US 11,011,882 B2

11

Mixed signal 312 can include the interference between the
electronic signal from oscillator 290 and the output signal
from cavity 280.

Band pass signal 314 can include an electronic signal that
is output from the band pass filter 266.

Servo signal 316 can include an electronic servo signal,
designed to actuate a temperature controller on cavity 280.

Circulator signal 318 can include an electronic signal
obtained from the output port of circulator 284.

Un-stabilized comb 304 is the ultrafast electro-optic laser
in which feedback to oscillator 290 has been disabled.

Stabilized comb 306 is the ultrafast electro-optic laser in
which feedback to oscillator 290 has been enabled.

Ultrafast electro-optic laser 200 can be made in various
ways. In an embodiment, a process for making ultrafast
electro-optic laser 200 includes: disposing continuous wave
laser 218 in optical communication with phase modulator
222 by polarization maintaining (PM) optical fiber; dispos-
ing phase modulator 222 in optical communication with
intensity modulator 226 by PM optical fiber; disposing lock
cavity 292 in optical communication with continuous wave
laser 218 by PM optical fiber; disposing dielectric resonant
oscillator 290 in electrical communication with phase modu-
lator 222 by an electrical cable; disposing intensity modu-
lator 226 in optical communication with amplifier 230.1 by
an electrical cable; disposing amplifier 230.1 in optical
communication with filter cavity 234 by an electrical cable;
disposing filter cavity 234 in optical communication with
pulse shaper 238 by PM optical fiber: disposing pulse shaper

238 in optical communication with amplifier 230.2 by 3

optical fiber; disposing amplifier 230.2 in optical commu-
nication with highly nonlinear fiber 242 by optical fiber;
disposing highly nonlinear fiber 242 in optical communica-
tion with compressor 246 by optical fiber and a free-space

optical beam; disposing compressor 246 in optical commu- 3

nication with waveguide 250 by a free-space optical beam;
disposing waveguide 250 in optical communication with
frequency difference crystal 256 by a free-space optical
beam; disposing frequency difference crystal 256 in optical
communication with filter 260 by a free-space optical beam;
disposing waveguide 250 in electrical communication with
mixer 264.1 by a free-space optical beam; disposing clock
270 in electrical communication with oscillator 272.1 and
oscillator 272.2 by an electrical cable; disposing mixer 264.1
in electrical communication with electrical amplifier 262.1
and oscillator 272.2 by an electrical cable; disposing wave-
guide 250 in electrical communication with mixer 264.1 by
an electrical cable; disposing mixer 264.1 in electrical
communication with band pass filter 266 by electronic cable;
disposing band pass filter 266 in electrical communication
with electrical amplifier 262.2 by an electronic cable rated
for the microwave frequency range; disposing electrical
amplifier 262.2 in electrical communication with divider
268 by an electronic cable rated for the microwave fre-
quency range; disposing mixer 264.2 in electrical commu-
nication with oscillator 272.1 and divider 268 by an elec-
tronic cable rated for the microwave frequency range;
disposing mixer 264.2 in electrical communication with
servo 276.1 by an electronic cable rated for the microwave
frequency range; disposing servo 276.1 in electrical com-
munication with stabilized local oscillator cavity 280 and
servo 276.2 by an electronic cable rated for the microwave
frequency range; disposing stabilized local oscillator cavity
280 in electrical communication with circulator 284 by an
electronic cable rated for the microwave frequency range;
disposing circulator 284 in electrical communication with
phase modulator 222 by an electronic cable rated for the

S

8

40

&

12

microwave frequency range: disposing waveguide 250 in
electrical communication with mixer 264.1 by an electronic
cable rated for the microwave frequency range: disposing
mixer 264.3 in electrical communication with circulator 284,
phase shifter 286.1, and servo 276.2 by an electronic cable
rated for the microwave frequency range: disposing phase
shifter 286.1 in electrical communication with dielectric
resonant oscillator 290 by an electronic cable rated for the
microwave frequency range; and disposing servo 276.2 in
electrical communication with dielectric resonant oscillator
290.1 by an electronic cable rated for the microwave fre-
quency range.

Ultrafast electro-optic laser 200 has numerous advanta-

geous and unexpected benefits and uses. In an embodiment,

a process for making stabilized comb 306 with ultrafast
electro-optic laser 200 includes: producing, by comb gen-
erator 210, frequency comb 228 by: receiving, by dielectric
resonant oscillator 290, stabilization signal 288; and pro-
ducing, by dielectric resonant oscillator 290, phase control
signal 300 from stabilization signal 288; receiving, by phase
modulator 222 in communication with dielectric resonant
oscillator 290, continuous wave light 220; receiving, by
phase modulator 222 from dielectric resonant oscillator 290,

5 phase control signal 300; producing, from continuous wave

light 220 and phase control signal 300, phase modulated
light 224; and producing phase modulation signal 308;
receiving, by intensity modulator 226 in communication
with phase modulator 222, phase modulated light 224;
receiving, by intensity modulator 226, intensity control
signal 302; and producing, frequency comb 228 from inten-
sity control signal 302 and phase modulated light 224;
producing, by optical tailor 212 in communication with
comb generator 210, tailored light 298 by: receiving, filter
cavity 234 in communication with intensity modulator 226,
frequency comb 228 from intensity modulator 226; produc-
ing filtered light 236 from frequency comb 228; receiving,
by pulse shaper 238 in communication with filter cavity 234,
filtered light 236 from filter cavity 234; producing shaped
light 240 from filtered light 236; receiving, by highly
nonlinear fiber 242 and compressor 246 in communication
with pulse shaper 238, shaped light 240 from pulse shaper
238; producing compressed light 248 from shaped light 240;
receiving, by waveguide 250 in communication with highly

5 nonlinear fiber 242 and compressor 246, compressed light

248; and producing tailored light 298 from compressed light
248; producing, by interferometer 214 in communication
with optical tailor 212, difference frequency 258 from tai-
lored light 298 with frequency difference crystal 256; and
producing, by electrical stabilizer 216 in communication
with interferometer 214 and comb generator 210, stabiliza-
tion signal 288 by: producing, by stabilized local oscillator
cavity 280, stabilized local oscillator signal 282; converting
stabilized local oscillator signal 282 into stabilization signal

5 288; and communicated stabilization signal 288 to dielectric

resonant oscillator 290 to make stabilization signal 288.

In the process for making stabilized comb 306, receiving,
by dielectric resonant oscillator 290, stabilization signal 288
can include a signal obtained from a PID servo controller
based on the interference of the microwave signal from
oscillator 290 and the microwave signal at the output of
cavity 280. This signal is electronically mixed in a double
balanced mixer 264.

In the process for making stabilized comb 306, producing,

5 by dielectric resonant oscillator 290, phase control signal

300 from stabilization signal 288 can include an amplified
signal from oscillator 290 in which the relative phase of the


US 11,011,882 B2

Sheet 12 of 12

May 18, 2021

U.S. Patent

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US 11,011,882 B2

19
flattened with a single passive optical attenuator. Under
these conditions, fluctuations in spectral intensity can be
kept within #3 dB over wavelengths spanning from 850 to
1450 nm while delivering more than 10 nW per mode in the

fiber at 10 GHz. Improved waveguide-to-fiber output cou- 5

pling, or free-space collimation combined with an appropri-
ate color filter, could further improve the power per mode.

‘After broadening in the SiN waveguide, the offset fre-
quency is detected with >30 dB signal-to-noise ratio (SNR),
suggesting that the scheme of combining normal- and
anomalous-dispersion media indeed allows us to overcome
the difficulties of producing a coherent supercontinuum
using pulses longer than a few hundred femtoseconds; see
FIG. 11 for SNR versus bandwidth. Stabilization of f) is
subsequently accomplished by feeding back to the fre-
quency-tuning port of the DRO. However, owing to optical
and electronic phase delay in this configuration, the feed-
back bandwidth is limited to ~200 kHz (FIG. 7A) and thus
is insufficient on its own to narrow the comb linewidth set
by the multiplied microwave noise of the DRO.

FIG. 7 shows aspects of EOM-comb phase noise. Panel A
shows optical phase noise of the comb offset frequency
measured at 775 nm (left axis) and scaled to the 10-GHz
repetition rate (right axis) under different locking conditions.
Prestabilizing the free-running RF oscillator (DRO) using a
high-Q microwave cavity in the stabilized-local-oscillator
(STALO) configuration lowers the phase noise by up to 20
dB at frequencies below 500 kHz. When servo feedback

from the optical fy signal is engaged, a tight phase lock is 3

achieved that suppresses low-frequency noise. The B-line
indicates the level above which phase noise causes an
increase in the comb linewidth. When both the STALO and
fy, locks are engaged, the phase noise remains below the

f-line at all frequencies, indicating that the coherence of the 3

CW pump laser is faithfully transferred across the entire
comb spectrum. Panels B to D show fy RF beats with effects
of each feedback loop. A coherent carrier signal is observed
in panel D when both the STALO lock and direct f, feedback
are engaged.

‘To reach the x-radian threshold for phase coherence
between the CW laser and electronic oscillator, the output of
one high-power microwave amplifier is stabilized to an
air-filled aluminum microwave cavity in the stabilized-local-
oscillator (STALO) configuration and yields an immediate
reduction in phase noise of up to 20 dB at frequencies less
than 500 kHz from the carrier.

In FIG. 7A, the -line distinguishes between regimes
where the linewidth of the comb offset f, is adversely
affected (phase noise above the f-line) and where there is no
linewidth contribution (phase noise below the f-line). Hav-
ing phase noise below the B-line at all points is approxi-
mately equivalent to an integrated phase noise below x
radians and provides a convenient visual way to assess the
impact of noise at different Fourier frequencies. For the
EOM comb from the ultrafast electro-optic laser, the f,
phase noise remains below the P-line at all frequencies only
when both the STALO lock and the f-2f lock are used in
tandem. Under these conditions, noise arising from the
microwave oscillator does not contribute appreciably to the
comb linewidth and thus, the CW laser stability is faithfully
transferred across the entire comb bandwidth. Equivalently,
integrating the phase noise of the fully locked {, beat (1.17
rad, 10 Hz to 4 MHz) yields a pulse-to-pulse timing jitter of
0.97 fs (1.9 fs if limited by the f line between 4 MHz and
5 GHz), indicating that the microwave envelope coherently
tracks the optical carrier signal with subcycle precision.

s

20

The progression of offset-frequency stabilization is also
shown by the beat frequencies as each lock is turned on
(FIG. 7, panel B to D). The coherent carrier seen in the offset
frequency when fully stabilized (FIG. 7D) indicates that
phase coherence has been achieved between individual
comb lines across the entire available spectral bandwidth.
The accuracy and precision of the stabilized EOM comb
were determined by beating the 10-GHz repetition rate
against the 40th harmonic of an independent mode-locked
laser operating at 250 MHz. After 2000 s of averaging, a
fractional stability of 3x10~'’ was obtained with no statis-
tically significant frequency offset observed. This level of
accuracy represents an improvement of more than three
orders of magnitude over previously demonstrated EOM-
comb systems and is likely only limited here by averaging
time and out-of-loop path differences between the two
combs.

To further show the versatility of the EOM comb as an
ultrafast source, pulses were made that had durations lasting
a few cycles of the optical field. Pulses in this regime
provide direct access to the carrier-envelope phase and high
peak intensities but require a well-controlled output spec-
trum exhibiting a high degree of spectral flatness and
coherence. However, achieving such pulses at gigahertz
repetition rates with mode-locked lasers is technically chal-
lenging. Still, high-repetition rate sources of few-cycle
pulses could be valuable for applications like optically
controlled electronics, where both fast switching speeds and
peak intensity are important. Similarly, coherent Raman
imaging of biological samples can benefit from transform-
limited ultrashort pulses, but the acquisition speed for broad-
band spectra is typically restricted by the megahertz-rate
mode-locked laser sources that are used. Extending to higher
repetition rates could reduce measurement dead time and
also prevent sample damage due to high peak powers.

