Characterization of a high coherence,
Brillouin microcavity laser on silicon
Jiang Li,
1
Hansuek Lee,
1
Tong Chen, and Kerry J. Vahala
∗
T. J. Watson Laboratory of Applied Physics,
California Institute of Technology, Pasadena, California 91125, USA
1
equal contributors
∗
vahala@caltech.edu
Abstract:
Recently, a high efficiency, narrow-linewidth, chip-based
stimulated Brillouin laser (SBL) was demonstrated using an ultra-high-Q,
silica-on-silicon resonator. In this work, this novel laser is more fully
characterized. The Schawlow Townes linewidth formula for Brillouin laser
operation is derived and compared to linewidth data, and the fitting is used
to measure the mechanical thermal quanta contribution to the Brillouin
laser linewidth. A study of laser mode pulling by the Brillouin optical
gain spectrum is also presented, and high-order, cascaded operation of the
SBL is demonstrated. Potential application of these devices to microwave
sources and phase-coherent communication is discussed.
© 2012 Optical Society of America
OCIS codes:
(190.5890) Stimulated; (290.5900) Stimulated Brillouin; (190.4390) Integrated
optics.
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1. Introduction
Ultra-high coherence (low frequency noise) is a priority in a remarkably wide range of appli-
cations including: high-performance microwave oscillators [1], coherent fiber-optic commu-
nications [2, 3], remote sensing [4] and atomic physics [5, 6]. In these applications, the laser
forms one element of an overall system that would benefit from miniaturization. For example,
in coherent communication systems a laser (local oscillator) works together with taps, splitters
and detectors to demodulate information encoded in the field amplitude of another coherent
laser source. Therein, narrow-linewidth lasers increase the number of information channels
that can be encoded as constellations in the complex plane of the field amplitude [2, 3]. In
yet another example, the lowest, close-to-carrier phase-noise microwave signals are now de-
rived through frequency division of a high-coherence laser source using an optical comb as the
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frequency divider [1]. The miniaturization of these all-optical microwave oscillators could pro-
vide a chip-based alternative to electrical-based microwave oscillators, but with unparalleled
phase noise stability. Moreover, with the advent of microcombs [7,8], such an outcome seems
likely provided that similar strides are possible in miniaturization of high-coherence sources
and reference cavities. Typically, however, miniaturization comes at the expense of coherence,
because quantum and technical noise contributions to laser coherence increase as laser-cavity
form factor is decreased. Recently, however, there has been remarkable progress in achieving
highly coherent, compact laser sources. Both Erbium and Raman microlasers with short-term,
Schawlow-Townes linewidths in the range of 10 Hz have been reported [9, 10]. Also, a fully
packaged narrow linewidth laser that uses feedback from an ultra-high-Q resonator to a semi-
conductor laser has also been demonstrated [11].
Recently, we reported a stimulated Brillouin laser that attains a high level of coherence and is
based on a new, ultra-high-Q resonator fabricated from silica on silicon [12]. Schawlow-Townes
noise of 0.06 Hz
2
/Hz is measured at an output power of approximately 400
μ
W. Also significant
is that the low-frequency technical noise is comparable to commercial fiber lasers. In the present
work, we explore further details of this laser’s operation including mode-pulling phenomena,
cascaded operation, and a study of the Schawlow-Townes linewidth for the Brillouin laser.
Concerning the latter, while conventional (inversion-based) optical lasers feature a Schawlow-
Townes noise that is immune from thermal quanta, Brilluoin lasers, on account of coupling to
the mechanical bath, feature a significant mechanical noise contribution to the laser phase noise.
We both derive this contribution and use the theory to extract the thermal quanta contribution
from data. Finally, the potential application of these devices as spectral purifiers for lower
coherence lasers is discussed.
