of 6
Microresonator soliton dual-comb imaging
Chengying Bao,
Myoung-Gyun Suh,
and Kerry Vahala
T. J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, California 91125, USA.
These authors contributed equally to this work.
Corresponding author: vahala@caltech.edu
Fast-responding detector arrays are commonly
used for imaging rapidly-changing scenes. Be-
sides array detectors, a single-pixel detector com-
bined with a broadband optical spectrum can
also be used for rapid imaging by mapping the
spectrum into a spatial coordinate and then
rapidly measuring the spectrum. Here, broad-
band optical frequency combs generated from
high-
Q
silica microresonators are used to imple-
ment this method. The microcomb is dispersed in
two spatial dimensions to measure a test target.
The target-encoded spectrum is then measured
rapidly by multi-heterodyne beating with another
microcomb having a slightly different repetition
rate. The rapid image acquisition capability is
also used to monitor the flow of microparticles in
a fluid cell. This demonstration establishes that
light sources and dual-comb detection methods
for this form of rapid imaging can have a compa-
rable chip-scale form factor to compact detector
arrays.
I. INTRODUCTION
The development of the rapid-frame-capture detec-
tor array sensors based on CCD (charge-coupled device)
and CMOS (complementary metal oxide semiconductor)
technology has revolutionized imaging
1
. Also, by com-
bining CCD/CMOS with streak cameras
2
, frame rates
of 100 billion per second are possible
3
. However, streak
cameras are complicated and expensive systems. More-
over, high speed CCD/CMOS-based imaging encounters
challenges such as compromised sensitivity at shorter ex-
posure times, heat concentration, and on-chip storage
memory and electronic readout speed
1,4
. As a result,
there has been interest in alternative imaging methods.
A recent approach uses the broadband spectrum of ul-
trashort optical pulses for fast imaging with a single-
pixel detector (not an array)
5
, and thereby avoids the
above challenges for CCD/CMOS. The method works by
mapping different optical frequencies of the broadband
spectrum into distinct spatial locations using spatial dis-
persers such as demonstrated in the technique of fem-
tosecond pulse shaping
6
. To create a 2-dimensional (2D)
map, a conventional grating disperses the spectrum in
one spatial dimension, while a virtually imaged phase ar-
ray (VIPA) disperses light into the other spatial dimen-
sion. As shown in Fig. 1A, the grating and the VIPA
create a ‘2D spectral shower’ in which distinct optical fre-
quencies have a one-to-one (spectral-spatial) correspon-
dence with coordinates in 2-dimensions
5,7,8
.
To recover the image, the spectrum can be mea-
sured by the time-stretch method, which converts the
spectrally-encoded spatial information into a temporal
waveform measured on a single-pixel photodetector
5
.
This approach measures the image on a shot-by-shot ba-
sis and 6 MHz frame rates have been demonstrated
5
.
As an alternative image recovery technique a dual-
frequency-comb spectrometer has also been recently
demonstrated
9
. This approach, termed here as dual-
comb imaging, parallels the technique of dual-comb
spectroscopy
10
by converting an optical spectrum into
a low-bandwidth radio-frequency (RF) electrical signal.
It can provide inteferometeric accuracy and precision for
imaging. However, the demonstrated image acquisition
rate is relatively low on account of the radio-frequency
pulse rates of mode-locked fiber laser combs
9
. Also, line-
scan spectral-spatial imaging using dual frequency combs
has also been recently reported
11,12
.
To generate broadband optical pulses for imaging,
table-top, mode-locked lasers have so far been used.
A recent advance in optical pulse generation and fre-
quency comb generation is based on dissipative Kerr
soliton mode locking in optical microcavities
13–16
. The
devices provide high repetition rate soliton streams
and their associated optical frequency combs feature
smooth spectral envelopes.
These miniature fre-
quency combs or microcombs
17
are considered a pos-
sible way to dramatically reduce the form factor of
conventional frequency comb systems.