The use of optical modulators to directly carve a train of
~1-ps pulses from a CW laser provides an effective method
for generating clean few-cycle pulses thanks to the soliton
self-compression effect. To achieve this, the pulse power and
chirp incident on the SiN waveguide are adjusted such that
the launched pulse approaches the threshold peak intensity
for soliton fission near the output facet of the chip. A
normal-dispersion single-element aspheric lens is then used
to out-couple the light without introducing appreciable
higher-order dispersion, and a 2-cm-long rod of fused silica
glass recompresses the pulse to near its transform limit. FIG.
8 shows the reconstructed pulse profile obtained through
frequency-resolved optical gating (FROG). Pulse durations
of 15 fs (2.8 optical cycles, full width at half maximum) and
out-coupled pulse energies in excess of 100 pJ (1 W average
power) are readily achievable at a repetition rate of 10 GHz.
With regard to FIG. 8, few-cycle pulse generation are shown
for (panel A) experimental and (panel B) reconstructed
FROG traces. Panel C shows a reconstructed temporal pulse

5. profile with a full width at half maximum duration of 15 fs

(2.8 optical cycles). Panel D shows a comparison of recon-
structed and experimental spectra. The quasi-CW spectral
wings of the initial comb spectrum near 1550 nm do not
contribute appreciably to the pulse and thus are not seen in
the reconstructed spectrum. At least 75% of the total optical
power is concentrated in the compressed pulse. More
sophisticated amplitude and phase compensation of the
initial comb spectrum could allow an even larger fraction of
the power to be compressed.

The combination of high-repetition rate pulse trains,
ultrastable broadband frequency synthesis, few-cycle pulse
generation, and extensible construction in our EOM-comb


U.S. Patent May 18, 2021 Sheet 3 of 12 US 11,011,882 B2

Unstabilized %'

Stabilized

FIG. 3


US 11,011,882 B2

13
microwave signals applied to phase modulators 222, 222.2,
and 222.3 are aligned using phase shifters 286.2 and 286.3

In the process for making stabilized comb 306, receiving,
by phase modulator 222 in communication with dielectric
resonant oscillator 290, continuous wave light 220 can
include laser light with a single frequency and a constant
intensity.

In the process for making stabilized comb 306, receiving,
by phase modulator 222 from dielectric resonant oscillator
290, phase control signal 300 can include an amplified signal
from oscillator 290 in which the relative phase of the
microwave signals applied to phase modulators 222, 222.2,
and 222.3 are aligned using phase shifters 286.2 and 286.3

In the process for making stabilized comb 306, producing,
from continuous wave light 220 and phase control signal
300, phase modulated light 224 can include continuous light
220 with the application of phase modulation sidebands at
the microwave frequency of oscillators 290 and with a phase
modulation index given by the power of microwave radia-
tion 300 applied to the modulator and the phase modulation
efficiency of phase modulator 222

In the process for making stabilized comb 306, producing
phase modulation signal 308 can include signal 300 after it
has passed through phase modulator 222.3.

In the process for making stabilized comb 306, receiving,
by intensity modulator 226 in communication with phase
modulator 222, phase modulated light 224 can include
continuous light 220 with the application of phase modula-
tion sidebands at the microwave frequency of oscillators 290
and with a phase modulation index given by the power of
microwave radiation 300 applied to the modulator and the
phase modulation efficiency of phase modulator 222.

In the process for making stabilized comb 306, receiving,
by intensity modulator 226 intensity control signal 302 can

include a microwave frequency signal that is derived from 3

oscillator 290 and whose phase is adjusted with shifter 286.4
to be aligned with the phase of signals 300 applied to phase
modulators 222, 222.2, and 222.3 and whose power is
adjusted to provide a 50% duty cycle intensity modulation of
light 224.3.

In the process for making stabilized comb 306, producing,
frequency comb 228 from intensity control signal 302 and
phase modulated light 224 can include continuous wave
light 220 with the application of phase modulation and a
50% duty cycle intensity modulation at the frequency of
oscillator 290.

In the process for making stabilized comb 306, receiving,
filter cavity 234 in communication with intensity modulator
226, frequency comb 228 from intensity modulator 226 can
include a Fabry Perot optical cavity of two mirrors in which
the medium between the mirrors is filled with air, vacuum,
or a low-loss optical material. The linewidth of the Fabry-
Perot cavity must be less than approximately 10 MHz. The
free-spectral range of the cavity must be aligned to the
frequency of oscillator 290. The resonance frequency of one
filter cavity mode must be aligned to the continuous wave
laser 218.

In the process for making stabilized comb 306, producing
filtered light 236 from frequency comb 228 can include light
232.1 after passing through the filter cavity. Light 236 has
been filtered by the filter cavity 234 such that the intensity
of radiation about each mode of the frequency comb light
228 and outside the bandwidth of the filter cavity 234 is
attenuated.

In the process for making stabilized comb 306, receiving,
by pulse shaper 238 in communication with filter cavity 234,
filtered light 236 from filter cavity 234 can include a

0

30

14

programmed line-by-line optical filter that enables intensity
and phase control of each mode of the frequency comb light
228 that is received from the filter cavity 236. Line-by-line
intensity and phase control enables generation of a com-
pressed pulse in which the relative phase difference between
the frequency comb modes is zero.

In the process for making stabilized comb 306, producing
shaped light 240 from filtered light 236 can include adjust-
ment and alignment of the phases of the comb modes
produced by phase modulation and intensity modulation
such that the relative line-by-line relative phase is zero.

In the process for making stabilized comb 306, receiving,
by highly nonlinear fiber 242 and compressor 246 in com-
munication with pulse shaper 238, shaped light 240 from

5 pulse shaper 238 can include shaping the pulse incident on

element 242 such that the pulse is compressed to its maxi-
mum peak intensity including the effects of amplifier 230.2.

In the process for making stabilized comb 306, producing
compressed light 248 from shaped light 240 can include
adjusting the applied second order dispersion with grating
compressor 246 by adjusting the relative separation of the
grating pair.

In the process for making stabilized comb 306, receiving,
by waveguide 250 in communication with highly nonlinear

5 fiber 242 and compressor 246, compressed light 248 can

include a pulse that is temporally compressed to achieve its
high peak intensity.

In the process for making stabilized comb 306, producing
tailored light 298 from compressed light 248 can include
utilizing a waveguide to create a supercontinuum spectrum
by soliton compression, soliton fission, and dispersive-wave
generation.

In the process for making stabilized comb 306, producing,
by interferometer 214 in communication with optical tailor
212, difference frequency 258 from tailored light 298 with
frequency difference crystal 256 can include use of light 298
that contains components at approximately 1550 nm, which
is frequency doubled to 780 nm, and 780 nm. Interference of
the frequency doubled light and the approximately 780 nm
light from element 298 is used to detect the carrier envelope
offset frequency of the ultrafast electro-optic laser 200.

In the process for making stabilized comb 306, producing,
by stabilized local oscillator cavity 280, stabilized local
oscillator signal 282 can include the signal from the oscil-
lator 290 after passing through phase modulator 222.3 and
the cavity 280.

In the process for making stabilized comb 306, converting
stabilized local oscillator signal 282 into stabilization signal
288 can include a phase quadrature comparison of the
oscillator signal 290 and the signal that is output from the
cavity 280. A double balanced mixer is used to perform the
phase comparison between signal 308 and the oscillator 290

In the process for making stabilized comb 306, commu-
nicating stabilization signal 288 to dielectric resonant oscil-

5 lator 290 to make stabilization signal 288 can include use of

a PID servo electronics to create the feedback signal 288 that
is applied to oscillator 290

‘The process for making stabilized comb 306 can include
receiving, by phase shifter 286 in communication with
dielectric resonant oscillator 290 and phase modulator 222,
phase control signal 300 from dielectric resonant oscillator
290 by microwave amplification of the signal from oscillator
290 and coordinating application of phase shifts with phase
shifters 286.

‘The process for making stabilized comb 306 can include
receiving, by phase shifter 286 in communication with phase
modulator 222 and intensity modulator 226, phase modula-


US 11,011,882 B2

25

repetition rates fdiff, can then be counted with a frequency
counter. The exact value of fdiff is defined solely in terms of
the known RF-synthesizer set points and can be used to
assess the absolute frequency synthesis accuracy of the
comb without any data fitting or drift correction,

Again, FIG. 9 shows the measured stability of the differ-
ence in comb repetition rates after an acquisition time of
11,000 s.

‘A zero-dead-time counter (H-type) is used to record the
RE beat between the two 10 GHz signals while the MDEV
is used for the stability calculations. At short averaging
times, t<2 s, the measured stability is limited by the counter
and the t-3/2 slope is indicative of white phase noise for two
mutually phase locked lasers. For 10<t<100 s, differential
noise in the system frustrates the phase coherent averaging,
though this noise could be reduced by path-length cancel-
lation of the optical paths, allowing the same degree of
stability to be reached at shorter averaging times. At 2,000
s of averaging time, the MDEV yields a minimum uncer-
tainty of 3.1x107!” (310 nHz) for a carrier frequency of 10
GHz. The measured 163-nHz frequency offset in the mean
of the acquisition is statistically consistent with zero syn-
thesis error at the demonstrated level of stability. As a result,
the demonstrated combination of operational reliability and
absolute accuracy may make the EOM comb is a tool for
long-term measurements of ultra-stable optical frequencies
and optical clock networks.

To determine the correct value of fdiff, the EOM-comb
pump-laser frequency vp is first expressed in terms of £0 and
frep for each comb:

Np hotN rep

Vp Pecan M rep aus Sa

where N and M are the mode numbers at the pump fre- 3

quency for the EOM comb and auxiliary comb, respectively.
fa is the frequency-offset set point used to phase lock the
auxiliary comb to the CW laser.

Rewriting the comb equations in terms of the repetition
rates yields:

Subtracting frep from the 40th harmonic of frep,aux
yields an expression for faiff in terms of the frequency set
points, mode numbers, and pump frequency:

40 1 40 1
Lag = 40 pans ~ fan = (59 ~ Fo Gq lO fa) 5 fi

In the experiment, N=19339. Thus, by tuning the auxiliary
comb such that M=40xN=773 560, the vp term is entirely
canceled. Using the experimental values of fa=40 MHz,
£0,aux=30 MHz, and f0=3542 MHz yields:

1
fait = Fy Sa ~ Foaue + fo) = 183670.303531723450 Hz.

While one or more embodiments have been shown and
described, modifications and substitutions may be made

45

50

35

60

65

26

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 (e.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. An ultrafast electro-optic laser for making a stabilized
comb, the ultrafast electro-optic laser comprising

a comb generator that produces a frequency comb and

comprises:
a dielectric resonant oscillator that:
receives a stabilization signal; and
produces a phase control signal from the stabilization
signal;
a phase modulator in communication with the dielectric
resonant oscillator and that:
receives continuous wave light;
receives, from the dielectric resonant oscillator, a
phase control signal;
produces, from the continuous wave light and the
phase control signal, phase modulated light; and
produces a phase modulation signal;
an intensity modulator in communication with the
phase modulator and that:
receives, from the phase modulator, the phase modu-
lated light;
receives an intensity control signal; and
produces a frequency comb from the intensity con-
trol signal and the phase modulated light;


US 11,011,882 B2

17

power into a frequency comb with a mode spacing given by
the microwave driving frequency f,,. The frequency of each
resulting mode n, counted from the CW laser at frequency
v,» can then be expressed as v,,-v,+nf,,. Equivalently, the
modes can be expressed as a function of the classic offset
frequency f, and repetition rate f,,,, parameters as v,—fy+
n'f,,.,» Where now the mode number n' is counted from zero
frequency and fy_,=fy,-

FIG. 1 shows carving femtosecond pulses from a con-
tinuous-wave (CW) laser with subcycle precision, wherein a
chirped pulse train is derived from a 1550-nm CW laser by
electro-optic phase and intensity modulation driven by a
10-GHz dielectric resonant oscillator (DRO) that is locked
to a high-Q microwave cavity in the stabilized-local-oscil-
lator (STALO) configuration. The pulse train is then opti-
cally filtered by a Fabry-Pérot cavity to suppress electronic
thermal noise on the comb lines before spectral broadening
in highly nonlinear fiber (HNLF) followed by a silicon-
nitride waveguide. Octave-spanning spectra allow detection
of the comb offset frequency in an f-2f interferometer that is
used to stabilize the DRO output. FIG. 3 shows, that without
stabilization, the microwave-derived pulse train exhibits
large pulse-to-pulse timing jitter relative to the CW carrier.
When the drive frequency is stabilized by feedback from the
comb offset frequency and the STALO cavity, sub-optical
cycle phase coherence between successive pulses is
achieved. Stabilized pulses are shown with zero carrier-
envelope offset. FIG. 4 shows, in a frequency-domain pic-
ture, the unstabilized comb exhibits large noise multiplica-

tion as the mode number n expands about zero. Mode 3

filtering suppresses high-frequency thermal noise. The fully
stabilized comb lines appear as 5-functions because the
CW-laser stability is transferred across the entire comb
bandwidth. FIG. 5 shows ab optical phase noise picture of

the comb, showing the effects of the f-2f stabilization, 3

STALO cavity, and filter cavity.