2. Lithographic fabrication of Brillouin lasers
Stimulated Brillouin scattering has been used to create narrow-linewidth fiber lasers [13] and
to study slow light phenomena [14] in optical fiber. However, on account of the challenge in
matching the Brillouin shift to a pair of cavity modes, only recently have the first microcavity-
based SBLs been demonstrated. These devices leverage a high spectral density of transverse
modes in CaF
2
[15] or microsphere resonators [16] to create a reasonable likelihood of fre-
quency matching. Even more recently, chalcogenide waveguides have been used to achieve
Brillouin oscillation [17]. In the present work, control of the resonator diameter using a new
ultra-high-Q resonator geometry [12] is applied to precisely match the free spectral range (FSR)
to the Brillouin shift. The resonators attain Q factors as high as 875 million [12], even exceed-
ing the performance of microtoroids [18]; and significantly, they are fabricated entirely from
standard lithography and etching. The combination of ultra-high-Q and precision control of
FSR has not previously been possible, and is essential for reliable fabrication of low-threshold,
microcavity-based, SBL lasers. Moreover, the same issue that has made SBL devices so diffi-
cult to fabricate in microcavity form (the relatively narrow gain spectrum) becomes an asset in
attaining highly stable, single-line laser oscillation.
Very briefly, the fabrication of these devices uses an 8-10 micron thick thermal oxide layer
that is lithographically patterned and etched into circular disks using buffered HF. The etched,
oxide disks then act as a mask for selective, dry-etching of the silicon. This dry etch process
creates a whispering gallery resonator through undercut of the silicon. By proper control of
both the wet and dry etching processes, the Q of the resulting resonator can be nearly 1 billion.
Moreover, the lithography and etching process provide diameter control of 1:20,000, giving
only 0.5 MHz of FSR uncertainty for a cavity of 10 GHz FSR. This level of control is more than
sufficient to place the microcavity FSR within the Brillouin frequency shift. Figure 1(b) shows
a top view of a resonator fabricated using this procedure. Additional details on fabrication and
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−0.05
0
0.05
0.1
0.15
0.2
−0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
t (ms)
Voltage (V)
pump
SBS
H.C. error signal
(a)
(b)
(c)
Fig. 1.
Experimental setup.
(a) A tunable CW laser is amplified through an EDFA and
coupled into the disk resonator using the taper-fiber technique. The SBL emission in the
backward direction propagates through the fiber circulator, and is monitored by a pho-
todetector (PD B) and an optical spectrum analyzer (OSA). The pump is monitored by a
separate photodetector (PD A) and is also coupled to a balanced-homodyne detection setup
(H
̈
ansch-Couillaud technique) to generate an error signal for locking the pump laser to the
cavity resonance. (b) A micrograph of the SBL disk resonator used in this experiment. The
disk has a diameter of approximately 6.02 mm. (c) Experimental oscilloscope traces for
transmitted pump, back-propagating SBL and H
̈
ansch-Couillaud error signal.
characterization of these resonators are described in [12].
3. Cascaded versus single-line Brillouin laser action
Figure 1(a) shows the experimental setup used to test the SBLs. Pump power is coupled into the
resonator by way of a fiber taper coupler [19, 20]. SBL emission is coupled into the opposing
direction and routed via a circulator into a photodiode and an optical spectrum analyzer. The
transmitted pump wave is monitored using a balanced homodyne receiver so as to implement a
H
̈
ansch-Couillaud locking of the pump to the resonator [21,22]. Figure 1(c) shows the typical
experimental traces for the transmitted pump, back-propagating SBL and the H
̈
ansch-Couillaud
error signal as the pump laser is scanned across the microcavity resonance.
By proper control of taper loading, the SBL can be operated in two distinct ways: cascade or
single-line. Figure 2(a) shows the optical spectrum of a single-line SBL and Fig. 2(b) shows the
spectrum for cascaded operation up to the 9th order. In cascade, the waveguide loading is kept
low so that once oscillation on the first Stokes line occurs, it can function as a pump wave for a
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1554
1554.2
1554.4
1554.6
−70
−60
−50
−40
−30
−20
−10
0
Wavelength (nm)
SBL spectrum (dB)
1554
1554.5
1555
−80
−70
−60
−50
−40
−30
−20
Wavelength (nm)
SBL spectrum (dB)
(a)
(b)
1st order SBL
pump
1st
3rd
5th
7th
9th
0
0.5
1
1.5
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Pump power (mW
)
1st Stokes power (mW
)
(c)
Fig. 2.
