of 3
Microresonator Brillouin gyroscope
J
IANG
L
I
,
1,2
M
YOUNG
-G
YUN
S
UH
,
1
AND
K
ERRY
V
AHALA
1,
*
1
T. J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, California 91125, USA
2
Present address: hQphotonics Inc., 2500 E. Colorado Blvd., Pasadena, California 91107, USA
*Corresponding author: vahala@caltech.edu
Received 14 November 2016; revised 6 February 2017; accepted 9 February 2017 (Doc. ID 280805); published 7 March 2017
Optical-based rotation sensors have revolutionized precision,
high-sensitivity inertial navigation systems. At the same time
these sensors use bulky optical fiber spools or free-space reso-
nators. A chip-based, micro-optical gyroscope is demonstrated
that uses counterpropagating Brillouin lasers to measure rota-
tion as a Sagnac-induced frequency shift. Preliminary work has
demonstrated a rotation-rate measurement that surpasses prior
micro-optical rotation-sensing systems by over 40-fold.
© 2017
Optical Society of America
OCIS codes:
(190.5890) Scattering, stimulated; (140.3370) Laser
gyroscopes; (130.0130) Integrated optics.
https://doi.org/10.1364/OPTICA.4.000346
Inertial sensors for rotation are used widely in commercial and
military systems. Driven by applications in consumer electronics
and miniature satellites, there has been intense interest in com-
pact, lightweight sensors that can be integrated with electronics.
MEMS-based sensors have captured this miniature lightweight
application space, but do not provide sensitivity and bias stability
that competes with ring laser gyros [
1
] and fiber-optic gyros [
2
].
Moreover, due to their mechanical nature, MEMS-based devices
are less immune to shock and vibration [
3
]. The prospect of ap-
plying micro-fabrication methods to optical-based gyro systems is
therefore appealing, both because it addresses environmental con-
cerns (even beyond conventional optical gyro systems) and it might
offer performance that exceeds MEMS-based systems. A new class
of micro-optical gyro is demonstrated that uses counterpropagating
Brillouin lasers in a chip-based optical resonator to measure rota-
tion as a frequency shift [
4
]. Preliminary work has measured sinus-
oidal rotations with rates as low as 22 deg/h, which surpasses prior
experimental micro-optical systems by over 40-fold [
5
,
6
].
A Brillouin laser ring gyro (BLRG) was studied in the 1990s
using an optical fiber resonator [
7
]. Brillouin scattering in silica
optical fiber results from the interaction of an optical pump wave
with microwave-rate phonons [
8
]. At sufficiently high pump
intensities, the process amplifies counterpropagating waves resid-
ing within a narrow frequency band (about 50 MHz wide) that is
downshifted relative to the pump frequency by 10
11 GHz (for
pumping near 1.55
μ
m). In a resonator, this amplification can
overcome round-trip losses to produce a lasing Stokes wave. In
the BLRG, a fiber ring resonator was bidirectionally pumped
to excite two counterpropagating Brillouin lasers [
7
]. Upon rota-
tion of the resonator, these counterpropagating lasers experienced
opposing frequency shifts caused by the Sagnac effect [
9
].
Heterodyne detection of the two laser signals allowed measure-
ment of the rotation rate. As in a conventional ring laser gyro,
the counterpropagating laser lines produce a narrow-linewidth
beatnote on account of laser action in a high-
Q
cavity. Co-lasing
within a common resonator also tends to cancel technical noise
contributions to the beatnote linewidth.
In this work, the Brillouin laser cavity is a high-optical-
Q
micro
resonator that measures only 18 mm in diameter and is fabricated
of silica on a silicon chip [
10
]. Also, the method of excitation
relies on a single pump wave to induce a Brillouin laser cascade
[
11
]. In this approach, a first Stokes wave is generated as before.
However, upon further pumping this Stokes wave increases in
power to a point where it will act to pump a second Brillouin
Stokes wave, propagating in a direction opposite to the first
Stokes wave. This cascade process can be made to continue for
many Stokes orders, each time producing a Stokes laser line that
is shifted to a lower optical frequency and counterpropagating rel-
ative to the previous line. Neighboring Stokes waves produced in
this cascaded fashion will experience opposing Sagnac shifts and are
well-suited for the gyro application. Moreover, because the neigh-
boring Stokes waves are distinct cavity modes separated in fre-
quency by over 10 GHz, the lock-in effect commonly present
in laser gyroscopes is not present. The free-spectral -range (FSR)
of the resonator is designed to precisely match an integer fraction of
the Brillouin shift (1/3 in the present case). The counterpropagat-
ing even- and odd-order Stokes waves are combined on a fast
photodetector to generate a microwave beat note with sub-
Hertz linewidth [
11
,
12
]. This beatnote is electrically processed
to provide the rotation readout [see Fig.
1(a)
].
A detailed schematic of our experimental setup is shown in
Fig.
1(b)
. The upper block contains the gyro sensing unit, which
at its core includes the high-
Q
disk microresonator and fast
photodetector. The optical pump laser (external cavity diode
laser) is evanescently coupled to the high-
Q
disk resonator using
a tapered fiber. The cavity mode used for stimulated Brillioun
scattering (SBS) generation has a loaded
Q
of 126 million.