For the EOM comb to achieve ultrastable coherence
between v, and f,,, integrated phase noise of each mode is
below x radians. In the temporal domain, this corresponds to
subcycle timing jitter, and for EOM combs this requirement
becomes more difficult to achieve as the comb bandwidth is
increased because of microwave-noise multiplication. For
octave-spanning spectra at a 10-GHz repetition rate, this
multiplication factor is n'~20,000 and corresponds to an
86-dB increase in phase noise. Thus, reaching the x-radian
threshold with an EOM comb involves treatment of the
noise at all Fourier frequencies.

Broadband thermal noise in the electronic components up
to the Nyquist frequency causes the phase-coherence thresh-
old to be exceeded. To compensate, a Fabry-Pérot cavity
optically filters the broadband thermal noise fundamental to
electro-optic modulation, resulting in a detectable carrier-
envelope offset frequency. However, the cavity linewidth
(typically a few megahertz) places a lower bound on the
range of frequencies where this suppression is possible.

In the stabilized EOM comb, e.g., as shown in FIG. 2, a
dielectric-resonator oscillator (DRO) has a nominal operat-
ing frequency of 10 GHz and 0.1% tuning range to drive the
modulators.

With regard to FIG, 2, comb generation and stabilization
includes fiber paths shown as solid lines; free-space paths
shown as dashed lines; and electrical shown as gray dotted
lines, wherein the following abbreviations or acronyms are
used: ULE, ultra-low expansion cavity, PM, phase modula-
tion; IM, intensity modulation; DRO, dielectric resonant
oscillator; PS, phase shifter; EDFA, erbium-doped fiber
amplifier; HNLF, highly nonlinear fiber; SiN, silicon-nitride

0

2

40

&

0

0

18
waveguide: BPF, band-pass filter; DBM, double-balanced
mixer; STALO,  stabilized-local-oscillator cavity; and
PPLN, periodically poled lithium niobate.

DRO output is amplified before driving phase modulators
to produce comb spectra, e.g., as FIG. 6A.

FIG. 6 shows high-repetition-rate supercontinuum for a
(panel A) spectrum of the 10-GHz EOM comb directly after
generation. Panel B shows a ten-gigahertz supercontinuum
Spectra spanning from 750 to 2750 nm for two different
silicon-nitride waveguide widths. The spectral intensity is
scaled to intrawaveguide levels. Also shown is the spectrum
of the first-stage highly nonlinear fiber (HNLF). Panel C
shows a ten-gigahertz supercontinuum optimized for spec-
tral smoothness by reducing incident power (blue). Between
830 and 1450 nm, a flat spectrum (+3 dB) is produced by a
single passive optical attenuator. Panel D shows a super-
continuum spectrum from a 30-GHz EOM comb. Top insets
show that comb coherence is maintained across the entire
spectrum (optical SNRs are spectrometer limited). Bottom
inset shows initial spectrum of the 30-GHz EOM comb.
They axes in both (C) and (D) show the power spectral
density (PSD) obtained in the output fiber.

After transmission through an optical-filter cavity to sup-
press thermal noise. the chirped-pulse output of the OM
comb is compressible to durations as short as 600 fs,
depending on the initial spectral bandwidth. Pulse durations
greater than ~200 fs have been contemplated for coherent
supercontinuum broadening in nonlinear media with anoma-
lous dispersion. If the nonlinear material exhibits normal
dispersion, broadening due to pure self-phase modulation is
produces lower-noise spectra owing to the suppression of
modulation instability. The ultrafast electro-optic laser
includes two-stage broadening from a normal-dispersion
highly nonlinear fiber (HNLF) to achieve initial spectral
broadening and pulse compression to 100 fs followed by an
anomalous-dispersion SiN waveguide for broad spectrum
generation.

High-repetition rate lasers (f,,,210 GHz) produce lower
pulse energies for the same average power, making it
challenging to use nonlinear broadening to produce the
octave bandwidths required for self-referencing. However,
patterned nanophotonic waveguides have high nonlinearity
and engineerable dispersion. Here, the ultrafast electro-optic
laser has input-coupling efficiency with a SiN waveguide of
up to 85% that enables a broadband supercontinuum to be
generated with pulses from high-repetition rate ultrafast
sources. The spectra generated with the 10-GHz EOM comb
from the ultrafast electro-optic laser spans wavelengths from
750 nm to beyond 2700 nm for two different waveguide
geometries (FIG. 6B), producing a total integrated power of
~1.1 W. Individual comb lines across the entire bandwidth
exhibit a high degree of extinction (50 dB at 1064 nm; see
FIG. 10 for data at 775, 1064, and 1319 nm) and do not
exhibit any intermodal artifacts such as sidebands, a com-

5 mon problem when mode filtering is used to convert low-

repetition rate combs to high repetition rates.

To investigate the scalability to even higher repetition
rates, we made additional supercontinuum measurements
using a 30-GHz EOM comb, which produced 600-fs, 70-pJ
pulses (FIG. 6D). Despite the three-times reduction in pulse
energy compared to the 10-GHz comb, similar broadband
spectra are readily obtained. In both cases, if the waveguide
input pulse energy is kept below ~100 pJ, smooth spectra
can be obtained with high power per comb mode.

For applications with flat spectra over broad bandwidths,
such as astronomical spectrograph calibration, supercon-
tinuum light can be collected in a single-mode fiber and


US 11,011,882 B2

7

specifically from 1 dB to 3 dB. In an embodiment, phase
modulator 222 includes a fiber-coupled, lithium-niobate
waveguide phase modulator.

Phase modulated light 224 can include light with an
instantaneous phase modulation that corresponds to a low
phase noise electronic signal. A wavelength of phase modu-
lated light 224 can be from 300 nm to 20,000 nm, specifi-
cally from 500 nm to 2500 nm, and more specifically from
1500 nm to 1600 nm. A power of phase modulated light 224
can be from 1 mW to 100 mW. A duty cycle of phase
modulated light 224 can be from 0% to 100%, specifically
from 10% to 100%. The frequency of the phase modulation
can be from 1 GHz to 50 GHz, specifically from 1 GHz to
30 GHz. In an embodiment, phase modulated light 224
includes a 1550 nm laser with 8 pi radians of phase modu-
lation applied at a frequency of 10 GHz

Intensity modulator 226 can include a modulator or series
of modulators that vary the instantaneous intensity of light
224. Exemplary intensity modulators 226 include modula-
tors in which light propagates in free space or modulators in
which light propagates in a guided mode, which may be
implemented with a circular cross section waveguide, a
rectangular cross section waveguide, or a photonic-crystal
waveguide. Moreover, intensity modulators can be imple-
mented in a Mach Zehnder configuration, or with electro
absorption, or with an optical resonator that is tuned with an
electronic signal. The half-wave voltage of intensity modu-
lator 226 can be from 0.001 Volts to 5 Volts, specifically
from 0.1 Volts to 3 Volts, and more specifically from 1 Volts

to 3 Volts. The loss of intensity modulator 226 can be from 3

0.1 dB to 5 dB and more specifically from 1 dB to 3 dB. The
bandwidth of intensity modulator 226 can be from 1 Ghz to
50 GHz, specifically from 1 GHz to 30 GHz. In an embodi-
ment, intensity modulator 226 includes a fiber coupled
lithium niobate Mach Zehnder modulator.

Frequency comb 228 can result from phase modulation
and intensity modulation of the continuous wave laser. The
frequency comb 228 can include instantaneous intensity and
phase modulation. The frequency comb can include modu-
lation sidebands with a frequency separation given by the
modulation control signals 300 and 302 and the phase and
intensity modulator electro-optical conversion efficiencies.

Phase shifter 286 adjusts the phase or temporal delay of
electronic signals that are applied to phase modulator 222
and intensity modulator 226. In an embodiment, phase shift
286 is a mechanical phase shifter with SMA connectors and
less than 1 dB insertion loss.

Stabilization signal 288 can include an electronic signal
communicated by an electronic wire for frequency stabili-
zation of DRO 290 with respect to cavity 280. In an
embodiment, signal 288 has a bandwidth from DC to 10
MHz.

Dielectric resonator oscillator (DRO) 290 can include an
electronic oscillator that produces a low-phase-noise output
frequency. The oscillation frequency of DRO 290 can be
from 1 GHz to 50 GHz, and specifically from 1 GHz to 30
GHz. The output power of the DRO can be from 0 dBm to
40 dBm, specifically from 5 dBm to 15 dBm. In an embodi-
ment, DRO produces a 10 GHz output frequency with phase
noise of -137 dBm/Hz at 100 kHz and -158 dBm/Hz at 1
MHz.

Lock cavity 292 can include an optical frequency refer-
ence cavity. Exemplary lock cavities 292 can include
ultralow expansion glass spacer cavities with low loss
dielectric mirrors and bulk fused silica solid cylinder cavi-
ties with one plano endface and one convex endface and low
loss dielectric mirror coatings applied to the endfaces. In an

S

8

2

40

&

8

embodiment, lock cavity 292 is an evacuated Fabry Perot
cavity implemented with fused silica mirror substrates with
10 ppm transmission dielectric reflector coatings for 1550
nm light, and the mirrors are supported by an ultralow
expansion glass spacer with a 15 cm length.

lock signal 294 can include the feedback signal for
frequency stabilization of the continuous wave laser 218 and
continuous wave laser light 220 to the lock cavity 292.

Mirror 296 can include a metallic or dielectric reflecting
surface.

Phase control signal 300 can include an electronic signal
of wide bandwidth. In an embodiment, phase control signal
300 is a low phase noise single frequency microwave tone
at 10 GHz or 30 GHz with a power level up to 36 dBm.

Intensity control signal 302 can include an electronic
signal of wide bandwidth. In an embodiment, intensity
control signal 302 is a low phase noise single frequency
microwave tone at 10 GHz or 30 GHz with a power level up
to 27 dBm.

Tailored light 298 can include light with a wide band-
width, high power, periodic structure in the temporal and
frequency domains, and high spectral coherence. The wave-
length of tailored light 298 can be from 300 nm to 30,000
nm, specifically from 500 nm to 3000 nm. In an embodi-

5 ment, tailored light 298 contains a supercontinuum spanning

from 780 nm to 2500 nm with 2000 mW of average power
and a pulse repetition frequency of 10 GHz.

Amplifier 230 can include an optical amplifier for the
frequency comb light 228. Exemplary amplifiers 230 can
include doped-fiber amplifiers and semiconductor amplifi-
ers. In an embodiment, amplifier 230.1 is an erbium doped
fiber amplifier with a maximum output power of 100 mW
and a required input power of | mW. In an embodiment,
amplifier 230.2 is an erbium doped fiber amplifier with a
maximum output power of 5000 mW and a required input
power of 1 mW.

Amplified light 232 can include frequency comb light 228
following optical amplification. Exemplary amplified light
232 can include light centered in the 1550 nm wavelength
region and include intensity modulation and phase modula-
tion. In an embodiment, amplified light 232 includes a
1550-nm-band laser with 100 mW of power and with 8 pi
radians of phase modulation and 50% duty cycle intensity
modulation applied at a frequency of 10 GHz.

Filter cavity 234 can include a standing-wave or traveling
wave optical cavity. In an embodiment, filter cavity 234 is a
Fabry-Perot cavity with a free-spectral range of 10 GHz, and
a resonance linewidth of 2 MHz.

Filtered light 236 can include light with instantaneous
phase and intensity modulation. A wavelength of filtered
light 236 can be from 300 nm to 20,000 nm, specifically
from 500 nm to 2500 nm, and more specifically from 1500
nm to 1600 nm. A power of filtered light 236 can be from 1
mW to 1000 mW. The frequency of the phase and intensity

5 modulation can be from 1 GHz to 50 GHz, specifically from

1 GHz to 30 GHz. In an embodiment, filtered light 236
includes a 1550-nm-band laser with 50 mW of power and
with 8 pi radians of phase modulation and 50% duty cycle
intensity modulation applied at a frequency of 10 GHz.
Pulse shaper 238 can include a programmable optical
filter with high frequency resolution to adjust the intensity
and phase of each line of the frequency comb light 228
Exemplary pulse shapers can include those created with a
spatial light modulator, using liquid crystal devices, or with

5a silicon photonics device.