SBL optical spectra and output power versus pump power for single-line op-
eration.
(a) A spectrum showing single-line SBL operation wherein only the 1st-order
emission line is excited. (b) Spectrum showing cascaded SBL operation up to the 9th or-
der. In both figures, the spectrum is collected in the backward direction with the pump and
even order SBL emission lines suppressed on account of their propagation in the forward
direction (i.e., the observed, weak level for these signals in the spectrum is a result of weak
back-reflection in the experimental setup). (c) Output power of the 1st-order Stokes wave
while adjusting the cavity loading so as to maintain critical coupling in each step. The
differential efficiency is around 95%.
second Brillouin wave and so on. Single-line operation, on the other hand, is often desirable in
system applications [1–3] and can be obtained by increasing the resonator waveguide coupling.
While cascading can still be made to occur at a sufficiently high pumping power, increased
waveguide loading forestalls this process by increasing the oscillation threshold. Significantly,
there is no penalty in efficiency as a result of the increased waveguide loading. Indeed, be-
cause the internal loading on the pump rises with increased Stokes power, one can preset the
waveguide loading to an over-coupled condition such that the pump wave will become critically
coupled only at the desired Stokes power. Alternately, in cases where waveguide coupling can
be varied, the coupling can be adjusted so as to always achieve critical coupling of the pump as
the 1st-Stokes wave increases in power. Figure 2(c) shows just this scenario. The power of the
1st-order Stokes laser line is plotted versus the pump power with the cavity loading adjusted
to maintain critical coupling in each step. A linear relationship is obtained and the differential
pumping efficiency is 95%.
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120
140
160
180
200
220
240
260
0
0.5
1
1.5
2
2.5
Pump power (
μ
W)
2nd Stokes power (
μ
W)
(a)
(b)
0
50
100
150
200
0
5
10
15
20
25
30
35
40
45
Pump power (
μ
W)
1st Stokes power (
μ
W)
Fig. 3.
SBL output power dependence on pump power in cascaded operation.
(a) Ex-
perimental output power of the 1st-order SBL versus the pump power. A threshold of 40
μ
W is obtained. The output power of the 1st-order SBL is clamped for pump power above
150
μ
W because the 2nd-order SBL begins oscillation. Also shown is the fitted curve using
P
th
(
√
P
pump
P
th
−
1
)
. (b) Experimental output power of the 2nd-order SBL versus the pump
power. Also shown is the linear fit with respect to the pump power.
It is also interesting to measure the dependence of the different SBL Stokes emission lines
with respect to the pump power. It was shown in [23,24] that for stimulated Raman scattering
from a UHQ toroid cavity, the 1st-order Raman Stokes power scales with the square root of the
pump power while the 2nd-order Stokes power scales linearly with the pump power (given a
fixed taper-fiber coupling condition). The stimulated Brillouin laser in this work satisfies quite
similar laser rate equations as the stimulated Raman laser in [23, 24]. Thus, similar pump-
power dependences of the different Stokes lines are expected for the SBL. Figure 3(a) shows
the output power of the 1st-order Stokes line versus pump power with the cavity loading fixed,
and also a curve fitting using
P
th
(
√
P
pump
P
th
−
1
)
. The flattening of the 1st-order power for pump
power exceeding 150
μ
W results from the onset of threshold for the 2nd-order Stokes line.
On account of gain clamping, the 1st-order Stokes line (now acting as the pump wave for the
2nd-order Stokes laser oscillation) experiences circulating power clamping beyond this power.
Figure 3(b) shows the output power of the 2nd-order Stokes emission versus input pump power
with the cavity loading fixed. The linear dependence is, again, consistent with observations
reported earlier for cascaded Raman laser action.
