The phase noise of the soliton repetition rate is experimentally characterized in silica microresonators. In conjunction with dispersive wave quieting of pump technical noise, spatio-temporal fluctuations of distinct transverse modes set a limit to performance

Bao, Chengying

Gao, Maodong

Ji, Qing-Xin

Shen, Boqiang

Vahala, Kerry

Wang, Heming

Wu, Lue

Yang, Qi-Fan

Yuan, Zhiquan

English

Kippenberg

Matsko

Kondratiev

Crossref

Impact of spatio-temporal thermal decoherence on soliton microcombs in multimode microresonators

Caltech Authors - Main

FTh3J.4.pdf CLEO 2020 © OSA 2020
Impact of spatio-temporal thermal decoherence
on soliton microcombs in multimode
microresonators
Qi-Fan Yang1,†, Qing-Xin Ji1,2,†, Lue Wu1,†, Boqiang Shen1, Heming Wang1,
Zhiquan Yuan1, Chengying Bao1, Maodong Gao1, and Kerry Vahala1,∗
1T. J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, California 91125,
USA
2School of Physics, Peking University, Beijing 100871 PRC
† These authors contributed equally to this work.
∗vahala@caltech.edu
Abstract: The phase noise of the soliton repetition rate is experimentally characterized
in silica microresonators. In conjunction with dispersive wave quieting of pump technical
noise, spatio-temporal fluctuations of distinct transverse modes set a limit to performance.
OCIS codes: (190.4360) Nonlinear optics, devices; (140.3945) Microcavities; (190.5530) Pulse propagation and
temporal solitons.
The demonstration of soliton mode-locking in optical microresonators has given rise to a new class of miniatur-
ized optical frequency combs that enable chip-based applications such as optical frequency synthesis and optical
clocks [1]. The stability of the soliton repetition rate is important across a wide range of applications, and also
when the comb functions as a stand-alone microwave signal source. While the intrinsic noise set by quantum-
limited motion of the solitons is very low [2], technical noise contributions are found to dominate. For example
phase noise in the optical pump can couple to the soliton repetition rate through a process driven by the Raman
self-frequency shift [3]. An effective method to suppress this coupling is by operation at a so-called quiet point
formed when a strong single-mode dispersive wave is emitted by the soliton [4]. Dispersive waves are generated
when a mode of the soliton forming mode becomes degenerate with a mode belonging to another mode family.
The spectral recoil from their interaction can be tuned to balance the Raman effect and thereby decouple the pump
noise at a specific operating point. Here we show that the suppression possible using this mechanism can be very
large. Moreover, we identify a fundamental limit set by spatio-thermal fluctuations of the two interacting modes.
Soliton microcombs are generated in an ultra-high-Q silica microresonator with 15.2 GHz free-spectral-range
(optical spectrum in Fig. 1(a)) [3]. Significantly, the spectrum features a strong dispersive wave that is used below
for quiet point operation. The microresonator is sealed in a metal package and mounted in an acoustic shield
for mechanical and thermal isolation. Photodetection of the soliton microcombs reveals high-contrast, narrow-
linewidth beatnotes as shown in Fig. 1(b). Figure 1(c) gives the relative Allan deviation of the beatnote, which
reaches 5×10−11 at 40 ms integration time with long-term drift less than 0.1 Hz/s.
R
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Averaging time (s)
10-9
10-10
10-3 10-2 10-1 100 101
Phase noise Drift
Wavelength (nm)
1530 1540 1550 1560 1570
P
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r 
(2
0
 d
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Pump
(a)
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Frequency (kHz+15.219370 GHz)
-40 -20 0 20 40
RBW
10 Hz Calibration
tone
(c)
(b)
Frequency