Accordingly,
they are being studied for several applications in-
cluding dual-comb spectroscopy
18,19
, ranging
20,21
, op-
tical communications
22
, optical frequency synthesis
23
,
and exoplant detection in astronomy
24,25
. Considering
their possible application to the spectral-spatial imag-
ing method, they offer not only a highly compact (chip-
based) mode-locked optical pulse source, but, on ac-
count of their high pulse repetition rates, microcombs
can increase image acquisition rates by several orders
of magnitude when applied using the dual-comb hetero-
dyne method. Also, the heterodyne method, when im-
plemented using microcombs, avoids fiber optics required
for the time-stretch image recovery method. As a result,
a miniature system-on-a-chip is possible (dashed box in
Fig. 1A). For these reasons, this work explores dual-comb
imaging using soliton microcombs. The imaging method
is demonstrated by measuring a test target and monitor-
arXiv:1809.09766v1 [physics.optics] 26 Sep 2018
2
Circulator
PD
PD
Soliton microcombs
Referenc
e
Signal
Grating
B
A
C
fast-moving microparticles
liquid flow
microparticle
Microresonator
Spherical Lens
static pattern
(USAF 1951)
VIP
A
Cylindrical Lens
Oscilloscope
Ch1
Ch2
Target
Collimator
9.39 GHz
1.86 GHz
10 mm
Frequency Domain
D
Optical Domain
RF Domain
Space Domain
frequency
f
rep2
f
rep1
rep
= f
rep1
- f
rep2
x - direction
y - direction
VIP
A FSR
VIP
A
FSR
Comb
spacing
‘2D spectral shower
on a target pattern
Si substrate
Si pillar
silica wedge disk
( top view )
( cross-sectional view )
lar
s
ilica we
dge
disk
optical mode
‘2D spectral shower
Target-encoded modulation
I. Reference comb
II. Signal comb
III. Signal RF comb
FIG. 1:
Dual-comb imaging using microresonator solitons
(A) A conceptual diagram showing the opera-
tional principle for spectral-spatial-mapping and rapid dual-microcomb imaging. Two soliton microcombs (signal
and reference) having slightly different repetition rates are generated using two on-chip microresonators. A 2D dis-
perser (VIPA+grating) maps frequencies from the signal microcomb into a 2D grid of spatial locations (spectral
shower) that are reflected by a target. The reflected signal spectrum is measured by multi-heterodyne detection
with the reference microcomb. (B) A photograph showing the top view of the two types of silica microresonators
used in the experiment (left). The resonators have free-spectral ranges (FSRs) of 1.86 GHz and 9.39 GHz. A
schematic cross-sectional view of the silica wedge microresonators with the spatial mode intensity indicated (right).
(C) Measurement targets used include a USAF 1951 resolution chart and also microparticles within a flow-cell. (D)
Spectral-spatial imaging proceeds by illuminating the target (right panel) with the 2D spectral shower formed as
shown in panel A. As shown in the left panel, the target reflection amplitude is encoded onto the signal comb. The
signal comb is then heterodyned with the reference comb to generate the RF comb.
f
rep1
,
f
rep2
, and ∆
f
rep
are the
frequency-line spacing of the reference comb, the signal comb, and the signal RF comb.
ing the flow of microparticles in a flow-cell (Fig. 1C). 200
kHz frame rates (5
μ
s integration time) are demonstrated
which is over a 10,000-fold increase compared with prior
heterodyne-based image recovery demonstrations using
mode-locked fiber lasers
9
.
II. RESULTS
Experimental setup.
High-
Q
silica-on silicon wedge
microresonators
26
with repetition rates of 1.86 GHz and
9.39 GHz
27
are used to generate the dual soliton streams.
3
1520
1530
1540
1550
1560
1570
1580
1590
Inten. (10 dB/div)
Freq. (GHz)
Wavelength (nm)
Soliton 1
f
rep
=9.3872 GHz
~
sech
2
9.385
9.390
A
B
ref.
sig.
C
E
Relative power (dB)
RF frequency (MHz)
f
VIPA
1540
1550
1560
Intensity (10 dB/div)
Wavelength (nm)
Inten. (10 dB/div)
Freq. (GHz)
Soliton 1
f
rep
=1.8592 GHz
~
sech
2
1.8588
1.8595
1545
1555
1565
1535
1570
f
VIPA
b
b
50
μ
m
50
μ
m
50
μ
m
50
μ
m
100
200
300
400
RF frequency (MHz)
Relative power (dB)
F
G
H
D
Intensity (10 dB/div)
Voltage (V)
Time (1
μ
s/div)
50
μ
m
0.67
μ
s
-1
1
-0.5
0.5
-15
200
300
400
500
0
optical 0.9 THz
optical 2.0 THz
-15
0
FIG. 2:
Dual-microcomb imaging of static targets.