Shaped light 240 can include light with instantaneous
phase and intensity modulation. A wavelength of shaped


U.S. Patent

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May 18, 2021

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US 11,011,882 B2

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US 11,011,882 B2

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light 240 can be from 300 nm to 20,000 nm, specifically
from 500 nm to 2500 nm, and more specifically from 1500
nm to 1600 nm. A power of shaped light 240 can be from 1
mW to 1000 mW. The frequency of the phase and intensity
modulation can be from 1 GHz to 50 GHz, specifically from
1 GHz to 30 GHz. In an embodiment, shaped light 240
includes a 1550-nm-band laser with 10 mW of power and
with 8 pi radians of phase modulation and 50% duty cycle
intensity modulation applied at a frequency of 10 GHz.

Highly nonlinear fiber 242 can include an optical fiber
with sufficiently large third-order nonlinear coeflicient. In an
embodiment, highly nonlinear fiber 242 is five meters in
length, includes GeO2 doped silica fiber with an operating
wavelength of 1550 nm, with a group-velocity dispersion
that is -1.3 ps/nm/km

Optical coupler 244 can include a high numerical aperture
lens to collimate the output of the highly nonlinear fiber 242.

Compressor 246 can apply a tunable quantity of second-
order group-velocity dispersion. Exemplary compressors
246 include optical grating compressors, fiber Bragg grating
compressors, optical fiber of a specific length, and program-
mable spatial light modulators. In an embodiment, compres-
sor 246 is a diffraction grating pair with a tunable separation
between the gratings in order to affect a change in the
applied second-order group-velocity dispersion.

Compressed light 248 can include light with instanta-
neous phase and intensity modulation. A wavelength of
compressed light 240 can be from 300 nm to 20,000 nm,
specifically from 500 nm to 2500 nm, and more specifically

from 1500 nm to 1600 nm. A power of shaped light 240 can. 3

be from 1 mW to 5000 mW. The frequency of the phase and
intensity modulation can be from 1 GHz to 50 GHz, spe-
cifically from 1 GHz to 30 GHz. In an embodiment, com-
pressed light 240 includes a 1550-nm-band laser with 4000

mW of power and with 8 pi radians of phase modulation and. 3

50% duty cycle intensity modulation applied at a frequency
of 10 GHz. The relative phase shift between the frequency-
comb modes that provide compressed light 248 are set to
zero to the extent possible by the system.

Waveguide 250 can include a chip-integrated nonlinear
waveguide made from either silicon nitride or tantalum
pentoxide that is deposited onto an oxidized silicon wafer.
Waveguide 250 can include other materials, including sili-
con, GaAs, InGaAs, InP, and vanadium pentoxide. The
waveguide 250 can include optimized chip-edge coupling
structures that include a tapered waveguide region that
enhances coupling efficiency to free-space optics or fiber
optics. Furthermore, the input and output tapering structures
can be different to optimize operation at different wave-
length. Moreover, waveguide 250 can include a section
designed for supercontinuum generation with an optimized
rectangular cross section and a length from 1 mm to 10,000
mm, specifically 1 mm to 1000 mm, and more specifically
1 mm to 100 mm. Furthermore, waveguide 250 can include
sections of differing rectangular cross section to separately
optimize soliton compression effects and soliton fission or
dispersive-wave generations effects. In an embodiment,
waveguide 250 includes silicon nitride with silicon dioxide
cladding. Waveguide 250 can have has tapered waveguide
structures at both ends with waveguide height that is
approximately 800 nm and width approximately 2000 nm
with waveguide length that is 15 mm.

Mirror 252.1 can include a metallic or dielectric reflecting
surface that is partially transmissive at one wavelength and
fully transmissive at another wavelength.

Lens 254 can include a lens to couple light from a free
space laser beam to a single mode optical fiber.

2

40

6:

10

Second-harmonic generation crystal 256 can include a
crystal designed to create second-harmonic light based on a
second-order nonlinearity.

Difference frequency 258 can include the carrier-envelope
offset frequency of ultrafast electro-optic laser 200. In an
embodiment, difference frequency 258 is the difference in
frequency between the second-harmonic of 1550-nm light
emitted by waveguide 250 and the 780-nm light emitted by
waveguide 250.

Exemplary photodetectors 260 include devices made
from silicon and InGaAs. In an embodiment, photodetector
260 includes a silicon photodiode with transimpedance
amplifier.

Electrical amplifier 262 includes a microwave frequency
electronic amplifier.

Mixer 264 can include an electronic double balanced
mixer,

Band pass filter 266 can include an electronic, frequency
tunable bandpass filter with less than 50 MHz bandwidth.
Exemplary filters include cavity filters and lumped element
filters.

Divider 268 can include an electronic digital frequency
divider that reduces the frequency of an electronic signal by
an integer ratio. In an embodiment, divider 268 reduces the
frequency of an input signal by a factor of 32

Clock 270 can include an electronic oscillator that pro-
vides a frequency reference for the ultrafast electro-optic
laser 200.

Oscillator 272 can include a RF oscillator that is phase
stabilized to an input RF clock. Exemplary oscillators
include direct-digital synthesis oscillators and phase locked
voltage-controlled oscillators.

Oscillator signal 274 can include a sine-wave electronic
signal with power level of 7 dBm.

Servo 276 can include a proportional, integral. and dif-
ferential (PID) electronic servo controller.

Set point 278 can include an electronic voltage signal that
is used as the reference for an electronic servo.

Stabilized local oscillator cavity 280 can include a high
quality factor electronic resonant cavity consisting of a
closed or mostly closed metal volume that stores microwave
radiation. Cavity 280 includes input and output coupling
ports with a coupling between a coaxial cable and the stored
microwave radiation inside the cavity. Exemplary cavities
include those constructed in the form of a circular cylinder
or rectangular box, and those constructed of metals such as
aluminum and copper and those in which the internal surface
is coated with a metal like gold or platinum. The cavity may
be highly polished on the internal surfaces to reduce scat-
tering of the microwave radiation, and polishing may be
obtained through precision machining, chemical vapor pol-
ishing, or mechanical polishing. The cavity may feature an

5 insertable element designed to distort the internal micro-

wave field shape and alter the resonant frequency of the
cavity. In an embodiment, cavity 280 includes aluminum in
which the internal surface has been precision machined and
mechanically polished.

Stabilized local oscillator signal 282 can include micro-
wave radiation that is incident upon the cavity 280.

Circulator 284 can include a passive, non-reciprocal
microwave frequency device with three ports.

Phase modulation signal 308 can include a phase modu-
lation of the signal incident upon the microwave cavity 280.

Clock signal 310 can include an electronic sine wave
signal at a single frequency.


U.S. Patent

May 18, 2021

Sheet 7 of 12 US 11,011,882

(A) 80 r t r t T
sok 4-20
Free-running DRO
40 —DRO with f, lock 4-40

Optical Phase Noise (dBc/Hz)

vn DRO with STALO
DRO with STALO +f, lock

Qut-of-loop 1070 nm beat
(left axis offset +7.7 dBe/Hz)

0
-20 -100
-40 120
60 140
-80 -160
-100 a L A ‘ at j-180
10! 407 40° 104 10° 40°
Frequency (Hz)
40
30 kHz RBW («c) 3kHz RBW @) tHZRBW
41 kHz VBW ~ 30 Hz VBW 4 Hz VBW
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Frequency (MHz) Frequency (kHz) Frequency (Hz)

FIG. 7

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10 GHz Phase Noise (dBc/Hz)


US 11,011,882 B2

21

system provides a versatile ultrafast source with other addi-
tional practical benefits. For instance, these combs could
also support further photonic integration through comple-
mentary metal-oxide-semiconductor (CMOS)-compatible
modulators, alignment-free construction, the use of com-
mercially available components, and straightforward user
customization. Moreover, whereas the optical and micro-
wave cavities currently limit the broad tuning capability of
the repetition rate, the ~300 THz of comb bandwidth places
a mode within 5 GHz of any spectral location in this range.
By overcoming several experimental challenges related to
broadening and stabilizing noisy picosecond-duration
pulses, our techniques are widely applicable to existing
technologies with demanding requirements, such as chip-
based microresonators or semiconductor lasers.

FIG. 9 shows frequency accuracy and stability for the
ultrafast electro-optic laser. Here, modified Allan deviation
(MDEV) had an out-of-loop frequency stability of the FOM
comb frep measured against a separate self-referenced fiber
comb with a two-sided 68% confidence intervals at each t
are calculated using 7? statistics. The top inset shows 11,000
s of frequency-counter data from which the MDEV curve
was calculated (expected frequency subtracted), and the
bottom inset shows a histogram of the data. The minimum
MDEV uncertainty of 3.1x10-17 at t=2,000 s implies there
is no statistical offset in the frequency synthesis of the comb.

The ultrafast electro-optic laser for production of 10-GHz
EOM comb, including both the optical and microwave
stabilization components, is shown in FIG. 2 Here, a central

mode of the EOM comb is formed from a 1550-nm CW laser 3

that is stabilized with sub-hertz linewidth to an ultra-low
expansion cavity. For maximal frequency tunability though,
the comb can also be operated successfully with an external-
cavity diode laser as the pump. The CW laser is then

transmitted through two to four lithium-niobate phase modu- 3

lators with low half-wave voltage (Vx=3 V), optically
connected in series, to produce a periodically chirped con-
tinuous waveform. The total number of modes generated by
a single-phase modulator is determined by the microwave
drive power and the modulator’s half-wave voltage, though
multiple modulators can be added in series with their
microwave phases aligned to linearly increase the number of
modes. In this case, at the highest drive power of 36 dBm,
each modulator can make approximately 40 comb lines. An
intensity modulator driven by the same microwave drive
then carves the chirped output into a 50% duty-cycle pulse
train that can be readily compressed to near the Fourier-
transform limit using single-mode optical fiber, though a
programmable pulse shaper is used here for ease of tunabil-
ity. All components in the comb generator are polarization-
maintaining for convenience and reliability. The comb out-
put is then amplified with a single-mode erbium-doped fiber
amplifier (EDFA, 25 dB gain, noise figure).

The optical filter cavity is a standard Fabry-Pérot filter
with a free spectral range matched to the comb repetition
rate and included two dielectric mirrors (99.9% reflectivity),
each with a 1-m radius of curvature. No thermal, mechani-
cal, or vacuum isolation is used. The rear surface of each
mirror is antireflection coated and one mirror is glued to a
piezoelectric transducer for length stabilization. Weak side-
bands at 22 MHz are put on the comb by driving one of the
comb’s phase modulators in reverse via the RF output port.
These sidebands are used to generate a Pound-Drever-Hall
error signal for locking the cavity to the comb. The total
fiber-to-fiber transmission of the cavity system is 75%.

The aluminum microwave cavity used to pre-stabilize the
10-GHz DRO has a cylindrical geometry and is operated in

2

40

45

22

the TEO11 mode with an unloaded Qfactor of 8300. The
cavity was machined in-house, though we note that compa-
rable commercial options are available. The RF output port
of one optical phase modulator is used to provide a power of
up to 30 dBm for coupling to the STALO cavity. By placing
the cavity after this modulator, phase noise introduced by
both the DRO and the amplifier can be suppressed. The
cavity is operated in a nearly critically coupled regime in
order to achieve the maximum carrier suppression (>30 dB)
and frequency-discrimination sensitivity from the reflected
signal. An error signal for locking the DRO to the cavity is
generated by mixing this reflected signal with the original
DRO output. Increasing the cavity Q or adding an additional
low-phase-noise amplifier before the STALO mixer can
improve the amount of phase-noise reduction that is achiev-
able due to the enhanced sensitivity of the frequency-
discrimination signal.

