ARTICLE
Received 9 Jun 2013
|
Accepted 20 Aug 2013
|
Published 17 Sep 2013
Spiral resonators for on-chip laser frequency
stabilization
Hansuek Lee
1,2
, Myoung-Gyun Suh
1
, Tong Chen
1
, Jiang Li
1
, Scott A. Diddams
3
& Kerry J. Vahala
1
Frequency references are indispensable to radio, microwave and time keeping systems, with
far reaching applications in navigation, communication, remote sensing and basic science.
Over the past decade, there has been an optical revolution in time keeping and microwave
generation that promises to ultimately impact all of these areas. Indeed, the most precise
clocks and lowest noise microwave signals are now based on a laser with short-term stability
derived from a reference cavity. In spite of the tremendous progress, these systems remain
essentially laboratory devices and there is interest in their miniaturization, even towards on-
chip systems. Here we describe a chip-based optical reference cavity that uses spatial
averaging of thermorefractive noise to enhance resonator stability. Stabilized fibre lasers
exhibit relative Allan deviation of 3.9
10
13
at 400
m
s averaging time and an effective
linewidth
o
100 Hz by achieving over 26 dB of phase-noise reduction.
DOI: 10.1038/ncomms3468
OPEN
1
T.J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, California 91125, USA.
2
hQphotonics, Pasadena, California 91106,
USA.
3
Time and Frequency Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA. Correspondence and requests for
materials should be addressed to K.J.V. (email: vahala@caltech.edu).
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A
pplications including gravity-wave detection
1
, optical
clocks
2
and high-performance microwave generation
3
have fuelled interest in frequency references for
stabilization of laser sources. Such references benefit from high
optical
Q
factor or equivalently long optical storage time and
systems in-use or under investigation include Fabry–Perot
cavities
4–6
, absorption spectral-hole burning in cryogenically
cooled crystals
7,8
and long-delay-line interferometers
1,9
. Bench-
top-scale systems based on Fabry–Perot optical cavities have
attained an Allan deviation 1
10
16
at 1 s averaging
5
. In these
systems, high-finesse-mirrors create a narrow resonance for laser
locking, whereas low-thermal-expansion housings and low-
thermal noise mirror coatings create immunity to thermal
fluctuations that perturb the resonant frequency
4–6,10,11
. With
the advent of ultra-high optical-
Q
, solid-state resonator systems
based on silica
12–14
and crystalline fluoride materials
15–17
attention has naturally turned towards miniature devices.
Besides their compact size, these devices, through their reduced
mass, can offer improved performance with respect to shock and
acceleration. In the case of chip-based devices, there is also the
potential for integration with other components.
In solid-state resonators, fluctuations arise from thermore-
fractive, thermo-mechanical, elasto-optic and photo-thermal
noise
18–20
. The first three mechanisms are fundamental, while
the fourth is determined by the transfer of the laser power
fluctuations into thermal changes of the cavity refractive index
and size. Crystalline resonators are advantageous for reduced
thermorefractive noise as the dependence of refractive index on
temperature is low in comparison with silica
19
. Along these lines,
locking of a laser to a MgF
2
resonator has attained stabilization to
6
10
14
at 0.1 s averaging time
21
. It has also been
demonstrated that dual-mode feedback control can be used to
stabilize the absolute frequency of a resonator by measuring
modal temperature using two, orthogonally polarized modes
22–24
.
Moreover, application of these resonators as frequency
stabilization elements in ring fibre lasers
25,26
and designs for
enhanced acceleration and vibration immunity have been
proposed
27,28
.
In this paper, we study the application of a chip-based, high-
Q
resonator in the form of a spiral for laser frequency stabilization.
Besides being the first chip-based reference cavities, the geometry
offers a high level of immunity to thermorefractive noise, as well
as thermo-mechanical and photo-thermal noise. Also, the
measurements are performed without any special vacuum
isolation and temperature control. Phase-noise spectra are
measured and show strong laser phase-noise suppression over
offset frequencies ranging from 1 Hz to 100 kHz. Frequency
fluctuations, as characterized by the Allan deviation, are also
measured.
Results
Design of low-thermal noise reference cavities
. In the absence of
resonator noise sources, the rms frequency difference of a locked
laser relative to a cavity line center depends upon the optical
Q
and signal-to-noise ratio (SNR) of the detected laser signal
through the following expression
29
,
D
n
rms
n
0
D
n
0
n
0
SNR
¼
1
Q
SNR
ð
1
Þ
where
Q
¼
n
0
/
D
n
0
has been used in the result from the study by
Drever
et al.
