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Low-Pump-Power, Low-Phase-Noise, and Microwave to Millimeter-Wave Repetition Rate
Operation in Microcombs
Jiang Li, Hansuek Lee, Tong Chen, and Kerry J. Vahala
*
T. J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, California 91125, USA
(Received 2 June 2012; revised manuscript received 24 August 2012; published 4 December 2012)
Microresonator-based frequency combs (microcombs or Kerr combs) can potentially miniaturize the
numerous applications of conventional frequency combs. A priority is the realization of broadband
(ideally octave spanning) spectra at detectable repetition rates for comb self-referencing. However, access
to these rates involves pumping larger mode volumes and hence higher threshold powers. Moreover,
threshold power sets both the scale for power per comb tooth and also the optical pump. Along these lines,
it is shown that a class of resonators having surface-loss-limited
Q
factors can operate over a wide range of
repetition rates with minimal variation in threshold power. A new, surface-loss-limited resonator
illustrates the idea. Comb generation on mode spacings ranging from 2.6 to 220 GHz with overall low
threshold power (as low as 1 mW) is demonstrated. A record number of comb lines for a microcomb
(around 1900) is also observed with pump power of 200 mW. The ability to engineer a wide range of
repetition rates with these devices is also used to investigate a recently observed mechanism in micro-
combs associated with dispersion of subcomb offset frequencies. We observe high-coherence phase
locking in cases where these offset frequencies are small enough so as to be tuned into coincidence. In
these cases, a record-low microcomb phase noise is reported at a level comparable to an open-loop, high-
performance microwave oscillator.
DOI:
10.1103/PhysRevLett.109.233901
PACS numbers: 42.65.Ky, 42.62.Eh, 42.65.Hw
The combination of a high optical
Q
factor and the Kerr
effect optical nonlinearity enables optical parametric oscil-
lation in microcavities [
1
,
2
]. Concomitant, nondegenerate
four-wave mixing multiplies the initial Stokes and anti-
Stokes waves creating a route to generation of frequency
combs [
3
]. This approach offers the potential for miniatur-
ization and integration with other devices, thereby magni-
fying the already remarkable impact of frequency combs
on science and metrology [
4
,
5
]. So far, microcombs (or
Kerr combs) have been demonstrated using silica microt-
oroids [
3
],
CaF
2
diamond-milled rods [
6
,
7
], fiber Fabry-
Perot resonators [
8
], silicon-nitride rings on silicon [
9
,
10
],
high-index silica rings on silicon [
11
], and fused-quartz
cavities [
12
]. Octave span operation has been demonstrated
in microtoroids [
13
] and in silicon nitride resonators [
14
],
with line spacings of 850 and 226 GHz, respectively, and a
microwave-repetition rate is possible in a range of devices
[
6
,
7
,
12
,
15
17
]. However, the combination of these prop-
erties, required for self-referenced operation, has not been
possible. Moreover, microwave-rate devices are also prone
to operate in a mode whereby oscillation occurs first on
non-native comb line separations [
18
]. This creates a situ-
ation in which many subcombs can ultimately oscillate on
the native comb spacing, but, significantly, not necessarily
with the same underlying offset frequencies. This disper-
sion in offset frequencies is now believed to contribute to
instability in the microwave beat note [
18
].
In this work, both of these problems related to
microwave-rate systems are investigated using a new opti-
cal resonator. It is silica based on a silicon chip and
provides
Q
factors as high as
8
:
75

10
8
[
19
]. Other
properties of the device, including surface roughness mea-
surements, are given in [
19
]. Because the devices are litho-
graphically defined and achieve ultra-high-
Q
operation
without the need for a reflow process [
20
], microcomb
operation is achieved across a record span (2.6–220 GHz)
of user-defined, repetition rates. Indeed, the rates presented
here are the lowest achieved to date for any microcomb.
Moreover, the devices are surface-loss-limited over a wide
range of diameters, a property that is shown to approxi-
mately decouple a strong dependence of pumping thresh-
old on repetition rate so that turn-on power remains less
than 5 mW for repetition rates between 4.4 and 220 GHz.
In the experiment, an external-cavity diode laser in the
C
band is amplified using an erbium-doped fiber amplifier
(EDFA) and then coupled to the disk resonator using a
tapered fiber coupler [
21
,
22
]. The pump (TE polarized) is
thermally locked to the resonance [
23
]. The generated
comb lines from the disk resonator are then coupled to
the same taper fiber through which spectral monitoring or
photodetection (demodulation) is straightforward. Spectral
monitoring is performed using both a telecom optical
spectrum analyzer (OSA) (600–1700 nm) and an infrared
OSA (1200–2400 nm). Comb lines are demodulated on a
high-speed photodetector having a bandwidth of 25 GHz.
The resulting photocurrent beat notes are analyzed on an
electrical spectrum analyzer and also using a phase noise
analyzer.
In Fig.
1(a)
, the spectrum of a 2 mm diameter disk [free-
spectral range (FSR) is 33 GHz] having a threshold of
PRL
109,
233901 (2012)
PHYSICAL REVIEW LETTERS
week ending
7 DECEMBER 2012
0031-9007
=
12
=
109(23)
=
233901(5)
233901-1
Ó
2012 American Physical Society
2 mW [Fig.
1(b)
] is shown for excitation only slightly
above threshold. This resonator featured an intrinsic
Q
of
2
:
7