Following the filter cavity, the 10 GHz and 30 GHz pulse
trains are amplified in an anomalous dispersion EDFA
designed for sub-picosecond pulses (maximum output
power 5 W, 45 dB gain, 5.8 dB noise figure) before under-
going two stages of nonlinear broadening. The first stage
uses highly nonlinear fiber (HNLF) with normal dispersion
at 1550 nm (D=-1.4 ps/nm/km) and is seeded with a total
optical power of 3.7 W. The HNLF has a free-space output
facet that is angle-cleaved to prevent back reflections and the
output beam is then directed to a pair of high-transmission
diffraction gratings (940 grooves/mm) to compensate the
HNLF dispersion. Following the compressor, sub-100-fs
pulses are delivered to the second-stage SiN waveguide with
energies of approximately 150 pJ.

The photonic waveguides used for the second-stage
broadening were made with a photonic damascene process
and low-pressure chemical-vapor-deposition (LPCVD) SiN,
are 15 mm in length, and have a thickness of 750 nm. For
self-referencing, a waveguide width of 1800 nm is chosen to
produce a dispersive wave near the second harmonic (775
nm) of the pump laser (1550 nm), though the spectrum is
adjustable by changing this parameter. By doubling the
pump laser in this way, the supercontinuum generation
process is decoupled from the frequency doubling, resulting
in very stable and reliable operation.

The waveguides have a fully oxide-clad (Si02) geometry
that serves to both protect the waveguide from contamina-
tion as well as likely improving the ability of the device to
withstand sustained thermal loads when incident with up to
several watts of optical power. Input coupling to the wave-
guide is accomplished using a molded-glass aspheric lens
with a design wavelength of 1550 nm and a numerical
aperture (NA) of 0.6 while output-coupling is achieved with
a 0.85-NA visible-wavelength microscope objective. Both
facets of the chip include inverse tapers (minimum dimen-
sion=150 nm, length 300 um) for improved coupling to
achieve a total power throughput greater than 70%.

‘As shown in panel C of FIG. 6, spectral flattening of the
waveguide output can be accomplished using a passive
in-line fiber attenuator with a fixed 20-dB attenuation coef-
ficient at 1550 nm. Due to an exponential roll-off in the
attenuation coefficient in going to shorter wavelengths, a
flatness of +3 dB is achieved spanning from 850 nm to 1450
am.

‘A fiber-coupled waveguide PPLN is used for second-
harmonic generation of residual 1550-nm pump light (100
mW) exiting the SiN waveguide for f-2f detection. The

5 PPLN output is temporally and spatially overlapped with the

775-nm supercontinuum light, coupled to single mode fiber,
and delivered to a 10-GHz-bandwidth photodetector with a


a2 United States Patent

US011011882B2

(10) Patent No.: US 11,011,882 B2

Papp et al. (45) Date of Patent: May 18, 2021
(54) ULTRAFAST ELECTRO-OPTIC LASER (58) Field of Classification Search
CPC ........ HOIS 3/0085; HO1S 3/005; HO1S 3/10;
(71) Applicant: Government of the United States of HO1S 3/0057; HO1S 3/0078;
America, as represented by the (Continued)
Secretary of Commerce, Gaithersburg,
MD (US) (56) References Cited
(72) Inventors: Scott Brian Papp, Boulder, CO (US): U.S. PATENT DOCUMENTS
David Richard Carlson, Boulder, CO 0.683.868 BD $017 F a
. . a + 653, ‘ermann et
Boeken CO (US), Seatt Alga 9.905.999 B2* 2/2018 Li Ho1s 3/0085
Diddams, Louisville, CO (US) (Continued)
(73) Assignee: GOVERNMENT OF THE UNITED OTHER PUBLICATIONS
STATES OF AMERICA, AS _ oo
REPRESENTED BY THE David R. Carlson et al. “Ultrafast electro-optic light with subcycle
SECRETARY OF COMMERCE, control” Science 361, 1358-1363 Sep. 28, 2018 (Year: 2018).*
Gaithersburg, MD (US) Primary Examiner —Tod T Van Roy
(*) Notice: Subject to any disclaimer, the term of this 4ssistant Examiner — Delma R. Fordé
patent is extended or adjusted under 35 (74) Attorney, Agent, or Firm — Office of Chief Counsel
US.C. 154(b) by 55 days for National Institute of Standards and Technology
(21) Appl. No.: 16/561,564 (67) ABSTRACT
. An ultrafast electro-optic laser makes a stabilized comb and
(22) Filed: Sep. 5, 2019 includes: a comb generator that produces a frequency comb;
+ eae a dielectric resonant oscillator; a phase modulator in com-
(65) Prior Publication Data munication with the dielectric resonant oscillator; an inten-
US 2020/0076149 Al Mar. 5, 2020 sity modulator in communication with the phase modulator;
an optical tailor in communication with the comb generator
Related U.S. Application Data and that produces tailored light; a filter cavity in commu-
(60) Provisional application No. 62/727,289, filed on Sep nication with the intensity modulator; a pulse shaper in
5, 2018 ° communication with the filter cavity; a highly nonlinear
, ° fiber and compressor in communication with the pulse
(1) Int. Ch shaper; an interferometer in communication with the optical
HOIS 3/10 (2006.01) tailor and that produces a difference frequency from the
HOIS 3/00 (2006.01) tailored light; and an electrical stabilizer in communication
Continued with the interferometer and the comb generator and that
(Continued) produces the stabilization signal with a stabilized local
(52) U.S. Cl oscillator cavity that produces a stabilized local oscillator
cpc . HOLS 3/0092 (2013.01); GO2F 1/01

(2013.01); GO2F 1/03 (2013.01); GO2F
170344 (2013.01);

(Continued)

signal that is converted into the stabilization signal and
communicated to the dielectric resonant oscillator.

20 Claims, 12 Drawing Sheets



U.S. Patent May 18, 2021 Sheet 10 of 12 US 11,011,882 B2

775 nm

Amplitude (dB)

Frequency (GHz)

1064 nm

0 20 40 60 80
Frequency (GHz)

1319 nm

= Heterodyne
Comb blocked
woe CW blocked
ss Electronic Noise Floor

RBW = 30 kHz
VBW = 100 Hz

Frequency (GHz)
FIG. 10


US.

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May 18, 2021 Sheet 9 of 12

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U.S. Patent May 18, 2021 Sheet 6 of 12 US 11,011,882 B2

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US 11,011,882 B2

15

tion signal 308 from phase modulator 222 by taking the
signal 300 that is output from phase modulator 222.3,
applying a phase shift, and applying it to intensity modulator
226.

The process for making stabilized comb 306 can include
producing clock signal 310 by use of a suitable clock source
as determined by the frequency stability needs of the ultra-
fast electro-optic laser 210.

‘The process for making stabilized comb 306 can include
signal processing and PID servo stabilization of the carrier-
envelope offset (CEO) frequency signal f,. The CEO signal,
a microwave-rate signal, may be amplified with amplifier
262.1, and it may be reduced in frequency with respect to an
electronic oscillator 272.2 that is phase locked to clock 270
using an electronic frequency mixer 264.1, and it may be
bandpass filtered by filter 266 in order to improve the signal
to noise ratio, and it may be further amplified by amplifier
262.2, and it may be frequency divided by an integer ratio
with digital frequency divider 268, and it is phase locked
with respect to the reference oscillator 272.1 by servo
feedback to the dielectric resonator oscillator 290. In a
subsequent process step, the process for making stabilized
comb 306 can include signal processing to further stabilize
the dielectric resonator oscillator 290 by stabilization with
respect to the cavity 280. Signal 308 emitted by phase
modulator 222.3 is delivered to cavity 280 and the output
signal 318 from cavity 280 is phase compared to oscillator
290. Signal 312.3, which represents the relative phase fluc-
tuations of oscillator 290 and cavity 280 are used for servo
stabilization of oscillator 290 with PID servo 276.2.

Ultrafast electro-optic laser 200 and processes disclosed
herein have numerous beneficial uses, including high-speed
linear and nonlinear spectroscopy of solid, liquid, and gas
samples, for high speed ranging measurements, calibration

of astronomical spectrographs, optical driving of particle 3

accelerators, for microwave and millimeter wave signal
generation, and high-speed optical communications sys-
tems. Advantageously, ultrafast electro-optic laser 200 over-
comes limitations of technical deficiencies of conventional
articles such as traditional mode locked laser technology that
do not operate at microwave rates with the ease and sim-
plicity of electro-optic lasers.

Ultrafast electro-optic laser 200 and processes herein
unexpectedly provides stabilization of an electro-optic laser
with sub-cycle accuracy and precision. Ultrafast electro-
optic laser 200 is a stabilized ultrafast pulse source with
sub-cycle accuracy and precision that does not involve mode
locking,

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

EXAMPLE

Ultrafast electro-optic light with subcycle control.

Generation of coherent optical frequency combs has had
an impact on precision metrology, imaging, and sensing
applications. Broadband white light generated through the
interaction of femtosecond mode-locked laser pulses is
composed of billions or trillions of precisely spaced wave-
lengths of light. An alternative to a mode-locked laser is
electro-optic modulation of a continuous-wave laser light
source that can generate optical frequency combs. The
electro-optic modulation techniques can operate at much
higher repetition rates than mode-locked lasers and yield
more precise measurements.

Light sources that are ultrafast and ultrastable enable
applications like timing with sub femtosecond precision and

S

40

50

6:

16

control of quantum and classical systems. Mode-locked
lasers have often given access to this regime, by using their
high pulse energies. The ultrafast electro-optic laser pro-
vides ultrastable control of low-energy femtosecond pulses
based on common electro-optic modulation of a continuous-
wave laser light source and provides 100-picojoule pulse
trains at rates up to 30 gigahertz and demonstrate sub-optical
cycle timing precision and output spectra spanning the near
infrared. The ultrafast electro-optic laser provides few-cycle
ultrafast pulses in an absence of mode locking and provides
high speed access to nonlinear measurements and rapid
transients.

Ultrafast lasers produce trains of femtosecond-duration
light pulses and can operate as frequency combs to provide

5 a time and frequency reference bridging the optical and

microwave domains of the electromagnetic spectrum.
Achieving phase control of these pulse trains to better than
a single optical cycle has enabled diverse applications
ranging from optical atomic clocks to controlling quantum
states of matter. These capabilities involve stability of a
suitable mode-locked resonator.

One alternative method that produces optical pulse trains
without mode locking is electro-optic modulation (EOM) of
a laser. These pulse generators, or EOM combs, have
tunability, reliability, commercialization, and spectral flat-
ness. Nevertheless, despite their broad appeal and decades of
development, the fundamental goal of electronic switching
with the optical-cycle precision are used to create ultrafast
trains of EOM pulses and has remained unmet, limited by
thermodynamic noise and oscillator phase noise inherent in
electronics.

The ultrafast electro-optic laser generates ultrafast and
ultrastable electro-optic pulses without any mode locking
and mitigates electro-optic noise by relying on the quantum-
limited optical processes of cavity transmission, nonlinear
interferometry, and nonlinear optical pulse compression, as
well as low-loss microwave interferometry. This results in
phase control of ultrafast electro-optic fields with a temporal
precision better than one cycle of the optical carrier. Because
electro-optic sources support pulse repetition rates greater
than 10 GHz, the ultrafast electro-optic laser opens up the
regime of high-speed, ultrafast light sources, enabling sam-
pling or excitation of high-speed transient events, as well as
making precision measurements across octaves of band-
width.

The ultrafast electro-optic laser has ultrafast phase control
by directly carving electro-optic pulse trains at 10 and 30
GHz with ~1-ps initial pulse durations and show that these
pulses can be spectrally broadened to octave bandwidths and
temporally compressed to less than three optical cycles (15
fs) in nanophotonic silicon-nitride (Si,N,, henceforth SiN)
waveguides. To deliver a femtosecond source timed with
subcycle precision, an EOM-comb configuration imple-
ments high-Q microwave-cavity stabilization of the 10-GHz
electronic oscillator. This oscillator is phase-locked to the
continuous-wave (CW) pump source via f-2f stabilization of
the carrier-envelope offset, enabling complete knowledge of
the 28,000 EOM-comb frequencies to 17 digits. Our imple-
mentation uses a cavity-stabilized CW laser to demonstrate
sub hertz-linewidth modes spanning the near infrared.

