)=n,+
y(@YQ2ng) and resonant susceptibility x(w)=%'(w)-ix"(@),
which for an isolated spectral line may be written using the
complex-valued line shape function £()

bop x __ImbLw,- eo) a

By ox” mpRELo, —0))"”

where ny is non-resonant refractive index of the sample and
Wo is the center of spectral line.

‘To assess the theoretical precision and speed limits of
CBDS compared to CRDS, we fitted the appropriate model
for each method to I,,,(t) signals simulated with Gaussian
noise. For both techniques, we considered signals with
identical signal-to-noise-ratio levels of

SINR = 3000, =1

Nox”

(which corresponds to a Lorentzian line shape at the point of
maximum dispersion), t,=30 1s, and various laser detuning
frequencies 5v=Sw/(2m). Here we used Eq. (2), assuming
infinitely fast laser switching. Fitted values of 5v from
CBDS and I’, from CRDS were converted to equivalent
absorption coefficient quantities, and the standard deviations
of these values, o,,, were evaluated from the resulting
distributions and treated as sensitivity parameters for each
technique. In FIG. 7, the lines show the dependence of o,, in
both cases upon the width of the fitting time window, T. The
lines are derived from analytical solutions for 0, as a
function of T which arise from an assumed least-squares
fitting routine. To calculate the analytical solutions for
CBDS, we again used Eq. (2) assuming infinitely fast laser
switching and followed a procedure like CRDS.

CBDS has substantially improved sensitivity relative to
CRDS as T decreases and 6v increases. Most interestingly,
CBDS has an inherent sensitivity advantage for shorter
measurement times, especially for fit windows where

S

20

40

45

16
Th,<1. Notably, when T/t,-0.1, CBDS provides a 30-fold
reduction in o,, relative to CRDS. Calculations not shown
here also reveal that CBDS measurements are subject to
substantially smaller biases than CRDS when T/t,<1. For
each chosen value of dv, the CBDS sensitivity advantage
over CRDS is maximized once Tdv>1. Further, the CBDS
advantage over CRDS converges to a constant value, inde-
pendent of 8v, once Tév>I for all 5v. Generally, the advan-
tage of CBDS disappears when T is shorter than the half-
period of the beat frequency 1/(25v). For long measurement
times, when T/z,>>1, the CBDS sensitivity converges to a
value which larger than the CRDS sensitivity by a factor of
2. This apparent twofold disadvantage predicted for CBDS
when T/r,>>1 could be fully recovered in a two-point

5 measurement scheme where, for CBDS, the chosen two

points are at the extrema of the imaginary line shape profile.
Finally, the vertical axis in graphs can be rescaled by the
factor proportional to (1-R)/L to further generalize these
results for cavities of other lengths L and mirror reflectivities
R. Therefore, the advantages of the CBDS can be also
exploited in systems with compact cavities.

The above discussion assumed the realistic case in which
optimized measurements of the light transmitted by the
ring-down cavity are not limited by the available laser

5 power, However, when noise in the buildup signal is laser-

power-limited, then increases in 5v will lead to decreases in
the SNR, because less radiation is coupled into the cavity
mode.

Immunity of CBDS accuracy to detection system nonlin-
earity.

To quantify the effect of detection system nonlinearity on.
the accuracy of CBDS, we simulated buildup signals and
assumed nonlinear quadratic or power-law deviations from
linearity of the signal amplitude. Conventional CRDS
absorption spectra also were analyzed in the same fashion.
Given the same degree of assumed nonlinear response, the
maximum relative errors in CBDS analyzed in the time-
domain (TD) and frequency-domain (FD) were found to be
independent of detuning dv,,,,.,. and 6 and 50 times smaller,
respectively than those acquired using CRDS. For the fre-
quency-domain CBDS case, maximum errors were 0.02%
for realistic non-linearities at the 2% level.