4. Frequency pulling in the SBL
Frequency/mode pulling in a conventional laser oscillator is well studied. In a laser having an
atomic gain medium, the atomic dispersion modifies the round-trip phase of the intra-cavity
field and “pulls” the laser oscillation frequency from the passive cold cavity value towards that
of the atomic resonance [25]. The Brillouin gain can also introduce dispersive phase shift inside
the microcavity. Recently, mode pulling in a fiber Brillouin laser was accounted for to explain
frequency tuning range under a novel strain tuning mechanism [26]. However, to the authors’
knowledge there has never been a quantitative measurement of mode pulling in Brillouin lasers.
To model the pulling, we introduce a pump field,
A
(frequency
ω
p
), 1st-order Stokes field,
a
(frequency
ω
s
), with corresponding “cold cavity” resonant frequencies
ω
0
and
ω
1
. The fields
are normalized so that their square modulus gives the photon number in the cavity. They satisfy
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the following equations of motion:
̇
A
o
=[
i
(
ω
p
−
ω
0
)
−
γ
/
2
]
A
o
+
i
√
γ
ex
s
−
g
c
|
α
|
2
A
o
(1)
̇
α
=[
i
(
ω
s
−
ω
1
)
−
γ
/
2
]
α
+
g
c
|
A
o
|
2
α
(2)
g
c
=
g
c
0
1
+
2
i
[
ω
p
−
ω
s
−
Ω
]
Γ
=
g
c
0
(
1
−
2
i
ΔΩ
Γ
)
1
+
4
ΔΩ
2
Γ
2
(3)
where
A
o
and
α
are the slowly varying amplitudes for the pump and the stokes fields,
ΔΩ
=
ω
p
−
ω
s
−
Ω
, and
Γ
is the full-width half maximum linewidth of the Brillouin gain.
Ω
is the
Brillouin shift frequency, which depends on the pump wavelength
λ
p
according to
Ω
/
2
π
=
2
nV
A
λ
p
,
n
is the refractive index of silica and
V
A
is the acoustic velocity in silica. Also,
γ
is the
photon damping rate of the loaded cavity, and
γ
ex
is the waveguide coupling rate.
s
is the input
pump field amplitude, normalized such that
|
s
|
2
gives the incident photon rate. (As an aside,
Eq. (3) is valid in the limit that the Brillouin linewidth is narrower than the Brillouin shift. This
condition is satisfied in the present system.)
The real part of Eq. (3) gives the Brillouin gain spectrum with Lorentzian line shape and
the imaginary part is dispersive component that will “pull” the Brillouin oscillation frequency.
Steady state solution of these equations yields the following pair of equations,
|
A
o
|
2
=
γ
2
1
+
4
ΔΩ
2
Γ
2
g
c
0
(4)
ω
s
−
ω
1
−
g
c
0
2
ΔΩ
Γ
1
+
4
ΔΩ
2
Γ
2
|
A
o
|
2
=
0
(5)
Equation (4) gives the threshold intra-cavity pump photon number. Equation (5) is the fre-
quency pulling equation. Substituting Eq. (4) into Eq. (5) gives the 1st-order Stokes lasing
frequency
ω
s
. In the experiment, the beat frequency between the pump and 1st-Stokes wave is
measured (
Δ
ω
beat
=
ω
p
−
ω
s
) and this is given by the following expression,
Δ
ω
beat
=
1
1
+
γ
Γ
(
Δ
ω
FSR
+
γ
Γ
Ω
)
(6)
where
Δ
ω
FSR
=
ω
0
−
ω
1
is the cold cavity free spectral range. Usually,
Γ
≈
2
π
×
(20 - 60)
MHz for silica waveguides. Also,
γ
≈
2
π
×
1 MHz in our cavity so that
γ
Γ
. Under these
conditions, Eq. (6) can be approximated in the following form,
Δ
ω
beat
−
Δ
ω
FSR
=
γ
Γ
(
Ω
−
Δ
ω
FSR
)
(7)
where
Δ
ω
beat
−
Δ
ω
FSR
=
ω
1
−
ω
s
is the frequency pulling caused by Brillouin dispersion. Note
that the effect of this equation is to pull the Stokes lasing frequency towards the line center of
the Brillouin gain (in analogy to the atomic resonance in conventional laser systems). Moreover,
when the FSR matches the Brillouin shift, the frequency pulling is zero.