The pump laser is locked to the cavity resonance using the
Pound
Drever
Hall technique. The pump threshold for the first
Brillouin Stokes wave is about 250
μ
W. Cascaded Brillouin
Stokes laser action is generated to the third order when the pump
power is increased to a few milliwatts. The pump wave and
Letter
Vol. 4, No. 3 / March 2017 /
Optica
346
2334-2536/17/030346-03 Journal © 2017 Optical Society of America
second-order Stokes wave propagate along the clockwise (CW)
direction and are coupled out of the resonator in the forward di-
rection, while the first and the third Stokes waves propagate along
the counterclockwise (CCW) direction and are coupled out of the
resonator in the backward direction. A fiber circulator is used to
route the backward-propagating waves. The second and third
Stokes waves are selected by a narrow-bandwidth optical bandpass
filter (OBPF). Finally, a fast photodetector is used to detect the
microwave beat note at 10.872 GHz between the second and the
third Stokes waves.
The lower block in Fig.
1(b)
creates the gyro readout. It is a
frequency-to-voltage converter consisting of a voltage-controlled
oscillator (VCO) locked to the Brillouin beatnote. The VCO is
compared against the Brillouin beatnote using a mixer and the
phase error signal from the mixer locks the VCO using a propor-
tional-integral (PI) servo. Because the PI servo output signal is
applied to the VCO tuning port with known tuning coefficient
(here at 10 kHz/V), the servo output signal is proportional to the
frequency change of the Brillouin beat note. Therefore, the servo
output signal can be used as the gyro readout signal and analyzed
on an electrical spectrum analyzer (ESA) or an oscilloscope.
To test the gyro, a sinusoidal rotation with angular amplitude
of 0.14° is applied to the Brillouin gyro. The rotation oscillates at
7.5 Hz. For the measurement, the resonator was packaged into a
small box with pigtailed connectors, as shown in Fig.
2(a)
.To
create the sinusoidal rotation, one corner of the box was hinged
while the other end was moved using a piezoelectric pusher.
Diagrams of the resonator being rotated are presented with the
corresponding gyro readout signal (servo output signal) and
the angular displacement signal (as acquired on an oscilloscope)
in Figs.
2(b)
2(d)
. There is a
π
2
phase shift between the angular
displacement signal and the gyro readout signal (SBS beat note
change) since the beatnote frequency change is proportional
to the angular velocity (derivative of angular displacement).
Moreover, the sign of the Brillouin beat note change indicates
the direction of rotation. In the measured configuration, a
CW rotation [indicated in Fig.
2(b)
and the blue-stripe regions
in Fig.
2(d)
] decreases the second Stokes wave frequency (
ν
2
) and
increases the third Stokes wave frequency (
ν
3
). Therefore, a CW
rotation induces a negative shift in the Brillouin beatnote fre-
quency (
ν
2
ν
3
). On the other hand, a CCW rotation [indicated
in Fig.
2(c)
and the red-stripe regions in Fig.
2(d)
] will induce a
positive shift in the Brillouin beatnote frequency.
(a)(b)
Fig. 1.
(a) Simplified schematic illustrating the principle of Brillouin laser gyroscope operation. Optical pumping (clockwise direction) induces
Brillouin laser action, which results in cascaded odd (counter-clockwise, CCW) and even (clockwise, CW) order Stokes lasers. These lasing modes
experience opposing Sagnac frequency shifts. Detection of the beat frequency of these co-lasing signals followed by a frequency-to-voltage readou
t
(f-V) provides rotation sensing. Laser action on odd Stokes (red) and even Stokes (blue) lines is shown. CW, rest, and CCW rotation induces beat
frequency shifts as indicated. (b) Upper panel is a detailed experimental schematic for the gyroscope. The microcavity (yellow) is optically pumped
.
The laser pump is locked to a microcavity resonance using a Pound
Drever
Hall lock. Second-order and third-order Stokes co-lasing optical signals are
coupled onto a photodetector using a circulator and bidirectional coupler. The laser lines are filtered using an optical band-pass filter (OBPF) bef
ore
detection. In the lower panel, the frequency-to-voltage readout system is shown. A voltage-controlled oscillator (VCO) is phase locked to the detec
ted beat
frequency and the servo output provides a calibrated frequency readout. The readout is analyzed using an oscilloscope (Scope) and an electrical spec
trum
analyzer (ESA). Also shown in the figure: PI, proportional integral servo; PM, phase modulator.
(b)
(c)
(d)
(a)
Fig. 2.
(a) A gyro resonator was packaged into a fiber-connectorized
box for rotation measurement. Left panel shows the box with the lid
removed, and the 18 mm diameter resonator is visible as the gray silicon
chip. (b), (c) CW rotation and CCW rotation of the SBS gyroscope with
second- and third-order Stokes laser signals as indicated. Background col-
oring of the two rotation cases presented in (b) and (c) corresponds to the
shaded regions in (d). (d) Time domain measurement of gyroscope out-
put under sinusoidal rotation. Blue, angular displacement applied to the
gyroscope; red, measured Sagnac frequency shift.