(A) Typical optical spectrum of the 9.39 GHz soliton mi-
crocombs showing sech
2
spectral envelope fit as a red line. The inset is the electrical spectrum of the photodetected
soliton pulse stream and gives the repetition rate. (B) An example of the measured interferogram in a 5
μ
s time
window from the reference arm and the signal arm (see Fig 1A). (C) RF spectrum representing 3 vertical bars that
are illuminated by the 9.39 GHz microcomb. The method to obtain this spectrum is described in the main text.
The integration time used to obtain the spectrum is 5
μ
s. (D) Image of three vertical bars recontructed from the
measured RF spectrum in panel C. (E) Typical optical spectrum of the 1.86 GHz soliton microcombs showing sech
2
spectral envelope fit as a red line. A notch near the spectral maximum is produced by a narrow-band filtering of
the optical pump. The inset is the electrical spectrum of the photodetected soliton pulse stream. (F) RF spectrum
representing 3 horizontal bars illumiated by the 1.86 GHz microcomb. The spectrum is obtained in the same way
as panel C. (G) Image of 3 horizontal bars reconstructed from the measured RF spectrum in panel F. (G) Image
of number ‘4’ on the USAF target produced using the 1.86 GHz microcombs. The dark discontinuity shown by the
arrows in (G, H) results from the spectral notch produced by filtering the optical pump (see panel E).
Images of the resonators are given in Fig. 1B and details
on methods used to trigger and stabilize the soliton mi-
crocombs are presented elsewhere
14
. The microcombs
are coupled directly to optical fibers using tapered-fiber
couplers
28,29
and the signal comb and reference comb are
conveyed along the optical train as shown in Fig. 1A.
The VIPA and grating (600 lines/mm) act together to
create the 2D spectral shower with the VIPA dispersing
the spectrum along the vertical direction and the grating
dispersing the spectrum along the horizontal direction.
The VIPA disperses light only within its free-spectral-
range (FSR) which means that optical frequencies
ν
and
ν
+
mf
VIPA
(where
m
is an integer and
f
VIPA
is the VIPA
FSR) will overlap in space. By adding a grating, frequen-
cies
ν
and
ν
+
mf
VIPA
can be further dispersed to create
the 2D spectral shower as illustrated in Figs. 1A, D.
The VIPA used in our experiment has an FSR of 60 GHz
(LightMachinery) and this limits pixel count along the
vertical direction to 32 pixels (1.86 GHz microcomb) and
6 pixels (9.39 GHz microcomb). Analysis of more opti-
mal designs is provided in the Discussion. The spectral
shower is reflected by the object, coupled back into the
fiber for return to a photodetector where it is hetero-
dyned with the reference microcomb. Fig. 1D illustrates
4
100 μm
Filtere
d pump
-20
-10
0
10
slope~
0.21 m/s
A
C
T
ime
(
50
μs/div)
Relative p
o
sition (
μm )
~ 0.25 m/s
~ 100 μm
microsphere
2D spectral shower
flow-cel
l
B
FIG. 3:
Monitoring flowing particles.
(A) An il-
lustration of the microparticle monitoring experiment.
Microparticles are suspended in water and flow inside
the cell. When a particle passes through the 2D spec-
tral shower, the particle can be imaged using the dual-
comb interferogram. (B) A snapshot of a reconstructed
microparticle. The dashed circle suggests the micropar-
ticle size (
100
μ
m.). The dark vertical band results
from filtering of the optical pump line. (C) Extracted
center position of the microparticle versus time. A lin-
ear fit gives a flow velocity of 0.21 m/s in reasonable
agreement with the set water flow velocity of 0.25 m/s.
how the image reflection amplitude is transferred from
the spectral shower to the signal RF spectrum produced
by dual-comb heterodyne.
Also shown in Fig. 1A are a collimator and a cylindri-
cal lens (focal length of 150 mm) that focuses the colli-
mated comb onto the VIPA. Additionally, the 2D spec-
tral shower is focused onto the target by a spherical lens
(focal length of 30 mm). In principle, the spherical lens
can be replaced with two orthogonal cylindrical lenses so
as to achieve independent control the 2D spectral shower
along the two axes
7
. The targets are placed at the focal
plane of the spherical lens and aligned to provide maxi-
mum reflection coupled into the fiber.
Imaging a static target.