Figure 4 summarizes the experimental results of the frequency pulling study. In this measure-
ment, the pump wavelength is sequentially tuned along the cavity modes within the same mode
family. The SBL threshold, cold-cavity FSR and Brillouin beat frequency are measured at each
wavelength. Also plotted are the linear fits to the cold cavity FSR and Brillouin beat as well as
quadratic fit to the threshold power. Considering the threshold behavior first, the quadratic fit-
ting of the threshold power is in agreement with Eq. (4). The minimum threshold corresponds to
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1530
1535
1540
1545
1550
1555
1560
10.895
10.896
10.897
10.898
10.899
10.9
10.901
Frequency (GHz)
Wavelength (nm)
1530
1535
1540
1545
1550
1555
1560
0
0.2
0.2
0.4
0.4
0.6
0.6
0.8
0.8
1
1.2
1.2
Threshold (mW)
Threshold (mW)
FSR
linear fit
SBL beat
linear fit
Threshold
quadratic fit
Fig. 4.
SBL mode pulling measurement.
The measured cold cavity FSR (circles), Bril-
louin beat frequency (squares) and SBL threshold power (triangles) are plotted versus
the pump wavelength. The linear fit of the cold cavity FSR gives a slope of
−
2
π
×
0.02
MHz/nm and the fit of the Brillouin beat frequency gives a slope of
−
2
π
×
0.19 MHz/nm.
The quadratic fit of the threshold power yields the Brillouin gain linewidth of 2
π
×
51 MHz.
excitation at the peak of the Brillouin Lorentzian gain spectrum (i.e. the cold cavity FSR = Bril-
louin shift), and the rise of the threshold corresponds to excitation at frequency detunings that
are progressively further away from the gain peak. It is easily shown that
d
Ω
d
λ
p
=
−
Ω
λ
p
=
−
2
π
×
7 MHz/nm [12], meaning that 1nm increase of the pump wavelength will decrease the Brillouin
shift by 7 MHz. Thus, from the quadratic fit, the Brillouin gain bandwidth is estimated to be
Γ
=
2
π
×
51 MHz. The cavity mode has intrinsic Q of 300 million , giving a corresponding
value for
γ
/
2
π
of 1.29 MHz at critical coupling . Thus from Eq. (7), where all terms depend
on
λ
p
, the frequency pulling coefficient
d
Δ
ω
beat
d
λ
p
is estimated to be
−
2
π
×
0.20 MHz/nm. The
linear fit in Fig. 4 gives
d
Δ
ω
beat
d
λ
p
=
−
2
π
×
0.19 MHz/nm (and
d
Δ
ω
FSR
d
λ
p
=
−
2
π
×
0.02 MHz/nm).
The theoretical and experimental pulling rates are therefore in good agreement.
5. Fundamental linewidth of stimulated Brillouin laser
The Hamiltonian for parametric coupling of a mechanical field,
b
(frequency
Ω
), and a Stokes
field,
a
(frequency
ω
1
), that is induced by a pump field
A
(
t
)
(via matrix element
μ
)isgiven
by [27–29]:
H
=
̄
h
ω
1
a
†
a
+
̄
h
Ω
b
†
b
+
̄
h
μ
2
(
A
(
t
)
∗
ba
+
A
(
t
)
a
†
b
†
)
.