29
and where the SNR depends upon the integration
time or servo-control bandwidth. Given a high enough
Q
factor
and large enough SNR, the stability of the laser locked to the
cavity becomes determined by fluctuations in the cavity line
centre, itself. Excluding technical noise sources such as
acceleration and acoustics, the largest contribution to these
fluctuations originates from thermorefractive noise
18,19
.
Intuitively, if one considers N, randomly dispersed fluctuators
that each contribute an rms frequency fluctuation
s
1
, then the
total rms frequency fluctuation will scale like
s
1
ffiffiffiffi
N
p
¼
s
1
ffiffiffiffiffiffiffiffiffiffi
r
V
p
(assuming the fluctuators are uncorrelated) where
r
is the density
of fluctuators and
V
is the mode volume. At the same time, if the
fluctuators have a fixed size, then the coupling of the fluctuators
to the mode will diminish as the mode volume increases and
s
1
will vary like 1/
V
. Therefore, the total rms frequency fluctuation
will scale like 1
=
ffiffiffiffi
V
p
. This scaling is apparent in models of
thermal-related fluctuations in resonators
18,19
. In optical fibre
reference cavity systems, this source of noise is reduced by
employing long fibre delays
9
.
To leverage this scaling on a silicon chip, a resonator in the
form of a spiral is used (see Fig. 1). Spiral resonators have
previously been used to create narrow free-spectral range devices
on a chip
30
. To attain both high-
Q
and large-mode volume
a special ultra-low-loss waveguide is used in the current
work, providing optical waveguide loss as low as 0.037 dB m
1
(refs 14,31). Using these waveguides we demonstrate resonators
that are over 1 m in length with
Q
factors in excess of 100 million,
but for which the device footprint is smaller than 5.4 cm
2
. Beyond
the thermorefractive noise immunity offered by these devices,
they also provide enhanced immunity to photo-thermal noise.
This happens because of their large mode volume, which greatly
reduces the circulating intensity at a given coupled optical power
and hence also the tendency for heating of the mode volume. As a
result, it is possible to obtain high SNR (see equation. (1)) without
degradation in resonator stability. Moreover, thermo-mechanical
noise is greatly suppressed as this form of noise varies inverse-
quadratically with resonator length
32
.
Representative long and short, round-trip path-length resona-
tors are shown in Fig. 1. The resonators contain two interleaved
spiral waveguides with
S
-turn adiabatic couplers at the spiral
centre. Details on the process used to fabricate the waveguides are
described in previous work
31
. Optical coupling to the resonators
occurrs in the upper-right corner of the chip and uses a fibre
taper
33,34
.
Q
measurements are performed by monitoring
transmitted optical power on the taper coupler while scanning
an external cavity semiconductor laser across a free-spectral range
(FSR) of the resonator. The lower right inset of Fig. 2 shows a
typical scan in the longest resonator having a round-trip physical
path length of 120 cm. The measured FSR of the device
(173 MHz) agrees well with the expected FSR based on the
round-trip length. The other resonances seen in the inset
Figure 1 | Photograph of spiral waveguide resonators.
Left: 1.2 m spiral
resonator. Upper-right: 4.5 cm spiral resonator used for studies of
Q
scaling.
Lower right: quarter shown to provide scale. Scale bar, 1 cm.
ARTICLE
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correspond to higher-order transverse modes. The spectrum is
remarkably uncluttered. We attribute this to spatial filtering of
higher-order transverse modes by the adiabatic couplers (
S
-bend
waveguide turns at the centre of each spiral)
35
. To verify the
dependence of
Q
factor on resonator length a range of device
lengths are tested (4.5, 8.7, 14, 21, 40, 62 and 120 cm). The results
are plotted in the main panel of Fig. 2 along with a theoretical
estimate of the
Q
factor based upon an adiabatic coupler loss of
0.02 dB per coupler and a waveguide loss of 0.15 dB m
1
. The
agreement is reasonable. Also, the waveguide loss here is higher
than reported in earlier work on account of using a contact
aligner for micro-fabrication as opposed to a projection (stepper)
lithography system
14,31
. Nonetheless, a maximum
Q
factor of
140 million is obtained.