The CBDS method utilizes a single-frequency light
source that is frequency-locked to the optical resonator. This
is illustrated in FIG. 3 where primary frequency 227 of
electromagnetic source 201 communicated to resonator 205
by coherent electromagnetic radiation 211 is frequency
locked at frequency f1 to primary cavity mode 229 having
primary resonance frequency 226. We use a double-polar-
ization frequency-locked laser scheme where one linear
polarization of laser light is frequency-locked to a cavity
mode while the orthogonal polarization (having a well-
controlled, constant frequency detuning Vy, from the lock-
ing point) is used for non-resonant excitation of the mea-

5 sured cavity mode. Additionally, the cavity length is

stabilized to prevent thermal drift of the comb of modes over
time scales >1 s. Also shown in FIG. 3, the buildup signal
is initiated after rapidly switching on using shutter 203 the
frequency-detuned probe beam with secondary frequency
228 at frequency {3 communicated by frequency shifted
radiation 214 to interact with secondary cavity mode 230 of
secondary resonance frequency 233, and the locking beam
remains on at frequency f1 during the entire cavity pumping
process, but does not contribute to the CBDS signal because

5 of a polarization-dependent optical filter discriminator 208

and the large frequency difference between probe and lock-
ing beams. Coherent averaging of repeated events in the


U.S. Patent Dec. 28, 2021 Sheet 2 of 12 US 11,209,314 B2

VL MOLRLIN :

X. MAM

209
205 232 N
214 —* ‘a , 218
e@ ©)

223.1 223.2
D

FIG. 2


US 11,209,314 B2

1
CAVITY BUILDUP DISPERSION
SPECTROMETER AND PERFORMING
CAVITY BUILDUP DISPERSION
SPECTROSCOPY

CROSS REFERENCE TO RELATED
APPLICATIONS

The application claims priority to U.S. Provisional Patent
Application Ser. No. 62/951,200 filed Dec. 20, 2019, the
disclosure of which is incorporated herein by reference in its
entirety.

STATEMENT REGARDING FEDERALLY
SPONSORED RESEARCH

This invention was made with United States Government
support from the National Institute of Standards and Tech-
nology (NIST), an agency of the United States Department
of Commerce. The Government has certain rights in the
invention. Licensing inquiries may be directed to the Tech-
nology Partnerships Office, NIST, Gaithersburg, Md.,
20899; voice (301) 975-2573; email tpo@nist.gov; refer-
ence NIST Docket Number 19-012US1

BRIEF DESCRIPTION

Disclosed is a cavity buildup dispersion spectrometer
comprising: a shutter that receives coherent electromagnetic

radiation, modulates the coherent electromagnetic radiation 3

at a shutter frequency; and produces modulated electromag-
netic radiation from the coherent electromagnetic radiation;
a frequency shifier in communication with the shutter and
that receives the modulated electromagnetic radiation from

the shutter, frequency shifts the modulated electromagnetic 3

radiation from the shutter frequency to a shifter frequency;
and produces frequency shifted radiation having the shifter
frequency from the modulated electromagnetic radiation: a
resonator in communication with the frequency shifter and
comprising: a plurality of mirrors separated by a distance; an
intracavity space interposed between the mirrors having the
distance as a length; and a plurality of cavity modes com-
prising: a primary cavity mode at a primary resonance
frequency; and a secondary cavity mode at a secondary
resonance frequency, such that the resonator: receives the
frequency shifted radiation from the frequency shifter;
receives coherent electromagnetic radiation; produces cavity
radiation, in the intracavity space, from the frequency
shifted radiation and the coherent electromagnetic radiation;
receives an analyte in the intracavity space; subjects the
analyte to the cavity radiation transmits the cavity radiation
as transmitted electromagnetic radiation; and a receiver in
communication with the resonator and that: receives the
transmitted electromagnetic radiation from the resonator;
and produces detector signal from the transmitted electro-
magnetic radiation, such that the detector signal comprises
a beat frequency that corresponds to a change in a motion of
resonator that comprises a change in the distance between
the mirrors or a change of refractive index of the analyte in
the intracavity space.