10
8
. The initial Stokes and anti-Stokes lines occur at
a multiple of 37 of the native line spacing, which is con-
sistent with an estimate of the parametric gain spectral
maximum based on calculated dispersion and known cav-
ity
Q
(see discussion in [
18
]). Only modest pumping above
threshold is required to generate a dense comb spectrum on
the native line spacing. About 200 comb lines are gener-
ated with a coupled pump power of only 7.5 mW [Figs.
1(c)
and
1(d)
]. A further increase of the coupled pump power to
200 mW leads to a broadband comb spectrum from 1320 to
1820 nm [Fig.
1(e)
]. This spectrum spans nearly half an
octave (62 THz) and contains about 1900 comb lines,
which is, to the authors’ knowledge, the largest number
of comb lines so far generated from a microcomb. Using a
larger FSR device (66 GHz), it was possible to obtain
3
=
4
octave span operation in a continuous spectrum [106 THz,
1180–2020 nm; see Fig.
2(a)
]. Spectra taken for a micro-
comb featuring a record-low FSR of 2.6 GHz are also
shown in Figs.
2(b)
and
2(c)
.
The threshold relation for parametric oscillation in a
microcavity [
1
] can be manipulated into the following
form:
P
th


8

n
n
2
!

!
FSR
A
Q
2
T
;
(1)
where

¼

e
=
is the coupling parameter (

and

e
are the
total and coupling-related cavity decay rates),
n
2
(
n
) is the
nonlinear index (refractive index),

!
FSR
(
!
) is the free-
spectral range (optical frequency),
A
is the mode area, and
Q
T
is the total optical
Q
factor. In the present device,
n
2
¼
2
:
2

10

20
m
2
=
W
(silica) and
A

30

m
2
for a 2 mm
disk cavity. All other factors held fixed, it is clear that
decreasing FSR (to achieve microwave-rate comb opera-
tion) adversely impacts turn-on power. Moreover, in
whispering-gallery resonators, the mode area,
A
, will gen-
erally increase with decreasing FSR, thereby causing fur-
ther degradation of power requirements. At the same time, it
is interesting to note the positive impact of increasing
Q
factor. Higher optical
Q
creates larger resonant buildup so
that a given coupled power induces a larger Kerr nonlinear
1540
1550
1560
1570
−80
−60
−40
−20
0
Wavelength (nm)
Power (dB)
2.6 GHz comb
1552.4
1552.6
1552.8
−44
−42
−40
−38
Wavelength (nm)
Power (dB)
2.6 GHz comb
1000
1200
1400
1600
1800
2000
2200
−80
−70
−60
−50
−40
−30
−20
−10
0
10
Wavelength (nm)
Power (dB)
66 GHz comb
(a)
)
c
(
)
b
(
1422
1426
−90
−70
−50
−30
FIG. 2 (color online). (a) A broadband comb spectrum with
106 THz span (1180–2020 nm) and repetition rate 66 GHz is
shown. Inset: reduced-span spectrum of the comb with comb
lines resolved. (b) An optical comb spectrum taken using a
2.6 GHz FSR device. (c) A reduced wavelength span of the
spectrum in (b) in which the individual comb lines are just
resolved by the OSA.
1
2
3
4
5
0
10
20
30
40
50
60
70
Pump power (mW)
Signal power (
μ
W)
1500
1540
1580
−60
−50
−40
−30
−20
−10
0
Wavelength (nm)
Power (dB)
1500
1540
1580
−70
−60
−50
−40
−30
−20
−10
0
Wavelength (nm)
Power (dB)
1544
1548
1552
−70
−60
−50
−40
−30
−20
−10
0
Wavelength (nm)
Power (dB)
1300
1400
1500
1600
1700
1800
1900
Wavelength (nm)
Power (dB)
(a)
(b)
(c)
(d)
(e)
0
−80
−70
−60
−50
−40
−30
−20
−10
10
FIG. 1 (color online). Panels (a)–(e) show data obtained using a 2 mm diameter (33 GHz FSR) disk microcomb device. (a) The 2 mm
disk comb spectrum is measured for excitation just above threshold. (b) The power of the first oscillating, higher-frequency, comb line
is plotted versus pump power and shows a threshold turn-on power of approximately 2 mW. (c) Approximately 200 comb lines are
generated with coupled pump power of 7.5 mW. (d) A reduced span scan of the spectrum in (c) is shown with comb lines resolved by
the OSA. (e) A broadband comb spectrum with 62 THz span is shown. The coupled pump power was 200 mW.
PRL
109,
233901 (2012)
PHYSICAL REVIEW LETTERS
week ending
7 DECEMBER 2012
233901-2