TT+T
Fig. 1. Optical and electrical spectra of soliton microcomb. (a) Optical spectrum of the soliton
microcomb. The pump (dashed line) and the highlighted dispersive wave belong to fundamental
and higher-order mode families, respectively. Inset right: silica microresonator in a package. Inset
left: spatio–temporal thermal tuning of soliton and dispersive wave modes. (b) Electrical spectrum
showing soliton repetition rate. (c) Allan deviation of repetition rate.
Authorized licensed use limited to: CALIFORNIA INSTITUTE OF TECHNOLOGY. Downloaded on September 21,2020 at 23:22:41 UTC from IEEE Xplore.  Restrictions apply. 
FTh3J.4.pdf CLEO 2020 © OSA 2020
@ 500 Hz
@ 1 kHz
@ 8 kHz
Technical noise 
suppression
Technical noise suppression (dB)
0 10 20 30 40
0
10
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P
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Pump noise
Spatio-temporal 
thermal noise
(b) (c)
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Frequency offset (Hz)
102 103 104 105
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-40
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101
Frequency offset (Hz)
102 103 104 105
-20
-40
-60
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-100
-120
-140
Measurement floor
(a)
36 dB
36 dB
106
Measurement
Spatiotemporal 
thermal decoherence
Quantum timing jitter
Thermo-refractive
Shot noise floor
Fig. 2. Quiet point and spatio-temporal thermal decoherence. (a) Phase noise and calibration
tone power at different detuning (indicated by color). Pump contributed noise corresponding to the
weakest calibration tone is also plotted (dashed line). (b) Plot of actual noise versus calibration tone
suppression at several offset frequencies. (c) Measured phase noise at maximum quiet point sup-
pression and calculated spatio-temporal thermal decoherence noise. Quantum timing jitter, thermo-
refractive noise and detector shot noise are also plotted.
Quiet-point operation is established as described in Ref. [4]. Plotted in Fig. 2(a) are phase noise traces of
the repetition rate while approaching the quiet point. Tuning control in this process is possible by adjusting the
detuning of the pump frequency relative to the cavity resonance that is pumped. In addition, calibration tones are
created by modulating the phase of the pump laser at 10 kHz. This enables active monitoring of the degree to
which pump phase noise is suppressed. At the quiet point 36 dB noise suppression is achieved, which is sufficient
to reduce the pump noise below the measured phase noise. Further comparison between the amount of reduction
in pump noise (as inferred by the tone) and measured phase noise reveals a regime dominated by another source
of noise (Fig. 2(b)).
Noise contributions to the repetition rate are calculated in Fig. 2(c), including quantum timing jitter [2], thermo-
refractive noise [5] and detector shot noise. And each source is too small to be a limiting factor in this work. A
new source of noise caused by spatio-temporal thermal decoherence is believed to set the observed noise limit.
Due to their spatial displacement, the soliton spatial mode and the transverse mode associated with the dispersive
wave are not in thermal equilibrium. Moreover, as illustrated in Fig. 1(a), their temperature difference δT changes
their frequency difference Δω , thereby altering the power of the dispersive wave and in turn the repetition rate [4].
The contribution of this spatio-temporal thermal fluctuation to the noise of soliton repetition rate can be shown
to be given by SST = (α2n2T ω2/n2o)SδT . Here, nT and no are the thermo-optic coefficient and the refractive index,
respectively; ω is the frequency of the dispersive wave and α = ∂ωr/∂Δω is the dependence of the repetition rate
ωr on Δω . The power spectral density SδT can be obtained numerically using the finite-element-method [5]. The
resulting calculated SST (Fig. 2(c)) is in good agreement with the measurement. In making this plot the coefficient
α is a fitting parameter and the fit value of -26 dB is close to the value -22 dB derived from measured soliton
properties based on the theory in Ref. [4].
In summary, we have studied the quiet point operation of a soliton microcomb for improved repetition rate
stability. Spatio-temporal thermal fluctuations are believed to present a limit on the stability at the quiet point. The
quiet point suppression mechanism, itself, was measured to provide up to 36 dB of pump-noise suppression.
References
1. T. J. Kippenberg, A. L. Gaeta, M. Lipson, and M. L. Gorodetsky, “Dissipative Kerr solitons in optical
microresonators,” Science 361 (2018).
2. A. B. Matsko and L. Maleki, “On timing jitter of mode locked Kerr frequency combs,” Opt. Express 21,
28862–28876 (2013).
3. X. Yi, Q.-F. Yang, K. Y. Yang, M.-G. Suh, and K. Vahala, “Soliton frequency comb at microwave rates in a
high-Q silica microresonator,” Optica 2, 1078–1085 (2015).
4. X. Yi, Q.-F. Yang, X. Zhang, K. Y. Yang, X. Li, and K. Vahala, “Single-mode dispersive waves and soliton
microcomb dynamics,” Nat. Commun. 8, 14869 (2017).
5. N. Kondratiev and M. Gorodetsky, “Thermorefractive noise in whispering gallery mode microresonators:
Analytical results and numerical simulation,” Phys. Lett. A 382, 2265–2268 (2018).
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Impact of spatio-temporal thermal decoherence on soliton microcombs in multimode microresonators

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