The EOM comb is derived from a microwave source that
drives an intensity modulator placed in series with multiple
phase modulators to produce a 50%-duty-cycle pulse train
with mostly linear frequency chirp as shown in FIG. 1, FIG.
3, FIG. 4, and FIG. 5. In the spectral domain, this process
results in a deterministic cascade of sidebands with pre-
scribed amplitude and phase that converts the CW laser


US 11,011,882 B2

27

an optical tailor in communication with the comb gen-

erator and that produces tailored light, the optical tailor

comprising:

a filter cavity in communication with the intensity
modulator and that:
receives the frequency comb from the intensity

modulator; and

produces filtered light from the frequency comb;

a pulse shaper in communication with the filter cavity
and that:
receives the filtered light from the filter cavity; and
produces shaped light from the filtered light;

a highly nonlinear fiber and compressor in communi-
cation with the pulse shaper and that:
receives the shaped light from the pulse shaper; and
produces compressed light from the shaped light;

a waveguide in communication with the highly non-
linear fiber and the compressor and that:
receives the compressed light; and
produces the tailored light from the compressed

light;

an interferometer in communication with the optical tailor
and that produces a difference frequency from the
tailored light, the interferometer comprising a fre-
quency difference crystal that receives the tailored
light; and

an electrical stabilizer in communication with the inter-
ferometer and the comb generator and that produces the
stabilization signal, the electrical stabilizer comprising:
a stabilized local oscillator cavity that produces a

stabilized local oscillator signal that is converted into
the stabilization signal and communicated to the
dielectric resonant oscillator.

2. The ultrafast electro-optic laser of claim 1, further

comprising:

a continuous wave laser in communication with the phase
modulator and that produces the continuous wave light.

3. The ultrafast electro-optic laser of claim 2, further

comprising:

a lock cavity in communication with the continuous wave
laser and that produces a lock signal to which the
continuous wave laser is locked.

4, The ultrafast electro-optic laser of claim 1, further

comprising:
a phase shifter in communication with the dielectric
resonant oscillator and the phase modulator, electroni-
cally interposed between the dielectric resonant oscil-
lator and the phase modulator, and that:
receives the phase control signal from the dielectric
resonant oscillator; and

shifts a frequency of the phase control signal before the
phase control signal is received by the phase modu-
lator.

5. The ultrafast electro-optic, laser of claim 1, further

comprising:
a phase shifter in communication with the phase modu-
lator and the intensity modulator, electronically inter-
posed between the phase modulator and the intensity
modulator, and that:
receives the phase modulation signal from the phase
modulator; and

shifts a frequency of the phase modulation signal to
produce the intensity control signal from the phase
modulation signal before the intensity control signal
is received by the intensity modulator.

6. The ultrafast electro-optic laser of claim 1, further

comprising:

10

20

30

35

40

45

60

28

an amplifier in communication with the intensity modu-
lator and the filter cavity, optically interposed between.
the intensity modulator and the filter cavity, and that:
receives the frequency comb from the intensity modu-
lator; and
amplifies the frequency comb to produce amplified
light from the frequency comb before the frequency
comb is received by the filter cavity as the amplified
light.

7. The ultrafast electro-optic laser of claim 1, further

comprising:

an amplifier in communication with the pulse shaper and
the highly nonlinear fiber, optically interposed between
the pulse shaper and the highly nonlinear fiber, and that:
receives the shaped light from the pulse shaper; and
amplifies the shaped light to produce amplified light

from the shaped light before the amplified light is
received by the shaped light as the amplified light.

8. The ultrafast electro-optic laser of claim 1, wherein the

electrical stabilizer further comprises:

a filter in communication with the frequency difference
crystal and that:
receives the difference frequency from the frequency

difference crystal; and
passes only the difference frequency into the electrical
stabilizer from the frequency difference crystal.

9. The ultrafast electro-optic laser of claim 8, wherein the

electrical stabilizer further comprises:

a clock that produces a clock signal;

a first oscillator in communication with the clock and that:
receives the clock signal from the clock; and
produces a first oscillator signal from the clock signal;

and

a first mixer in communication with the filter and the first
oscillator and that:
receives the difference frequency from the filter;
receives the first oscillator signal from the first oscil-

lator; and
produces a first mixed signal from the first oscillator
signal and the difference frequency.

10. The ultrafast electro-optic laser of claim 9, wherein

the electrical stabilizer further comprises:

a band pass filter in communication with the first mixer
and that:
receives the first mixed signal from the first mixer; and
produces a band pass signal from the first mixed signal;

and

a divider in communication with the band pass filter and
that:
receives the band pass signal from the band pass filter;

and
produces a second oscillator signal from the band pass
signal

11. The ultrafast electro-optic laser of claim 10, wherein

the electrical stabilizer further comprises:

a second oscillator in communication with the clock and
that:
receives the clock signal from the clock; and
produces a third oscillator signal from the clock signal;

and

a second mixer in communication with the divider and the
second oscillator and that:
receives the third oscillator signal from the second

oscillator;
receives the second oscillator signal from the divider;
and


US 11,011,882 B2

Sheet 2 of 12

May 18, 2021

U.S. Patent

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US 11,011,882 B2

1
ULTRAFAST ELECTRO-OPTIC LASER

CROSS REFERENCE TO RELATED
APPLICATIONS

The application claims priority to U.S. Provisional Patent
Application Ser. No. 62/727,289 filed Sep. 5, 2018, 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 and with support from the Department of
Defense, Defense Advanced Research Projects Agency
DODOS program in the form of a Military Interdepartmen-
tal Purchase Request, the the Air Force Office of Scientific
Research (AFOSR) under award no. FA9550-16-1-0016.
The Government has certain rights in the invention. Licens-
ing inquiries may be directed to the Technology Partnerships
Office, NIST, Gaithersburg, Md., 20899; voice (301) 301-
975-2573; email tpo@nist.gov.

BRIEF DESCRIPTION

Disclosed is an ultrafast electro-optic laser for making a 3

stabilized comb, the ultrafast electro-optic laser comprising:
a comb generator that produces a frequency comb and
comprises: a dielectric resonant oscillator that: receives a
stabilization signal; and produces a phase control signal

from the stabilization signal; a phase modulator in commu 3

nication with the dielectric resonant oscillator and that:
receives continuous wave light; receives, from the dielectric
resonant oscillator, a phase control signal; produces, from
the continuous wave light and the phase control signal,
phase modulated light; and produces a phase modulation
signal; an intensity modulator in communication with the
phase modulator and that: receives, from the phase modu-
lator, the phase modulated light; receives an intensity control
signal; and produces a frequency comb from the intensity
control signal and the phase modulated light; an optical
tailor in communication with the comb generator and that
produces tailored light, the optical tailor comprising: a filter
cavity in communication with the intensity modulator and
that: receives the frequency comb from the intensity modu-
lator; and produces filtered light from the frequency comb;
a pulse shaper in communication with the filter cavity and
that: receives the filtered light from the filter cavity; and
produces shaped light from the filtered light; a highly
nonlinear fiber and compressor in communication with the
pulse shaper and that: receives the shaped light from the
pulse shaper; and produces compressed light from the
shaped light; a waveguide in communication with the highly
nonlinear fiber and the compressor and that: receives the
compressed light; and produces the tailored light from the
compressed light; an interferometer in communication with
the optical tailor and that produces a difference frequency
from the tailored light, the interferometer comprising a
frequency difference crystal that receives the tailored light;
and an electrical stabilizer in communication with the inter-
ferometer and the comb generator and that produces the
stabilization signal, the electrical stabilizer comprising: a
stabilized local oscillator cavity that produces a stabilized

0

40

5B:

2

local oscillator signal that is converted into the stabilization
signal and communicated to the dielectric resonant oscilla-
tor.

Disclosed is a process for making a stabilized comb with
an ultrafast electro-optic laser, the process comprising: pro-
ducing, by a comb generator, a frequency comb by: receiv-
ing, by a dielectric resonant oscillator, a stabilization signal;
and producing, by the dielectric resonant oscillator, a phase
control signal from the stabilization signal; receiving, by a
phase modulator in communication with the dielectric reso-
nant oscillator, continuous wave light; receiving, by the
phase modulator from the dielectric resonant oscillator, a
phase control signal; producing, from the continuous wave
light and the phase control signal, phase modulated light;
and producing a phase modulation signal; receiving, by an
intensity modulator in communication with the phase modu-
lator, the phase modulated light; receiving, by the intensity
modulator an intensity control signal; and producing, the
frequency comb from the intensity control signal and the
phase modulated light; producing, by an optical tailor in
communication with the comb generator, tailored light by:
receiving, a filter cavity in communication with the intensity
modulator, the frequency comb from the intensity modula-
tor; producing filtered light from the frequency comb;
receiving, by a pulse shaper in communication with the filter
cavity, the filtered light from the filter cavity; producing
shaped light from the filtered light; receiving, by a highly
nonlinear fiber and compressor in communication with the
pulse shaper, the shaped light from the pulse shaper; pro-
ducing compressed light from the shaped light; receiving, by
a waveguide in communication with the highly nonlinear
fiber and the compressor, the compressed light: and produc-
ing the tailored light from the compressed light; producing,
by an interferometer in communication with the optical
tailor, a difference frequency from the tailored light with a
frequency difference crystal; and producing, by an electrical
stabilizer in communication with the interferometer and the
comb generator, the stabilization signal by: producing, by a
stabilized local oscillator cavity, a stabilized local oscillator
signal; converting the stabilized local oscillator signal into
the stabilization signal; and communicated the stabilization
signal to the dielectric resonant oscillator to make the
stabilization signal

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 an ultrafast electro-optic laser;

FIG, 2 shows an ultrafast electro-optic laser;

FIG. 3 shows a graph of intensity versus time for an
un-stabilized comb in panel A and a stabilized comb in panel

FIG. 4 shows a graph of amplitude versus frequency;
FIG. 5 shows a graph of optical phase noise versus
frequency;

FIG. 6 shows a graph of amplitude versus wavelength in
panel A, a graph of intensity versus wavelength in panel B,
a graph of intensity versus wavelength in panel C, and a
graph of intensity versus wavelength in panel D;

FIG. 7 shows graph optical phase noise in panel A and
graphs of amplitude versus frequency in panels B, C, and D;

FIG. 8 shows a graph of frequency versus delay in panels
A and B, a graph of amplitude versus time in panel C, and
graph of amplitude versus wavelength in panel D;


US 11,011,882 B2

5

In an embodiment, phase shifter 286 is in communication
with phase modulator 222 and intensity modulator 226 and
can be electronically interposed between phase modulator
222 and intensity modulator 226 to receive phase modula-
tion signal 308 from phase modulator 222 and to shift a
frequency of phase modulation signal 308 to produce inten-
sity control signal 302 from phase modulation signal 308
before intensity control signal 302 is received by intensity
modulator 226,

According to an embodiment, amplifier 230 is in com-
munication with intensity modulator 226 and filter cavity
234, optically interposed between intensity modulator 226
and filter cavity 234, and receives frequency comb 228 from
intensity modulator 226; and amplifies frequency comb 228
to produce amplified light 232 from frequency comb 228
before frequency comb 228 is received by filter cavity 234
as amplified light 232

In an embodiment, amplifier 230 is in communication
with pulse shaper 238 and highly nonlinear fiber 242,
optically interposed between pulse shaper 238 and highly
nonlinear fiber 242, and receives shaped light 240 from
pulse shaper 238; and amplifies shaped light 240 to produce
amplified light 232 from shaped light 240 before amplified
light 232 is received by shaped light 240 as amplified light
232

In an embodiment, electrical stabilizer 216 also includes
filter 260 in communication with frequency difference crys-
tal 256 and that: receives difference frequency 258 from
frequency difference crystal 256; and passes only difference

frequency 258 into electrical stabilizer 216 from frequency 3

difference crystal 256. Clock 270 produces clock signal 310.
Oscillator 272.2 is in communication with clock 270 and
receives clock signal 310 from clock 270 and produces
oscillator signal 274.4 from clock signal 310. Mixer 264.1 is
in communication with filter 260 and second oscillator 272.2
and receives difference frequency 258 from filter 260;
receives oscillator signal 274.4 from oscillator 272.2; and
produces mixed signal 312.1 from oscillator signal 274.4
and difference frequency 258. Band pass filter 266 is in
communication with mixer 264.1 and receives mixed signal
312.1 from mixer 264.1; and produces band pass signal 314
from mixed signal 312.1. Divider 268 is in communication
with band pass filter 266 and receives band pass signal 314
from band pass filter 266; and produces oscillator signal
274.2 from band pass signal 314. Oscillator 272.1 is in
communication with clock 270 and receives clock signal
310 from clock 270; and produces oscillator signal 274.1
from clock signal 310. Mixer 264.2 is in communication
with divider 268 and oscillator 272.2 and receives oscillator
signal 274.1 from oscillator 272.1; receives oscillator signal
274.2 from divider 268; and produces oscillator signal 274.3
from oscillator signal 274.1 and oscillator signal 274.2
Servo 276.1 is in communication with mixer 264.2 and
receives oscillator signal 274.3 from mixer 264.2; produces
servo signal 316 and set point 278.1 from oscillator signal
274.3; and communicates servo signal 316 to stabilized local
oscillator cavity 280, from which a temperature of stabilized
local oscillator cavity 280 is controlled. Phase shifter 286.1
is in communication with dielectric resonant oscillator 290
and receives phase control signal 300 from dielectric reso-
nant oscillator 290 and shifts a frequency of phase control
signal 300 before phase control signal 300 is received by
mixer 264.3. Mixer 264.3 is in communication with circu-
lator 284 and dielectric resonant oscillator 290 via phase
shifter 286.1 and receives phase control signal 300 from
phase shifter 286; receives circulator signal 318 from cir-
culator 284; mixes phase control signal 300 and circulator