Letter
Vol. 4, No. 3 / March 2017 /
Optica
347
When the gyroscope is at rest, the
frequency noise of the Brillouin
beat note within the VCO locking bandwidth determines the
rotation sensitivity of the gyrosc
ope. This frequency noise can be
measured from the servo output signal using the ESA. According
to the Sagnac effect, the
rotation sensitivity (
ffiffiffiffiffiffiffi
S
δ
Ω
p
)ofthegyroscope
is related to the frequency noise (
ffiffiffiffiffiffi
S
δν
p
) of the beatnote between
the two counterpropagating Brillouin lasers:
ffiffiffiffiffiffiffi
S
δ
Ω
p

n
λ
D
ffiffiffiffiffiffi
S
δν
p
,
where
n
is the refractive index of the cavity medium,
λ
is the laser
wavelength in vacuum, and D is the diameter of the microresonator.
ThebluenoisespectruminFig.
3(a)
shows the measured rotation
sensitivity of the gyroscope at rest. A white frequency noise of
about
0.6 Hz
ffiffiffiffiffiffi
Hz
p
(rightaxis)isobtainedfrom3Hzto1kHz
offset, which corresponds to a rotation sensitivity of about
15 deg
h
ffiffiffiffiffiffi
Hz
p
(left axis) from 3 Hz to 1 kHz bandwidth.
When the gyroscope undergoes a sinusoidal rotation [as shown
in Fig. (
2
)], the output signal also shows a sinusoidal modulation.
Figure
3(a)
shows the electrical spectrum of the gyroscope readout
when the gyroscope undergoes a sine rotation at 7.5 Hz with the
following rms rotation rates: 0.24 deg/s (black curve), 0.13 deg/s
(green curve), and 0.067 deg/s (red curve). A corresponding
change in the modulation tone amplitude at 7.5 Hz in the spec-
trum can be seen. The resolution bandwidth in the measurement
is 1 Hz. In Fig.
3(b)
, the blue circles give a series of rms Sagnac
frequencies (recorded from the ESA) plotted versus the rms
angular rotation rate at the 7.5 Hz modulation rate. The red line
is calculated from the Sagnac formula and agrees with the
measurement (Sagnac formula:
δ
Ω

n
λ
D

δν
, where
δ
Ω
is
the rotation rate and
δν
is the frequency shift of the Brillouin
beat note). Moreover, a minimum rms rotation rate value of
6.3
×
10
3
deg
s
(or 22 deg/h) is detected. Compared with the pre-
vious reported sensitivity of a passive micro-optical gyro
(900 deg/h, and gyro bandwidth of 9 Hz) [
5
], this represents
a 40-fold improvement of minimum rotation rate detection,
and with more than 1 kHz of gyro bandwidth.
In conclusion, an on-chip Brillouin gyroscope has been dem-
onstrated with a sensitivity of
15 deg
h
ffiffiffiffiffiffi
Hz
p
and with detec-
tion bandwidth of more than 1 kHz. A minimum rotation rate of
22 deg/h was measured, which represents a 40-fold improvement
over previous micro-resonant gyroscopes. Improvements directed
to the linewidth of the Brillouin lasers will directly improve the
gyro sensitivity. For example, a 10-fold improvement in linewidth
would place the sensitivity in the range of a few degrees/hour. The
X-band-rate beat frequency produced by the counterpropagating
Brillouin waves presents challenges with respect to gyroscope bias
stability and drift [
13
]. Current efforts are focused on addressing
these environmental-drift-related issues. With future improve-
ments this gyroscope might provide complementary performance
to conventional bulk ring laser gyros and fiber-optic gyroscopes
by offering miniature size, light weight, and low power consump-
tion with improved resistance to shock and vibration.
During the preparation of this paper, a conference proceeding by
Maleki
etal.
on a resonant optical micro-gyroscope was reported [
14
].
Funding.
Defense Advanced Research Projects Agency
(DARPA) (DARPA PRIGM:AIMS program); Kavli Nanoscience
Institute.
Acknowledgment.
The authors would like to thank Seung
Hoon Lee for helpful discussions.
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Frequency (Hz)
10
0
10
1
10
2
10
3
10
0
10
1
10
2
10
3
10
4
no rotation
sine rota. (rms) 0.067 deg/s
sine rota. (rms) 0.13 deg/s
sine rota. (rms) 0.24 deg/s
0.1
1
10
100
sinusoidal rotation rms (degree/s)
S
Ω
(deg/hour/
Hz)
S
ν
(Hz/
Hz)
(b)
(a)
0.1
0.001
1
SBS beat note FM range rms (Hz)
0.1
1
10
100
0.01
Fig. 3.
(a) Measurement of sinusoidal rotations using an electrical spectrum analyzer. The rms rotation rates are given in the legend. Left scale gives the
gyroscope sensitivity as set by the white noise floor. An alternate scale giving the frequency-noise spectral density is provided on the right axis. (
b) Plot of
rms Sagnac frequency shift versus rms angular rotation rate measured as shown in (a).
Letter
Vol. 4, No. 3 / March 2017 /
Optica
348