To demonstrate this ap-
proach, a USAF 1951 test target (negative) is imaged.
Target patterns within Group 3 Element 4 of the tar-
get were illuminated. In a first measurement, two silica
microcombs with repetition rates close to 9.39 GHz are
used. The spectrum of one of the microcombs is shown
in Fig. 2A and features a sech
2
-shaped spectral enve-
lope. The spectral spurs in the spectrum result from
the dispersive wave emission induced by avoided-mode-
crossings, which also assists single soliton generation
30
.
The detected electrical spectrum for this comb is shown
in the inset to Fig. 2A. The other microcomb has a simi-
lar spectrum, but its repetition rate differs from the first
microcomb by
1.5 MHz. The close matching of repeti-
tion rates is possible by precise microfabrication control
of the resonator diameters
26
. In Fig. 2B, typical exam-
ples of the heterodyned dual-comb interferograms mea-
sured over a 5
μ
s interval from the reference arm (upper
panel) and signal arm (lower panel) are shown. While
the reference interferogram contains a readily identifiable
periodic signal resulting the difference in repetition rates
of the signal and reference microcombs, the signal inter-
ferogram contains complex structure associated with the
image.
To construct an image, an RF spectrum is first cal-
culated by taking the fast Fourier transform (FFT) of
the signal interferogram produced by illuminating a pat-
terned region of the target and normalizing it by the FFT
of the reference interferogram. Then, the same procedure
is applied using a non-patterned (uniform) region of the
target. Finally, the resulting normalized RF spectrum of
the patterned region is further divided by the normalized
RF spectrum of the non-patterned region to extract the
target-encoded modulation, shown in Fig. 2C. The spec-
tral lines with amplitudes larger than 0 dB might result
from non-uniformity of the target (for example glints).
These amplitudes, however, have a negligible affect on
the resulting image because they represent small pixel
values in the image (inverse reflectivity is used for recon-
struction as a negative target is used). This 1D spectrum
is sorted into a 2D matrix with each column being one
VIPA FSR to recover the image (Fig. 2D). Both Fig.
2C and Fig. 2D should be compared with the spectrum
and image in Fig. 1D. Some of the differences in the
two cases result from the target in the actual experiment
overlapping with multiple columns of the spectral shower
as opposed to a single column as in Fig. 1D.
The granular-like features in the image result from the
limited pixel number in the measurement (
6
×
34). To il-
lustrate improved resolution possible using a denser grid
of pixels, two 1.86 GHz soliton microcombs were also
tested in the imaging setup (see Fig. 2E for the optical
and electrical spectrum of one of the microcombs). In
this case, the pixel number in the vertical direction in-
creases from 6 to 32 using the same 60 GHz VIPA and
improved resolution results (see Fig. 2F and Fig. 2G for
three horizontal bars). The increased pixel number in
the vertical direction also enables resolution of the num-
ber ‘4’ on the test target as shown in Fig. 2H. As an
aside, the two 1.86 GHz soliton microcombs feature a
f
rep
=0.7 MHz, and Figs. 2G, H are recorded within a
time interval of 10
μ
s.
Monitoring a flowing microparticle.
The frame rate
of the heterodyne image reconstruction approach is de-
5
termined by the requirement to just resolve the RF sig-
nal comb. Accordingly, because the electrical comb lines
have a frequency separation equal to the difference in the
repetition rates of the signal and reference soliton micro-
combs, this difference in repetition rates is close to the
frame rate and can be quite high when using soliton mi-
crocombs.
To demonstrate measurement of a rapidly-changing
scene, two 9.39 GHz soliton microcombs are used to mon-
itor a microparticle moving in a high-speed flow-cell (Fig.
3A and Fig. 1C). For this purpose a
0.25 m/s lami-
nar flow cell (cross section 0.2 mm
×
8 mm) was set up
and microparticles with diameter of
100
μ
m were sus-
pended in water to flow through the cell. To improve
signal-to-noise a mirror was placed behind the cell which
has transparent surfaces. When a microparticle passes
through the spectral shower, it modulates lines in the
spectral shower. An image of a recorded flowing mi-
croparticle is shown in Fig. 3B. The size of the recon-
structed microparticle (dashed circle in figure) is consis-
tent with the particle actual size. The particles are not
well resolved on account of the limited pixel number. To
illustrate the measured motion of the microparticle, its
center position is plotted versus time in Fig. 2C. A linear
fit gives a flowing velocity of 0.21 m/s, consistent with
the flow-cell set-point velocity of 0.25 m/s. A 200 kHz
frame-rate was used in this measurement.