S

40

&

6

signal 318; and produces mixed signal 312.3 from phase
control signal 300 and circulator signal 318. Servo 276.2 is
in communication with mixer 264.3 and servo 276.1 and
receives set point 278 from servo 276.1; receives mixed
signal 312.3 from mixer 264.3; and produces stabilization
signal 288, which is communicated comb generator 210,
from set point 278 and mixed signal 312.3

In ultrafast electro-optic laser 200, comb generator 210
includes elements to produce frequency comb 228 from
inputs such as continuous wave light 220 and stabilization
signal 288. It is contemplated that continuous wave laser 218
can include lasers with a narrow linewidth and high-speed
frequency control bandwidth. Exemplary continuous wave
lasers 218 include semiconductor-based lasers assembled
from discrete elements, or heterogeneously integrated, semi-
conductor-based lasers fabricated with semiconductor pro-
cessing techniques, or doped-fiber-based lasers. Moreover,
laser 218 features an output with a single frequency of light,
a narrow linewidth, high-power, and a single polarization of
the electromagnetic field. In an embodiment, continuous
wave laser 218 includes a laser with 1 kHz linewidth and 10
mW output power.

Continuous wave laser 218 produces continuous wave
light 220. Continuous wave light 220 can include light
guided in single mode, polarization-maintaining optical
fiber, single mode optical fiber, or light propagating in free
space. Exemplary continuous wave lights 220 include light
of a single frequency that is guided in a polarization main-
taining fiber coupled together with angled physical contact
fiber optic (FC/APC) connectors. A wavelength of continu-
ous wave light 220 can be from 300 nm to 20,000 nm,
specifically from 500 nm to 2500 nm, and more specifically
from 1500 nm to 1600 nm. A power of continuous wave light
220 can be from 1 mW to 100 mW, specifically from 25 mW
to 50 mW, and more specifically from 40 mW to 50 mW.
Power can refer to the number of photons per second in a
single mode of the electromagnetic field. In an embodiment,
continuous wave light 220 includes light with a single
frequency, a single linear polarization, and a single spatial
mode profile that is guided in a single mode polarization
maintaining optical fiber with FC/APC connectorization.

Phase modulator 222 can include a modulator or series of
modulators that vary the instantaneous phase of continuous
wave light 220. Exemplary phase modulators 222 include
modulators in which light propagates in free space or
modulators in which light propagates in a guided mode,
which can be implemented with a circular cross section
waveguide, a rectangular cross section waveguide, or a
photonic-crystal waveguide. The phase modulator may be
implemented with a traveling wave mode, a traveling wave
resonator mode, or a standing wave mode. The modulator
may either accept free-space light or light in a guided mode.
Moreover, the modulator can include low loss of light 220
and high conversion efficiency of the phase control signals

5 300 into modulation of the light 220. It is contemplated that

the modulator efficiency can be described by the half-wave
voltage and the modulator loss can be described in decibels
of light power. Furthermore, the phase modulator can
include a lithium niobate device, a silicon-on-insulator
device, a lithium tantalate device, or a tantalum pentoxide
device. Phase modulators 222 can be optically disposed
serially in ultrafast electro-optic laser 200 and can receive
independent phase control signals 300. The half-wave volt-
age of phase modulator 222 can be from 0.001 Volts to 5

5 Volts, specifically from 0.1 Volts to 3 Volts, and more

specifically from 1 Volts to 3 Volts. The loss of phase
modulator 222 can be from 0.1 dB to 5 dB and more


US 11,011,882 B2

Sheet 1 of 12

May 18, 2021

U.S. Patent

T Old



US 11,011,882 B2

23
built-in trans-impedance amplifier. The offset frequency of
the comb must match the intrinsic offset frequency of the
filter cavity in order to be transmitted efficiently. A beat
frequency is detected near 3.5 GHz and is determined by the
exact cavity geometry and mirror dispersion. However, the
~3 MHz cavity linewidth still supports a tuning range of a
few-hundred megahertz for the offset while maintaining
high transmission of the comb. After detection, this beat is
electronically mixed down to 960 MHz before filtering and

frequency division by 32. A phase-locked loop locks the |

resulting 30-MHz signal to an RF synthesizer by adjusting
the voltage set point of the microwave cavity lock. An
integrated version of the main feedback loop’s output volt-
age is also used to provide a slow thermal correction to the
microwave cavity through resistive heaters affixed to the
outside.

The phase noise of the comb is obtained via the photo
detected offset frequency at 775 nm. At this wavelength, the
RF noise of the electronics that drive the comb generation is
multiplied by a factor of N=19340 (the number of comb
lines away from the CW pump laser) and thus provides a
sensitive way to calculate the noise on the 10-GHz repetition
rate. The measured phase noise of the optical beat can then
be reduced by a factor 20 log 10(N)=85.7 dB to obtain the
estimated microwave noise. The resulting curve is integrated
to compute the RMS timing jitter of the electronic oscillator,
and the optical pulse train that is directly derived from it.
This integration (from 10 Hz to 4 MHz) yields a total jitter

of 0.97 fs relative to the 1550-nm optical carrier for the fully ~

locked 10 GHz comb.
To confirm that noise up to the 5-GHz Nyquist limit does
not adversely contribute to the pulse stability, use the f-line.

If the timing-jitter calculation is assumed to be (-line limited ,.

2

between 4 MHz and 5 GHz, the total integrated jitter ~

becomes 1.9 fs, which is still less than half of an optical
cycle at 1550 nm. However, because of the high signal-to-
noise ratio (SNR) of the coherent carrier on the offset
frequency, the noise is considerably less than the f-line in
this frequency range and should not significantly affect the
timing jitter beyond 4 MHz.

Individual comb lines in the silicon-nitride supercon-
tinuum spectrum exhibit a degree of extinction across the
entire bandwidth, as shown by the CW heterodyne beats in
FIG. 10. With regard to FIG. 10, a high-resolution optical
spectrum of the 10-GHz EOM comb was obtained from
heterodyne beats with CW lasers. Clean, high-contrast comb
modes are obtained across the entire bandwidth of the
supercontinuum spectrum. The fall-off in signal-to-noise
ratio in the 775-nm band at higher frequencies is due to
reduced efficiency of the doubling crystal used to generate
the CW light.

For each wavelength region shown, the spectra are
obtained by stepping the frequency of a CW laser in 10 GHz
increments and recording the down-mixed optical spectrum
in the radio-frequency (RF) domain at each step. Band-
widths greater than 10 GHz are recorded by stitching
together multiple acquisitions at each wavelength. Each
individual 10 GHz span then contains a beat between the
CW laser and the two nearest comb modes. Individual noise
floor contributions from the CW laser and the comb are
obtained at each wavelength by blocking the appropriate
arm and recording a new trace.

Comb lines closest to the 1550-nm pump wavelength
exhibit the highest degree of contrast (nearly 60 dB at 1319
nm). However, even at the edge of the spectrum near 775

40

&

24

nm, more than 35 dB of contrast is obtained. In all cases the
spectra exhibit very clean modes without any visible inter-
mode artifacts or sidebands.

Broad supercontinuum generation using narrow-band-
width seed pulses poses challenges for low-noise perfor-
mance. In conventional all-anomalous dispersion media,
modulation instability can lead to noisy spectra and degra-
dation of the comb coherence. The problem is mitigated by
the first-stage broadening in normal-dispersion HNLF. FIG.
11 shows the offset-frequency beat notes as a function of
EOM-comb bandwidth for the offset-frequency beat notes of
the 10-GHz EOM comb as a function of the number of
modes in the initial spectrum. Narrower-bandwidth comb
spectra have reduced coherence after supercontinuum gen-

s eration. The beat note pedestal results from residual micro-

wave noise in the electronic oscillator and is a representation
of the selected signal. The inset shows beat note SNR versus
the number of initial comb lines, relative to the background
noise floor.

Each curve in the plot is obtained by symmetrically
filtering the initial comb spectrum in increasing amounts
using a programmable pulse shaper. At each step, the
amplifier power is adjusted to maximize the achievable SNR
of the beat. The SNR increases monotonically with the

s number of comb modes, indicating it is advantageous to

maximize the microwave drive power and the number of
phase modulators for best performance.

‘An unexpected benefit of the ultrafast electro-optic laser
is its inherent reliability. To generate absolute optical fre-
quencies, the ultrafast electro-optic laser was continuously
operated for more than 16 hrs. In this configuration, the
cavity-stabilized pump source was replaced with a tunable
external-cavity diode laser that was frequency-stabilized
through feedback from the comb offset f0. The repetition
rate, on the other hand, was generated by a low-noise
microwave synthesizer, to which the DRO was phase
locked. Both comb parameters were derived from an SI-
second-referenced hydrogen maser and thus provide abso-
lute calibration of the comb modes. FIG. 12A shows fre-
quency counter data (gate time 1 s) of the in-loop comb
offset frequency. No glitches are observed during the entire
data set, indicating that neither temperature drifts nor beam-
pointing fluctuations due to coupling watt-level powers to
the SiN chip pose a significant obstacle for continuous

5 operation.

The absolute frequency of the comb is verified during this
same acquisition by counting a heterodyne beat between the
EOM-comb pump laser and an independent self-referenced
fiber frequency comb (FIG. 12B). Gaps in the record are due
to the secondary comb exceeding the range of its stabiliza-
tion actuators and losing phase lock. FIG. 12 shows reliable
continuous operation, wherein panel A shows in-loop coun-
ter data for continuous glitch-free operation for more than 16
hrs (30 MHz set point subtracted). Panel B shows out-of-

5 loop absolute frequency verification during acquisition (off-

set by expected value of 30.6 MHz). Time gaps in the data
are due to the reference fiber comb losing phase lock.

For precision-measurement applications, the absolute
accuracy and stability of the comb is an important metric for
comb performance. To assess these aspects of the low-noise
EOM comb from the ultrafast electro-optic laser, the
10-GHz repetition rate was compared against the 40th
harmonic of an auxiliary self-referenced fiber comb operat-
ing at frep,aux=250 MHz. By phase locking the appropriate

5 tooth of the reference comb to the same CW laser serving as

the pump of the EOM comb, the drift of the CW laser can
be completely canceled. The frequency difference between


US 11,011,882 B2

Page 2
(51) Int. Cl. 2001/3542: G02B 26/02; GO2B 26/06:
HOLS 3/11 (2006.01) G02B 5/20; GO1J 1/16; GO1J 3/02; GO1I
GO2F 1/01 (2006.01) 9/02
GO2F 1/03 (2006.01) See application file for complete search history.
GO2F 1/35 (2006.01)
GOLJ 1/16 (2006.01) (56) References Cited
GOLI 3/02 (2006.01)
GOLI 9/02 (2006.01) U.S. PATENT DOCUMENTS
(52) 10,048,567 B2* 8/2018 Papp GO2F 1/0344
cesses HOLS 3/0057 (2013.01); HOLS 3/0078 10,585,332 B2* 3/2020 Plascak GO2F 1/353
(2013.01); HOIS 3/10 (2013.01); HOLS 3/1106 2007/0229937 A1* 10/2007 Josef Moeller ...... GO2F 1/3534
(2013.01); GOLF 1/16 (2013.01); GOLJ 3/02 359/326
(2013.01); GOLJ 9/02 (2013.01); G02F 1/0128 2015/0029575 Al* 1/2015 Hara ciearend
(2013.01); GO2F 1/35 (2013.01); GO2F yy: 59936784 AL* 82015. Vs isos
2203/36 (2013.01); GO2F 2203/56 (2013.01) 70150236784 AI* 82015 Vahala HOA 8
(58) Field of Classification Search 2015/0372447 A1* 12/2015 Song HOIS 3/0057
CPC .... HO1S 3/0092; HO1S 3/1301; HOIS 3/1305; ; 372/21
GO2F 1/01; GO2F 1/0121; GO2F 1/0123; 2016/0254646 Al* 9/2016 Li HO1S 3/0627
s . 372/32
GO2P 1/0102; GO2F 1/011; GO2F 1/0105; 2017/0012705 A1l* 1/2017 Vahala HO4L 7/0091

GO02F 1/35-397; GO2F 1/03-0344; GO2F
2203/56; GO2F 2203/26; G0O2F

* cited by examiner


US 11,011,882 B2

29

produces a fourth oscillator signal from the third oscil-
lator signal and the second oscillator signal.