Disclosed is a process for performing cavity buildup
dispersion spectroscopy with a cavity buildup dispersion
spectrometer, the process comprising: receiving, by a shut-
ter, coherent electromagnetic radiation; modulating, by the
shutter, the coherent electromagnetic radiation at a shutter
frequency; producing, by the shutter, modulated electromag-
netic radiation from the coherent electromagnetic radiation;

S

3

40

60

2

a frequency shifter in communication with the shutter and
that receiving, by a frequency shifter, the modulated elec-
tromagnetic radiation from the shutter; frequency shifting,
by the frequency shifter, the modulated electromagnetic
radiation from the shutter frequency to a shifter frequency;
producing, by the frequency shifter, frequency shifted radia-
tion having the shifter frequency from the modulated elec-
tromagnetic radiation; receiving, by a resonator, the fre-
quency shifted radiation from the frequency shifter, the
resonator comprising: a plurality of mirrors separated by a
distance; an intracavity space interposed between the mir-
rors having the distance as a length; and a plurality of cavity
modes comprising: a primary cavity mode at a primary
resonance frequency; and a secondary cavity mode at a

5 secondary resonance frequency, such that the resonator:

receiving, by the resonator, coherent electromagnetic radia-
tion; producing, by the resonator, cavity radiation, in the
intracavity space, from the frequency shifted radiation and
the coherent electromagnetic radiation; receiving, by the
resonator, an analyte in the intracavity space; subjecting the
analyte to the cavity radiation transmitting the cavity radia-
tion as transmitted electromagnetic radiation from the reso-
nator; receiving, by a receiver, the transmitted electromag-
netic radiation from the resonator; and producing, by the

5 receiver, a detector signal from the transmitted electromag-

netic radiation to perform cavity buildup dispersion spec-
troscopy, wherein the detector signal comprises a beat
frequency that corresponds to a change in a motion of
resonator that comprises a change in the distance between
the mirrors or a change of refractive index of the analyte in
the intracavity space.

BRIEF DESCRIPTION OF THE DRAWINGS.

The following description should not be considered lim-
iting in any way. With reference to the accompanying
drawings, like elements are numbered alike

FIG. 1 shows a cavity buildup dispersion spectrometer;

FIG. 2 shows a cavity buildup dispersion spectrometer;

FIG. 3 shows a spectrum for cavity buildup dispersion
spectrometry;

FIG. 4 shows a graph of intensity versus time for a shutter
operation and resonator response for cavity buildup disper-
sion spectroscopy:

FIG. 5 shows graphs of intensity versus time;

FIG. 6 shows graphs of Intense intensity versus fre-
quency;

FIG. 7 shows a graph of absorption coefficient purses
normalized signal analysis period and signal analysis period;

FIG. 8 shows a graph of absorbance versus wavenumber;

FIG. 9 shows Graphs of intensity versus time in panels A
and C and respective graphs of intensity versus frequency in
panels B and D;

FIG. 10 shows: top panels, intermode cavity buildup

5 spectroscopy (ICBUS); bottom panels, half cycle with the

pumping frequency nominal on-resonance (HD-CRDS);
FIG. 11 shows a graph of Allan deviation of AVjeq:3 and
FIG. 12 shows a radiofrequency cavity buildup dispersion
spectrometer.

DETAILED DESCRIPTION

A detailed description of one or more embodiments is
presented herein by way of exemplification and not limita-

3 tion.

It has been discovered that a cavity buildup dispersion
spectrometer provides high-precision optical measurements