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where this Hamiltonian omits energy non conserving terms. Introducing slowly varying op-
erators for the Stokes and the mechanical fields, and also treating the blue pump mode as a
classical, non-dynamical field, the relevant equations of motion are:
̇
β
†
=
−
Γ
2
β
†
+
i
μ
2
A
∗
o
α
e
i
ΔΩ
t
+
F
(
t
)
(8)
̇
α
=
[
i
(
ω
s
−
ω
1
)
−
γ
2
]
α
−
i
μ
2
A
o
β
†
e
−
i
ΔΩ
t
+
f
(
t
)
(9)
where
α
and
β
are the slowly varying operator fields for the Stokes and the mechanical fields;
Γ
(
γ
) is the mechanical (optical) energy decay rate,
ΔΩ
=
ω
p
−
ω
s
−
Ω
, and where
F
(
t
)
and
f
(
t
)
are Langevin operators with the standard normalization for damped oscillators [30,31]. We
now restrict the solution of these equations to a regime in which the mechanical field is much
more strongly damped than the optical field. This is a case typical of the devices considered
in this study. The resulting adiabatic elimination of the more strongly-damped field results in
corresponding amplification of the other, less-strongly damped field. In the regime (
γ
Γ
)
elimination of
β
gives:
̇
α
=
[
i
(
ω
s
−
ω
1
)
−
γ
2
]
α
+
g
c
|
A
o
|
2
α
+
h
(
t
)
where
g
c
is the gain parameter introduced in the discussion of frequency pulling and is related
to the matrix element
μ
by
g
c
0
=
μ
2
/
2
Γ
.
h
(
t
)
is fluctuation operator that depends upon the
original operators introduced in Eqs. 8 and 9. As an aside, the adiabatic approximation applied
in this analysis eliminates the possibility of contributions from the optical pump to the SBL
phase noise. These contributions have been studied in Brillouin fiber ring lasers [32, 33] and
also analyzed in the first reports of SBS laser action in microresonators (see Eq. (4) in [15]).
They are suppressed by a factor
(
1
+
Γ
/
γ
)
2
or about 2000X in the current device. Nonetheless,
they are interesting and potentially important in cases where pumps have large amounts of phase
noise. In the current study, there was no evidence of these fluctuations in the Schawlow-Townes
noise spectrum discussed below.
Analysis of the phase noise in the Stokes field using the standard approach gives the follow-
ing linewidth formula:
Δ
ν
=
γ
4
π
̄
N
S
(
n
T
+
N
T
+
1
)
(10)
where
Δ
ν
is the laser linewidth in Hertz. Also,
̄
N
S
and
N
T
are the number of coherent and ther-
mal quanta in the Stokes field while
n
T
is the number of thermal quanta in the mechanical field.
N
T
is negligible at optical frequencies and has been included here only to indicate the symmet-
rical form of thermal noise contributions from the optical and mechanical degrees of freedom.
The unity term in the expression is of quantum origin, and results from the two underlying
degrees of freedom (optical and mechanical oscillator fields) each contributing 1/2 to the zero
point (in addition to the already noted thermal occupancy). The cumulative contribution from
these two sources provides the unity in the above expressions. It is also interesting to note that
based upon analysis in [15] we would expect a small correction factor to Eq. (10) of the form
(
1
+
γ
/
Γ
)
−
2
resulting from the adiabatic approximation made above. This correction would be
of order of a few percent using the system parameters.
The above form of the linewidth can be rewritten in terms of more-readily-measurable quan-
tities as follows:
Δ
ν
=
̄
h
ω
3
4
π
PQ
T
Q
E
(
n
T
+
N
T
+
1
)
(11)
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where
Q
T
,
E
are the total and external Q factors, and P is the output power of the Brillouin laser.
In this form, the expression is similar to the Schawlow-Townes formula for an inversion-based
laser. In comparing this formula to the conventional Schawlow-Townes formula, the presence
of the mechanical thermal quanta (as well as their zero-point contribution) is new and alters
the magnitude of the linewidth. In the present case of Brillouin oscillation near a mechanical
frequency of 10.8 GHz,
n
T
=
569 and this factor greatly increases the value of the linewidth
over its vacuum-noise-limited value.