Phase-noise spectrum and linewidth
. To measure the frequency
stability of the spiral resonators, the experimental setup shown in
Fig. 3 was used. It includes two, fibre lasers (Orbits Lightwave, at
optical frequencies near 193.43 THz) that are locked with separate
Pound–Drever–Hall systems
29
to two, high-
Q
, silica-on-silicon
spiral resonators. In the measurements,
B
3 mW of laser power is
in the fibre-taper waveguide and about 1 mW of this power is
coupled into the resonator. The locked fibre lasers were
heterodyned to produce a beat signal near 350 MHz. This beat
note directly reveals the combined phase-noise of the two
stabilized lasers, and it was analysed using an electrical spectrum
analyser, a phase-noise analyser (Rohde & Schwarz FSUP26) and
a frequency counter (Tektronix FCA3120 and Pendulum CNT-
91). Acoustic shielding was placed around the entire setup to
attenuate environmental sound; also, pumps and instrumentation
in adjoining rooms were turned-off during measurements.
Measurements were performed for several cases: free-running
fibre lasers, lasers locked to the 1.2 m spiral reference cavities,
and, for comparison purposes, lasers locked to independent
conventional disk resonators of varying diameters (3, 7.5 and
15 mm)
14
. In prior work, linear drift has been substracted
from data
9,21
. In the present work, no linear drift correction
was performed.
Figure 4a shows the phase-noise spectral density function for
the heterodyned signals both with and without the locking
systems engaged. Data are shown for the free-running lasers,
3 mm disk resonators and the 1.2 m spiral cases. The spectra were
measured over offset frequencies from 1 Hz to 10 MHz and an
instrument smoothing algorithm has been applied to show the
trend. Within the bandwidth of the feedback control system
(bandwidth limit is delineated by the servo-control bumps visible
near 200 kHz in the phase-noise spectrum) an average of 26 dB
suppression of fibre-laser phase-noise was measured when the
fibre lasers were locked to the 1.2 m spirals. In comparison, only
10 dB of suppression was achieved with the 3 mm diameter disks
(measured at 1 kHz offset frequency). Below 1 kHz offset
frequency even better suppression was observed for spiral locking
versus disk locking. We believe this is caused by better immunity
to photo-thermal noise in the spiral resonators on account of
their larger mode volume. For example, the 3 mm disk, phase-
noise spectrum degrades at offset frequencies less than 1 kHz,
which is consistent with the thermal corner frequency observed in
other silica-based resonators
36
. In the inset of Fig. 4a, the noise
suppression improvement relative to the free-running fibre laser
case is plotted for each of the resonators measured. The data here
are taken at 1 kHz offset and also at 100 Hz offset to illustrate the
improved suppression of noise at lower offset frequency provided
by the spiral resonator. Overall, there is roughly a 1/
f
3
dependence of phase-noise on frequency. This is indicative of
flicker noise and the dependence is consistent with resonator
modelling of thermorefractive noise, which generally feature a
roll-off in frequency that is faster than 1/
f
2
down to low-offset
frequencies
18,19
.
Figure 4b shows a comparison of the measured electrical
spectrum generated upon heterodyne detection with the
0
5
10
15
−0.2
0
0.2
0.4
0.6
0.8
1
Relative frequency (MHz)
Normalized transmission
Transmission
Lorentzian fit
Interferometer
Sinusoidal fit
10
6
10
7
Quality factor
10
8
10
9
0.01
0.1
Resonator round trip length (m)
110
0.0
0
50
100
150
Relative frequency (MHz)
200
250
300
Normalized transmission
0.2
0.4
FSR = 173 MHz
Transmission
Estimated Q
Measured Q
Interferometer
0.6
0.8
1.0
Figure 2 | Intrinsic
Q
factor measured for the various resonator lengths.
The maximum
Q
factor obtained was 140 million at a length of 1.2 m.
The blue curve is a theoretical prediction for the
Q
versus length that
assumes a waveguide loss of 0.15 dB m
1
. Upper left: a typical optical
spectrum in blue. The sinusoidal curve is an interferometer scan that is
used to calibrate the linewidth. Lower right: spectral scan in excess of one
free-spectral range for the TE polarization. The black curve is the
interferometer calibration trace.
ESA
PID
EOM
50/50
Phase noise
analyzer
50/50
Optical signal
Electrical signal
EOM
50/50
PID
Mixer
Mixer
Fast PD
PD
Spiral resonator
~
LO
LO
PDH locking loop
1
PDH locking loop
2
PD
~
Spiral resonator
Fiber laser
Fiber laser
Counter
Figure 3 | Experimental setup.
Two, fibre lasers independently locked to
high-
Q
spiral reference cavities using Pound–Drever–Hall (PDH) locking
systems. Each PDH locking loop includes a photodiode (PD), electro-optic
modulator (EOM), local oscillator (LO) and proportional-integral-
differential feedback controller (PID). The outputs of the separately locked
lasers were combined on a photodetector and the resulting photocurrent
was analysed using an electrical spectrum analyser (ESA), a frequency
counter and a phase-noise analyser. All components are on the same
optical table.