US 11,209,314 B2

5

tion and decay of cavity radiation 224 in resonator 205, e.g.,
in accord with FIG. 4 that shows a graph of intensity versus
time for production of modulated electromagnetic radiation
213 by shutter 203 and measurement period MP of resonator
205 over an exemplary cycle of operation of shutter 203.
Here, shutter 203 produces modulated electromagnetic
radiation 213 with intensity il from time t0 to time tl. At
time t1, shutter 203 starts to increase intensity of modulated
electromagnetic radiation 213. During rise time RT, shutter
203 increases intensity of modulated electromagnetic radia-
tion 213 from intensity i1 to intensity i2 and continues to
produce modulated electromagnetic radiation 213. From
time 12 to time t3, shutter 203 continues to produce modu-
lated electromagnetic radiation 213 during on time OT with
intensity from intensity i2 to intensity i3. During an arbitrary
period of on time OT, resonator 205 receives radiation (e.g.,
frequency shifted radiation 214, coherent electromagnetic
radiation 211), produces cavity radiation 224, and subjects
analyte 225 to cavity radiation 224 from interaction time IT1
to interaction time IT2. At time 13, shutter 203 starts to
decrease the intensity of modulated electromagnetic radia-
tion 213. During fall time FT from time t3 to time t4, shutter
203 decreases intensity of modulated electromagnetic radia-
tion 213 from intensity i3 to intensity i4. Thereafter, during
dead time DT from time t4 to t5, shutter 203 decreases the
intensity of modulated electromagnetic radiation 213 from
intensity i4 to intensity il. It should be appreciated that times
(t1, 12, 13, t4, 15) and durations of periods (RT, OT, FT, DT,
MP) are arbitrarily selectable and tailored for operation of

shutter 203 for production of a selected intensity of modu- 3

lated electromagnetic radiation 213 and a corresponding
amount of frequency shifted radiation 214. Moreover, fall
time FT of modulated electromagnetic radiation 213 pro-
vided by shutter 203 is rapid enough so that decay of cavity

radiation 224 in intracavity space 232 of resonator 205 3

provides transmitted electromagnetic radiation 218 with
discernable frequency data so that the change in distance D
of resonator 205 or the change in refractive index of analyte
225 can be determined from detector signal 220.

Frequency shifter 204 receives modulated electromag-
netic radiation 213 from shutter 203 and produces frequency
shifted radiation 214 from modulated electromagnetic radia-
tion 213 by frequency shifting modulated electromagnetic
radiation 213 relative to coherent electromagnetic radiation
211 by a shifter frequency. Frequency shifter 204 can
include an acousto-optic frequency shifter, electro-optic
frequency shifter, and the like. Frequency shifted radiation
214 can be optical radiation or radiofrequency radiation that
has a wavelength that is different than the wavelength of
coherent electromagnetic radiation 211 by the shifter fre-
quency. The shifter frequency can be from 1 hertz (Hz) to
300 GHz, specifically 1 kHz to 500 MHz, and more spe-
cifically 500 kHz to 1 MHz.

Resonator 205 receives frequency shifted radiation 214
from frequency shifter 204 and produces, cavity radiation
224, second coherent radiation 215 or transmitted electro-
magnetic radiation 218 from frequency shifted radiation
214. An exemplary resonator 205 includes a Fabry-Perot
resonator with mirrors 223 separated at distance D by
intracavity space 232. Resonator 208 is configured to
receive analyte 225 in intracavity space 232, a volume of
which can be from 1 um? to 10° m’, specifically from | mm*
to 10 m?, and more specifically from 1 cm? to 10 m?
Distance D can be from 1 um to 10° m, specifically from 1
mm to 10 m, and more specifically from 1 cm to 10 m
Analyte 225 can be a gas, liquid, gas, or any combination
thereof having a refractive index that is subject to change,

S

3

40

&

6

which can be interrogated via cavity radiation 224. Exem-
plary gases are monatomic gases or polyatomic gases that
can be inert or reactive. Exemplary liquids include pure
liquids as well as compositions of solutes in a solvent or
flocculants involving particles dispersed in a liquid. Exem-
plary solids include homogeneous and heterogeneous solids
that are transmissive to cavity radiation 224. Exemplary
sensing media include homogeneous and heterogeneous
materials that are transmissive to cavity radiation 224 and
are responsive to electric and magnetic fields.