III. DISCUSSION
Because pixel count (
N
×
M
) is equal to the num-
ber of microcomb lines, it follows that
N
×
M
=
B/f
rep
where
B
is the microcomb bandwidth and
f
rep
is the microcomb repetition rate. Large comb band-
widths are therefore highly advantageous for improv-
ing resolution. Along these lines, dispersion engineer-
ing of the microresonator
31
or spectrally broadening
the microcomb either through intracavity dipersive wave
generation
32,33
or external (chip-based) broadeners
34
can
provide octave-span spectral coverage. The assignment
of these pixels to horizontal and vertical axes is con-
trolled through the VIPA FSR (
f
VIPA
) such that
N
=
f
VIPA
/f
rep
and
M
=
B/f
VIPA
.
For a square array
(
N
=
M
) one must have
f
2
VIPA
=
Bf
rep
. As exam-
ples, a 20 THz comb bandwidth (
1/6 of an octave at
1.55
μ
m) would enable a horizontal pixel number of 100
using a 200 GHz VIPA (custom design available at Light-
Machinery). For the vertical direction, the pixel number
could be increased to over 107 (21) using the 1.86 GHz
(9.39 GHz) microcombs. These should be compared to
the existing spectral shower array dimensions of
32
×
15
for the 1.86 GHz microcomb and
6
×
34 for the 9.39 GHz
microcomb.
Finally, there is a trade-off between the frame rate and
pixel number given by by
N
×
M < f
rep
/
(2∆
f
rep
). This
expression results from the need to avoid spectral folding
of the RF comb lines. ∆
f
rep
is related to the frame rate
by ∆
f
rep
=
Cf
frame
where
C
is the number of periods in
the interferogram that must be intregrated to determine
the signal and is set by signal-to-noise. In the present
work,
C
7. Accordingly, this expression can also be
written as follows:
N
×
M
×
Cf
frame
< f
rep
/
2. Thus, an
N
×
M
=10,000 pixel spectral shower produced using an
f
rep
=1.86 GHz (9.39 GHz) microcomb, will provide a
maximum frame rate of approximately 14 kHz (70 kHz).
It is also possible to eliminate
N
×
M
in the above expres-
sions to arrive at:
f
frame
< f
2
rep
/
(2
BC
), which illustrates
the importance of higher repetition rate to achieve higher
frame rate, making microcombs attractive for this appli-
cation.
Although not demonstrated here, the dual-comb
method is a coherent measurement. As a result, phase
information can also be retrieved, enabling acquisition of
3 dimensional information on the target
9
. For this pur-
pose, the two combs must be phase locked with distinct
repetition rates. Counter-propagating solitons within a
single microresonator are accordingly a promising candi-
date for this coherent phase retrieval as they have high
mutual coherence
35,36
. Finally, because the dual-comb
measurement can resolve single comb lines, the spatial
resolution is set by the imaging system only. This is in
contrast to the time-stretch method where spatial reso-
lution can also be limited by the ability to resolve the
frequency components
5
.
In summary, imaging using soliton microcombs has
been demonstrated. Frame rates as high as 200 kHz en-
abled measurement of the high speed flow of micropar-
ticles. The current demonstration was in the 1.55
μ
m
band, but can be readily shifted to the 1
μ
m band which
could be more suitable for biological applications
37
. The
method can find widespread applications in life science
as well as in industrial production. For example, it could
be a useful tool to study biochemical waves in cells
38
and
for flow cytometry applications
39,40
.
Acknowledgments
The authors thank Taeyoon Jeon
for helpful discussions on the flow-cell experiment. This
work is supported by the Defense Advanced Research
Projects Agency under the SCOUT program (award no.
W911NF-16-1-0548), the Air Force Office of Scientific
Research (award no. FA9550-18-1-0353) and the Kavli
Nanoscience Institute. CB gratefully acknowledges sup-
port from a postdoctoral fellowship from the Resnick In-
stitute, Caltech.
Author Contributions
All the authors conceived the
experiment, analyzed the data and wrote the manuscript.
CB and MGS conducted the experiments under the su-
pervision of KV.
Author Information
Correspondence and requests
for materials should be addressed to KV (va-
hala@caltech.edu).
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