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free-running fibre lasers to the case when the lasers are
independently locked to the 1.2 m long resonators. For this
measurement, the resolution bandwidth (RBW) of the electrical
spectrum analyser was set to 50 Hz, resulting in an 80 ms sweep
time over the 200 kHz span. As an additional comparison, we
have calculated the effective linewidths for the beat note of the
two, stabilized lasers from the phase-noise spectra
37
and found
900 Hz (free-running lasers), 400 Hz (locked to 3 mm disks) and
100 Hz (locked to 1.2 m spiral resonators). The individual laser
linewidths will be narrower than these values. The calculated,
beatnote linewidth of the lasers locked to 1.2 m spiral resonators
is consistent with both the electrical spectrum measurement of
the beatnote as well as the Allan deviation measurement result.
Allan deviation measurement
. In order to further confirm the
frequency stabilization by the spiral resonators, Allan deviation
measurements
38
were carried out using a Tektronix FCA3120
frequency counter (Fig. 5). As an additional check the measure-
ments were also confirmed using a Pendulum CNT-91 frequency
counter. Zero dead-time measurements were performed using
both frequency counters. Over the range of gate times from 5
m
s
to 3 s, Allan deviations of the spiral-locking case were improved
in comparison with the free-running (unlocked) case. At a
gate time of 400
m
s, a minimum relative Allan deviation of
5.5
10
13
was measured, which is ten times lower than that of
the free-running case. If the two lasers are assumed to be inde-
pendent, then the relative deviation of a single, stabilized laser is
3.9
10
13
, or an equivalent Allan deviation of 75 Hz. After this
minimum there is a rise, then decrease and final rise in the Allan
deviation. The resulting local maximum near 10 ms is believed to
result from environmental fluctuations and to also be associated
with the corresponding increase around 10–60 Hz in the phase-
noise spectrum in Fig. 4a. It was also noteworthy that stability
improvement of locked signal at longer gate times is consistent
with the phase-noise suppression at low-offset frequency
(
o
10 Hz).
Mechanically induced noise
. Measurements of thermo-
mechanical-induced noise were also conducted using both the
disk and spiral resonators. The optomechanical coupling para-
meter is expected to vary inversely with cavity length so that
phase-noise exhibits an inverse quadratic dependence on
length
32
. This dependence was observed over a range of cavity
lengths by using the Ha
̈
nsch Couillard technique
39,40
. Spectral
–140
–10
L
(f) improvement (dB)
0
0.01
0.1
Round trip length (m)
1
10
20
30
40
1
10
100
1 k
Offset frequency (Hz)
10 k
100 k
1 M
10 M
–120
–20
Free-running
1.2 m sprials
RBW = 50 Hz
–40
–60
–80
RF power (dBm)
–100
–120
–100
–50
0
50
Relative frequency (kHz)
100
–100
D
= 3 mm disks
100 Hz 1 kHz
Free-running
D
= 3 mm disks
L
= 1.2 m spirals
L
= 1.2 m spirals
D
= 7.5 mm disks
D
= 15 mm disks
L
= 1.2 m sprials
–80
–60
–40
L
(f) (dBc Hz
–1
)
–20
0
20
40
60
80
100
Figure 4 | Phase-noise spectra and beat-note spectral measurement.
(
a
) Phase-noise spectra measured for two, free-running 193 THz fibre lasers
(black), fibre lasers independently locked to two, 3 mm disk resonators
(blue), and fibre lasers independently locked to two, 1.2 m long spiral
resonators (red). To test measurement reproducibility, resonators were
characterized on multiple days. Measurement of the 1.2 m long resonators
on a second day is shown as the dark-red trace. The data for the spiral
resonator show an average suppression by 26 dB of the fibre laser noise
when locked to the spiral resonators. In comparison, 10 dB of noise
suppression is observed using the 3 mm device. The servo-control noise
bumps appear at around 200 kHz for the locked phase-noise spectra. The
inset is a plot of the noise suppression at 100 Hz and 1 kHz offset
frequencies plotted versus resonator length for each of the resonators
tested. (
b
) The electrical spectrum of the fibre lasers’ beat note for both
free-running and locked configurations. Spectral narrowing and noise
suppression are apparent in the locked spectrum.