Cavity radiation 224 is radiation received by resonator
205 (e.g., coherent electromagnetic radiation 211 or fre-
quency shifted radiation 214) that propagates in intracavity
space 232 and accordingly can include frequency shifted

s radiation 214 in combination with coherent electromagnetic

radiation 211. That is, photons of frequency shifted radiation
214 and coherent electromagnetic radiation 211 reflect
between mirrors 223 such that a portion of cavity radiation
224 exits from intracavity space 232 via first mirror 223.1
(or antenna 223.3) as second coherent radiation 215 that
propagates from resonator 205 to receiver 206 for provision
of feedback control signal 217 to electromagnetic source
201. Further, a portion of cavity radiation 224 exits from
intracavity space 232 via second mirror 223.2 (or antenna

S 223.4) as transmitted electromagnetic radiation 218 that

propagates from resonator 205 to receiver 209 or discrimi-
nator 208 for provision of detector signal 220 from receiver
209. Accordingly, transmitted electromagnetic radiation 218
can include multiple wavelengths of light, ie., frequency
shifted radiation 214 or coherent electromagnetic radiation
241.

Receiver 206 receives second coherent radiation 215 and
produces electronic error signal 216 from second coherent
radiation 215. Receiver 206 is selected according to a
wavelength of second coherent radiation 215 so that receiver
206 can electrically transduce electronic error signal 216.
Exemplary receivers 206 include a photo detector, photo
multiplier, photo diode, spectrum analyzer, RF network
analyzer, and the like.

Loop filter 207 receives electronic error signal 216 from
receiver 206 and produces feedback control signal 217 based
on electronic error signal 216. Loop filter 217 can include a
fine tune input port to receive a fine tune signal from a phase
detector; a coarse tune input port to receive a coarse tune

5 signal from a coarse tuner; an output port; a summing

element coupled to the fine tune and coarse tune input ports
to sum the fine tune and coarse tune signals and to output a
summed tune signal; a voltage divider coupled to the sum-
ming element to receive the summed tune signal and output
a voltage divided signal; and a smoothing filter coupled to
the voltage divider and the output port to smooth the voltage
divided signal and output a final tune signal as feedback
control signal 217 to tune electromagnetic source 201
Inan embodiment, cavity buildup dispersion spectrometer

5 200 includes discriminator 208 receives transmitted electro-

magnetic radiation 218 from resonator 205 and produces
discriminator signal 219 from transmitted electromagnetic
radiation 218. Here, discriminator 208 selectively transmits
a band of radiation to receiver 209. Exemplary optical
discriminators include differential delay interferometers, a
polarizing beam splitter, an optical filter implemented as a
fiber Bragg grating (FBG), a planar waveguide grating, or a
Fabry-Perot filter (FPF), and the like. A radio frequency
discriminator can include a limiter-amplifier and a detector

5 diode.

According to an embodiment, receiver 209 receives trans-
mitted electromagnetic radiation 218 from resonator 205. In


U.S. Patent Dec. 28, 2021 Sheet 1 of 12 US 11,209,314 B2

Ib
iS

FIG. 1


US 11,209,314 B2
Page 2

the distance between the mirrors or a change of refractive
index of the analyte in the intracavity space.

16 Claims, 12 Drawing Sheets

(51) Int. CL

GLI 3/12 (2006.01)
GOL 3/10 (2006.01)
GOLI 3/02 (2006.01)
(56) References Cited

U.S. PATENT DOCUMENTS

7,012,696 B2 3/2006 Orr et al.
82 B2 2/2014 Plusquellic et al.

8,642,982
2017/0269389 Al* 9/2017 Kie Ling GO2F 1/3501

OTHER PUBLICATIONS

Cygan, A. et al, “One-dimensional frequency-based spectros-
copy”, Optics Express, 2015, p. 14472-14486, vol. 23 No. I

He, Y., et al., “Rapidly swept, continuous-wave cavity ringdown
spectroscopy with optical heterodyne detection: single- and multi-

wavelength sensing of gases”, Applied Physics B, 2002, p. 267-280,
vol. 75.

He, ¥, et al., “Optical heterodyne signal generation and detection in
cavity ringdown spectroscopy based on a rapidly swept cavity”,
Chemical Physics Letters, 2001, p. 215-220, vol. 335,

Lehmann, K., et al., “The superposition principle and cavity ring-
down spectroscopy”, The Journal of Chemical Physics, 1996, p
10263-10277, vol. 105 No. 23.

Levenson, M.D., et al., “Optical heterodyne detection in cavity
ring-down spectroscopy”, Chemical Physics Letters, 1998, p. 335-
340, vol. 290.