12. The ultrafast electro-optic laser of claim 11, wherein

the electrical stabilizer further comprises:
a first servo in communication with the second mixer and
that:
receives the fourth oscillator signal from the second
mixer;

produces a servo signal and a set point from the fourth
oscillator signal; and

communicates the servo signal to the stabilized local
oscillator cavity, from which a temperature of the
stabilized local oscillator cavity is controlled.

13. The ultrafast electro-optic laser of claim 12, wherein

the electrical stabilizer further comprises:

a phase shifter in communication with the dielectric
resonant oscillator and that receives the phase control
signal from the dielectric resonant oscillator and shifts
a frequency of the phase control signal before the phase
control signal is received by a third mixer; and

the third mixer in communication with a circulator and the
dielectric resonant oscillator via the phase shifter and
that:
receives the phase control signal from the phase shifter;
receives a circulator signal from the circulator;
mixes the phase control signal and the circulator signal;

and
produces a third mixed signal from the phase control
signal and the circulator signal

14. The ultrafast electro-optic laser of claim 13, wherein 3

the electrical stabilizer further comprises:
a second servo in communication with the third mixer and
the first servo and that:
receives the set point from the first servo;

receives the third mixed signal from the third mixer; 3

and
produces the stabilization signal, which is communi-
cated to the comb generator, from the set point and
the third mixed signal.
15. A process for making a stabilized comb with an
ultrafast electro-optic laser the process comprising:
producing, by a comb generator, a frequency comb by:
receiving, by a dielectric resonant oscillator, a stabili-
zation signal; and
producing, by the dielectric resonant oscillator, a phase
control signal from the stabilization signal;
receiving, by a phase modulator in communication with
the dielectric resonant oscillator, continuous wave
light:
receiving, by the phase modulator from the dielectric
resonant oscillator, a phase control signal;
producing, from the continuous wave light and the
phase control signal, phase modulated light; and
producing a phase modulation signal;
receiving, by an intensity modulator in communication
with the phase modulator, the phase modulated light;
receiving, by the intensity modulator an intensity con-
trol signal; and
producing, the frequency comb from the intensity con-
trol signal and the phase modulated light;
producing, by an optical tailor in communication with the
comb generator, tailored light by:
receiving, a filter cavity in communication with the
intensity modulator, the frequency comb from the
intensity modulator;
producing filtered light from the frequency comb:

3

40

60

65

30
receiving, by a pulse shaper in communication with the
filter cavity, the filtered light from the filter cavity;
producing shaped light from the filtered light;
receiving, by a highly nonlinear fiber and compressor
in communication with the pulse shaper, the shaped
light from the pulse shaper;
producing compressed light from the shaped light;
receiving, by a waveguide in communication with the
highly nonlinear fiber and the compressor, the com-
pressed light; and
producing the tailored light from the compressed light;
producing, by an interferometer in communication with
the optical tailor, a difference frequency from the
tailored light with a frequency difference crystal; and
producing, by an electrical stabilizer in communication
with the interferometer and the comb generator, the
stabilization signal by:
producing, by a stabilized local oscillator cavity, a
stabilized local oscillator signal;
converting the stabilized local oscillator signal into the
stabilization signal; and
communicated the stabilization signal to the dielectric
resonant oscillator to make the stabilization signal.
16. The process of claim 15, further comprising:
receiving, by a phase shifter in communication with the
dielectric resonant oscillator and the phase modulator,
the phase control signal from the dielectric resonant
oscillator; and
shifting a frequency of the phase control signal before the
phase control signal is received by the phase modulator.
17. The process of claim 15, farther comprising:
receiving, by a phase shifter in communication with the
phase modulator and the intensity modulator, the phase
modulation signal from the phase modulator; and
shifting a frequency of the phase modulation signal to
produce the intensity control signal from the phase
modulation signal before the intensity control signal is
received by the intensity modulator.
18. The process of claim 15, farther comprising:
producing a clock signal;
producing a first oscillator signal from the clock signal;
producing a first mixed signal from the first oscillator
signal and the difference frequency;
producing a band pass signal from the first mixed signal;
and
producing a second oscillator signal from the band pass
signal.
19. The process of claim 18, further comprising:
producing a third oscillator signal from the clock signal;
producing a fourth oscillator signal from the third oscil-
lator signal and the second oscillator signal;
producing a servo signal and a set point from the fourth
oscillator signal;
stabilizing a temperature of the stabilized local oscillator
cavity;
shifting a frequency of the phase control signal;
mixing the phase control signal and a circulator signal:
and
producing a third mixed signal from the phase control
signal and the circulator signal.
20. The process of claim 19, further comprising:
producing the stabilization signal from the set point and
the third mixed signal; and
communicating the stabilization signal to the comb gen-
erator.


US 11,011,882 B2

Sheet 11 of 12

May 18, 2021

U.S. Patent

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US 11,011,882 B2

3

FIG. 9 shows a graph of fractional stability versus aver-
aging time;

FIG. 10 shows graphs of amplitude versus frequency;

FIG. 11 shows a graph of signal-to-noise ratio versus
frequency; and

FIG. 12 shows graphs of frequency versus time in panels
Aand B.

DETAILED DESCRIPTION

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

It has been discovered that an ultrafast electro-optic laser
and processes described herein overcomes technical limita-
tions of conventional apparatus in making a stabilized comb.
The ultrafast electro-optic laser extends frontiers of physical
measurements and enable techniques in areas such as chem-
istry, biology, information science, medicine, and manufac-
turing. Conventional ultrafast lasers involve mode-locked
resonators, but the ultrafast electro-optic laser includes ultra-
stable control of femtosecond pulses based on electro-optic
modulation of light. The ultrafast electro-optic laser pro-
duces unique, high-speed pulse trains with a rate up, e.g., to
30 GHz and provides sub-optical cycle timing precision with
output spectra that spans from ultraviolet to near infrared.

The ultrafast electro-optic laser is an ultrafast light source
that produces femtosecond pulses with sub-cycle timing
jitter and includes electro-optic switching of a continuous-

wave (cw) laser. The ultrafast electro-optic laser includes an 3

electro-optic (EO) frequency comb; microwave-cavity sta-
bilization to suppress electronic oscillator noise; an optical
noise filtering cavity; a nanophotonic waveguide for broad
spectrum generation; and an electronic feedback loop for
microwave noise reduction via f-2f offset stabilization.

The ultrafast electro-optic laser has EO phase and inten-
sity modulation of a ew laser to make a train of optical pulses
driven directly by an electronic oscillator. The resulting
frequency comb is spectrally broadened in a nanophotonic
waveguide, and the ultrafast electro-optic laser generates
ultrashort few-cycle pulses of light and self-referenced fre-
quency stabilization and suppresses electronic noise of the
comb at frequencies that can be, e.g., less than about 100
kHz. Electronic noise in the frequency range up to several
megahertz is suppressed via locking the electronic oscillator
to a narrow-linewidth microwave cavity and noise at fre-
quencies extending up to the Nyquist frequency are filtered
with the optical cavity. The ultrafast electro-optic laser
reduces microwave noise that can limit conventional EO
comb performance to below a noise of an optical carrier
wave. Accordingly, the ultrafast electro-optic laser provides
ultrastable timing precision of the pulse train.

Advantageously, the ultrafast electro-optic laser generates
ultrashort pulses of light with extremely low timing and
phase noise from cavity stabilization of a microwave elec-
tronic oscillator, a photonic waveguide for pulse compres-
sion and spectral broadening, and self-referencing of the
comb for microwave phase noise reduction. Moreover, the
ultrafast electro-optic laser produces pulses at a rate, e.
greater than 10 GHz and fills a need for a stable high-
repetition-rate comb source that can be used, e.g., in com-
munications, spectroscopy. and real-time biological imaging
as well as microscopy of a chemical or biological target.

The ultrafast electro-optic laser overcomes technical limi-
tation of conventional apparatus and has a repetition rate that
can be directly synchronized to a microwave drive at a same
frequency. An optical phase of pulses from the ultrafast

2

40

&

60

4

electro-optic laser can be controlled relative to a pulse
repetition rate with sub-optical-cycle precision. A frequency
domain spectrum of the pulses can be engineered to extend
from the visible and near infrared spectrum, e.g., from 600
nm to 2400 nm. Moreover, a repetition rate and center
wavelength of the ultrafast electro-optic laser can be
selected.

Ultrafast electro-optic laser 200 makes stabilized comb
306. In an embodiment, with reference to FIG. 1 and FIG.
2, ultrafast electro-optic laser 200 includes comb generator
210 that produces frequency comb 228. Comb generator 210
includes dielectric resonant oscillator 290 that receives
stabilization signal 288 and produces phase control signal
300 from stabilization signal 288; and phase modulator 222
in communication with dielectric resonant oscillator 290 and
that receives continuous wave light 220; receives, from
dielectric resonant oscillator 290, phase control signal 300;
produces, from continuous wave light 220 and phase control
signal 300, phase modulated light 224; and produces phase
modulation signal 308. Comb generator 210 also includes
intensity modulator 226 in communication with phase
modulator 222 and that receives, from phase modulator 222,
phase modulated light 224; receives intensity control signal
302; and produces frequency comb 228 from intensity
control signal 302 and phase modulated light 224. Ultrafast
electro-optic laser 200 also includes optical tailor 212 in
communication with comb generator 210 and that produces
tailored light 298. Optical tailor 212 includes filter cavity
234 in communication with intensity modulator 226 that
receives frequency comb 228 from intensity modulator 226
and produces filtered light 236 from frequency comb 228.
Pulse shaper 238 is in communication with filter cavity 234
and receives filtered light 236 from filter cavity 234 and
produces shaped light 240 from filtered light 236. Highly
nonlinear fiber 242 and compressor 246 are in communica-
tion with pulse shaper 238 and receive shaped light 240 from
pulse shaper 238 and produce compressed light 248 from
shaped light 240. Waveguide 250 is in communication with
highly nonlinear fiber 242 and compressor 246 and receives
compressed light 248 and produces tailored light 298 from
compressed light 248. Ultrafast electro-optic laser 200 also
includes interferometer 214 in communication with optical
tailor 212 and that produces difference frequency 258 from
tailored light 298. Interferometer 214 includes frequency
difference crystal 256 that receives tailored light 298. Elec-
trical stabilizer 216 is in communication with interferometer
214 and comb generator 210 and produces stabilization
signal 288. Electrical stabilizer 216 includes stabilized local
oscillator cavity 280 that produces stabilized local oscillator
signal 282, which is converted into stabilization signal 288
that is communicated to dielectric resonant oscillator 290
from electrical stabilizer 216.

In an embodiment, ultrafast electro-optic laser 200

5 includes continuous wave laser 218 in communication with

phase modulator 222 and that produces continuous wave
light 220. Lock cavity 292 can be in communication with
continuous wave laser 218 to produce lock signal 294 to
which continuous wave laser 218 is locked.

In an embodiment, phase shifter 286 is in communication
with dielectric resonant oscillator 290 and phase modulator
222 and can be electronically interposed between dielectric
resonant oscillator 290 and phase modulator 222 to receive
phase control signal 300 from dielectric resonant oscillator

5 290 and to shift a frequency of phase control signal 300

before phase control signal 300 is received by phase modu-
lator 222.