0.1
0.2
0.3
0.4
0
0.2
0.4
0.6
SBL power (mW)
S
ν
(Hz
2
/Hz)
Fig. 5.
Measurements of the SBL Schawlow-Townes-like, frequency noise character-
istics
(Original data appeared in the supplemental information of [12]). The dashed line is
an inverse power fit to the data.
The Schawlow-Townes-like noise of this device has been reported in [12] and that data is
reproduced in Fig. 5. Briefly, to characterize this frequency noise, a Mach-Zehnder interferom-
eter having a free spectral range of 6.72 MHz is used as a discriminator and the transmitted
optical power is detected and measured using an electrical spectrum analyzer (ESA). The white
noise portion of the resulting spectrum can then be measured and plotted as a function of output
power. Figure 5 shows this data and also an inverse power curve fitting according to Eq. (11).
The thermal quanta of the mechanical field can be derived from the measurement values of the
ST noise levels. For the device in the measurement,
Q
T
= 140 million,
Q
E
= 390 million, which
gives
n
T
≈
600. This is in good agreement with the theoretical thermal quanta value at room
temperature (569). The minimum value of 0.06 Hz
2
/Hz for the Schawlow-Townes noise is to
our knowledge the lowest recorded ST noise for any chip-based laser.
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6. Discussion and conclusion
The combined effect of adiabatic suppression of pump noise and very low Schawlow-Townes
noise means that the SBL device studied here acts as a spectral purifier, boosting the coherence
of the pump wave. The relatively small frequency shift created in this process (about 11 GHz)
can be easily compensated. For example, low coherence DFB lasers are manufactured with
wavelengths set on the ITU grid by control of an integrated grating pitch with fine-control pro-
vided by temperature tuning of the fully packaged device. A DFB laser could be tuned through
this same process to function as an SBL pump so that the emitted SBL wavelength resides at
the desired ITU channel. In this way, the existing WDM infrastructure could be adapted for
high-coherence operation in optical QAM systems. The frequency noise levels demonstrated
here exceed even state of the art monolithic semiconductor laser by 40dB [34]. Using the meas-
ured phase noise, it is estimated that Square 1024-QAM formats could be implemented using
an SBL generated optical carrier at 40GB/s.
While the current devices use a taper coupling for launch of the pump and collection of
laser signal, the ability to precisely control the resonator boundary enables use of microfabri-
cated waveguides for this process. Several designs are under investigation, the implementation
of which will extend the range of applications of the SBL devices. For example, the SBLs
demonstrated here are candidates for locking to a reference cavity so as to create Hertz or
lower long-term linewidths. Such a source on a chip might one day be combined with micro-
comb technology [8] to realize a compact and high-performance microwave oscillator. At the
tabletop scale, these comb-based systems have recently exceeded the performance of cryogenic
electronic oscillators [1]. Also, another approach for stable, microwave generation relies upon
heterodyne mixing of stable Brillouin laser lines in optical fiber [35]. The present devices would
be interesting candidates for this same approach.
In conclusion, we have characterized single-line and cascaded operation up to the 9th-order
in a novel chip-based Brillouin laser. Moreover, a technique for controllable operation with or
without cascade has been demonstrated. Frequency pulling induced by the SBS nonlinear phase
shift has been modeled and observed. A theoretical formula for the foundamental linewidth of
the SBL has been derived and we have used it to show that the thermal quanta of the mechanical
mode greatly enhances the Schawlow-Townes noise of the SBL. Existing data on ST noise
has been analyzed using this model to infer a value for the thermal quanta in the mechanical
mode of the present laser system. The inferred value is in good agreement with the theory of
a mechanical mode in thermal equilibrium. Finally, the SBL in this work features the lowest
fundamental linewidth recorded for any chip-based laser.
Acknowledgments
The authors would like to acknowledge helpful discussions with Scott Diddams and Scott Papp.
The authors are also grateful for financial support from the DARPA ORCHID program, the
Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support
of the Gordon and Betty Moore Foundation, and the Kavli NanoScience Institute.
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20180