Long, D.A., et al., “Quantum-noise-limited cavity ring-down spec
troscopy”, Applied Physics B, 2014, p. 149-153, vol. L15
Rosenblum, S., et al., “Cavity ring-up spectroscopy for ultrafast
sensing with optical microresonators”, Nature Comunications, 2015,
p. 6788, vol. 6.

‘Truong, G-W,, et al., “Frequency-agile, rapid scanning spectros-
copy”, Nature Communications, 2013, p. 532-534, vol. 7
Wojtewicz, S., et al., “Response of an optical cavity to phase-
controlled incomplete power switching of nearly resonant incident
light”, Optics Express, 2018, p. 5644-5654, vol. 26 No. 5

Ye, M-E,, et al., “Theory of cavity ring-up spectroscopy”, Optics
Express, 2017, p. 3295-32400, vol. 25 No. 26.

Ye, J., et al., “Cavity ringdown heterodyne spectroscopy: High
sensitivity with microwatt light power”, Physical Review A, 2000,
p. 061802, vol. 61.

* cited by examiner


U.S. Patent Dec. 28, 2021 Sheet 11 of 12 US 11,209,314 B2

10! : :
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bs
ad
8
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to? :
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FIG. 11


US 11,209,314 B2

3

ofa complex refractive index, wherein laser light attenuation
and optical phase shifts attributable to an analyte are simul-
taneously encoded in transient light intensity exiting an
optical resonator containing the analyte, e.g., in an effective
transient oscillating optical heterodyne beat signal. Encod-
ing of the instantaneous analyte complex refractive index
into transmitted intensity overcomes technical deficiencies
of conventional devices. The cavity buildup dispersion spec-
trometer and process described herein can include a fre-
quency-agile laser system, high finesse optical resonator,
and models for signal extraction from time-domain wave-
forms. The cavity buildup dispersion spectrometer and pro-
cess can be used for physical sensing or determining length
displacement.

Cavity buildup dispersion spectrometer 200 performs
cavity buildup dispersion spectroscopy. In an embodiment,
with reference to FIG. 1, FIG. 2, and FIG. 3, cavity buildup
dispersion spectrometer 200 includes: shutter 203 that
receives coherent electromagnetic radiation 212, modulates
coherent electromagnetic radiation 212 at shutter frequency;
and produces modulated electromagnetic radiation 213 from
coherent electromagnetic radiation 212; frequency shifter
204 in communication with shutter 203 and that receives
modulated electromagnetic radiation 213 from shutter 203,
frequency shifts modulated electromagnetic radiation 213
from shutter frequency to shifter frequency; and produces
frequency shifted radiation 214 having shifter frequency
from modulated electromagnetic radiation 213; resonator
205 in communication with frequency shifter 204 and

including: a plurality of mirrors 223 separated by a distance 3

D; intracavity space 232 interposed between mirrors 223
having the distance as a length; and a plurality of cavity
modes including: primary cavity mode 229 at primary
resonance frequency 226; and secondary cavity mode 230 at

secondary resonance frequency 233, such that resonator 3

205: receives frequency shifted radiation 214 from fre-
quency shifter 204; receives coherent electromagnetic radia-
tion 211; produces cavity radiation 224, in intracavity space
232, from frequency shifted radiation 214 and coherent
electromagnetic radiation 211; receives analyte 225 in intra-
cavity space 232; subjects analyte 225 to cavity radiation
224 transmits cavity radiation 224 as transmitted electro-
magnetic radiation 218; and receiver 209 in communication
with resonator 205 and that: receives transmitted electro-
magnetic radiation 218 from resonator 205; and produces
detector signal 220 from transmitted electromagnetic radia-
tion 218, such that detector signal 220 includes beat fre-
quency 231 that corresponds to a change in a motion of
resonator 205 that includes a change in the distance between.
the mirrors or a change of refractive index of analyte 225 in
intracavity space 232.