10
1
10
–6
10
–5
10
–4
10
–3
10
–2
Gate time (s)
10
–1
10
0
10
1
10
2
Allan deviation at 193.43 THz (Hz)
10
3
10
4
10
5
10
6
Free-running fiber lasers
Fiber lasers locked to 1.2 m spirals
5x10
–9
5x10
–10
5x10
–11
5x10
–12
5x10
–13
Relative Allan deviation
5x10
–14
Figure 5 | Allan deviation measurement result.
Allan deviation of the beat
frequency between the two, free-running fibre lasers (black squares), and
for the lasers independently locked to two, 1.2 m long spiral resonators (red
circles) is shown. A minimum Allan deviation of 100 Hz at an optical
frequency of 193 THz, corresponding to a relative Allan deviation of
5.5
10
13
, was measured at a gate time of 400
m
s for 10 dB improvement
compared with the free-running case. Assuming the fibre lasers are
independent and equivalent, a relative Allan deviation of 3.9
10
13
is
expected for each locked laser.
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features believed to be thermally excited mechanical resonances
were observed at offset frequencies greater than 1 MHz, and
steadily diminished in amplitude to levels below the sensitivity
limit of the system for the largest spirals measured (1.2 m path
length). As confirmed in Fig. 4a, there was no evidence of
mechanical noise in the phase-noise spectra measurements.
Discussion
It is noteworthy that ideal frequency division of the 193 THz
optical carrier to 10 MHz would provide a signal with close-to-
carrier phase-noise of
B
100/
f
3
dBc Hz
1
. This is a level that
is already competitive with the state-of-the-art oven-controlled
crystal oscillators, and the basic architecture to accomplish this
has been demonstrated with the combination of laboratory
frequency combs and electronic division
41
. It is intriguing to
consider that the spiral cavity demonstrated here could be the
frequency reference for a chip-integrated platform, that together
with advances in microcomb technology
42,43
would ultimately
provide broad-bandwidth synthesis of low-phase-noise signals
from the optical to the RF. In addition, the ability to reduce the
effective linewidth of a fibre laser by a factor of 10X using only a
chip-based device is of practical importance in any applications
requiring high coherence. This includes coherent fibre-optic
communications
44,45
, remote sensing
46
and atomic physics
4,47
.
Moreover, aside from simple acoustical shielding of the
experimental setup and operation on a floated optical table,
there has been no attempt to thermally stabilize or vibration
isolate these devices. Likewise, there has been no drift correction
of the data. Concerning future performance improvements,
optical-fibre-based reference systems using 1 km fibre delays
have attained a phase-noise level of
83 dBc Hz
1
at 1 kHz
offset frequency
9
. In the current chip-based design, 27 metre long
delay lines have been demonstrated and lengths in excess of
100 m are feasible
31
. Finally, thicker oxides may be possible if
thermal oxidation is replaced by processes such as the flame
hydrolysis method. The combination of these methods could
produce a 1,000-fold increase in mode volume relative to the
current results.
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Acknowledgements
We thank Andrew Ludlow and Scott Papp (NIST, Boulder CO) for helpful discussions
and comments on this manuscript. We gratefully acknowledge the Defence Advanced
Research Projects Agency under SB121-001, the iPhoD program, and also the QuASAR
program, the Kavli Nanoscience Institute and the Institute for Quantum Information and
Matter, an NSF Physics Frontiers Centre with support of the Gordon and Betty Moore
Foundation. The views expressed are those of the authors and do not reflect the official
policy or position of the Department of Defence or the US Government. Distribution
A—approved for public release; distribution is unlimited.
Author contributions
H.L., T.C. and K.J.V. conceived the devices and all authors helped to design the
experiment. H.L. fabricated the devices with assistance from T.C. M.G.S. measured the
devices with assistance from the other authors. All authors helped to write the paper.
Additional information
Competing financial interests
Two authors declare competing financial interests. H.L. is
an employee of hQphotonics. H.L. and K.V. are founders of hQphotonics.
Reprints and permission
information is available online at http://npg.nature.com/
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How to cite this article:
Lee, H.
et al.
Spiral resonators for on-chip laser frequency
stabilization.
Nat. Commun.
4:2468 doi: 10.1038/ncomms3468 (2013).
This article is licensed under a Creative Commons Attribution 3.0
Unported Licence. To view a copy of this licence visit http://
creativecommons.org/licenses/by/3.0/.
ARTICLE
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms3468
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NATURE COMMUNICATIONS
| 4:2468 | DOI: 10.1038/ncomms3468 | www.nature.com/naturecommunications
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2013
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