Inan embodiment, cavity buildup dispersion spectrometer
200 further includes frequency locking loop 222 in commu-
nication with resonator 205 and second coherent electro-
magnetic source 202 and that: receives second coherent
radiation 215 from resonator 205; produces coherent elec-
tromagnetic radiation 211 from second coherent radiation
215; and communicates coherent electromagnetic radiation
211 to second coherent electromagnetic source 202.

In an embodiment. resonator 205 produces second coher-
ent radiation 215 from cavity radiation 224, and resonator
205 communicates second coherent radiation 215 to fre-
quency locking loop 222.

In an embodiment, frequency locking loop 222 includes:
receiver 206 in communication with resonator 205 and
receives second coherent radiation 215 from resonator 205
and produces electronic error signal 216 from second coher-

S

3

40

&

4

ent radiation 215; loop filter 207 in communication with
receiver 206 and that receives electronic error signal 216
from receiver 206 and produces feedback control signal 217
from electronic error signal 216; and electromagnetic source
201 in communication with loop filter 207 and that: receives
feedback control signal 217 from loop filter 207, produces
coherent electromagnetic radiation 211 from feedback con-
trol signal 217, and communicates coherent electromagnetic
radiation 211 to second coherent electromagnetic source 202
and resonator 205.

In an embodiment, cavity buildup dispersion spectrometer
200 includes second coherent electromagnetic source 202 in
communication with shutter 203 and electromagnetic source
201 of frequency locking loop 222 and that: receives coher-

5 ent electromagnetic radiation 211 from electromagnetic

source 201; produces coherent electromagnetic radiation
212 from coherent electromagnetic radiation 211; and com-
municates coherent electromagnetic radiation 212 to fre-
quency locking loop 222.

In an embodiment, resonator 205 receives coherent elec-
tromagnetic radiation 211 from electromagnetic source 201.

Inan embodiment, cavity buildup dispersion spectrometer
200 includes discriminator 208 in communication with
resonator 205 and receiver 209 and that: receives transmitted

5 electromagnetic radiation 218 from resonator 205; produces

discriminator signal 219 from transmitted electromagnetic
radiation 218; and communicates discriminator signal 219 to
receiver 209, such that receiver 209 produces detector signal
220 from discriminator signal 219.

Inan embodiment, cavity buildup dispersion spectrometer
200 includes analyzer 210 in communication with receiver
209 and that: receives detector signal 220 from receiver 209;
and produces analyzer signal 221 from detector signal 220

Electromagnetic source 201 provides coherent electro-
magnetic radiation 211 and can include a laser such as a
solid state laser. Coherent electromagnetic radiation 211 can
be optical radiation (e.g., ultraviolet light, visible light,
infrared light, and the like) or radiofrequency radiation such
as microwave radiation.

Second coherent electromagnetic source 202 receives
coherent electromagnetic radiation 211 from electromag-
netic source 201 and produces coherent electromagnetic
radiation 212 from coherent electromagnetic radiation 211
Second coherent electromagnetic source 202 can include a
laser such as a solid state laser. Coherent electromagnetic
radiation 212 can be optical radiation (e.g., ultraviolet light,
visible light, infrared light, and the like) or radiofrequency
radiation such as microwave radiation. It is contemplated
that second coherent electromagnetic source 202 is fre-
quency locked to electromagnetic source 201 so that a
frequency (e.g., an optical frequency or microwave fre-
quency) of coherent electromagnetic radiation 212 matches
a frequency of coherent electromagnetic radiation 211

Shutter 203 receives coherent electromagnetic radiation
212 from second coherent electromagnetic source 202 and
produces modulated electromagnetic radiation 213 from
coherent electromagnetic radiation 212 by modulating
coherent electromagnetic radiation 212 at a shutter fre-
quency. Shutter 203 can include a modulation device such as
a chopper wheel, an amplitude optical modulator, an electro-
optic modulator, and the like. Modulated electromagnetic
radiation 213 can be optical radiation or radiofrequency
radiation that has a wavelength that is the same as a
wavelength of coherent electromagnetic radiation 212. The
shutter frequency can be from 1 hertz (Hz) to 300 GHz,
specifically 1 kHz to 500 MHz, and more specifically 500
kHz to 1 MHz. Operation of shutter 203 predicates produc-