Optomechanics in an ultrahigh-
Q
two-dimensional photonic crystal cavity
Amir H. Safavi-Naeini, Thiago P. Mayer Alegre, Martin Winger, and Oskar Painter
a
Thomas J. Watson, Sr., Laboratory of Applied Physics, California Institute of Technology, Pasadena,
California 91125, USA
Received 20 June 2010; accepted 8 October 2010; published online 4 November 2010
We demonstrate an ultrahigh-
Q
slotted two-dimensional photonic crystal cavity capable of obtaining
strong interaction between the internal light field and the mechanical motion of the slotted structure.
The measured optical quality factor is
Q
=1.2
10
6
for a cavity with an effective modal volume of
V
eff
=0.04
3
. Optical transduction of the thermal motion of the fundamental in-plane mechanical
resonance of the structure
m
=151 MHz
is performed, from which a zero-point motion
optomechanical coupling rate of
g
/
2
=320 kHz is inferred. Dynamical back-action of the optical
field on the mechanical motion, resulting in cooling and amplication of the mechanical motion, is
also demonstrated. ©
2010 American Institute of Physics
.
doi:
10.1063/1.3507288
The strength of the interaction between light and matter,
which is fundamental to many applications in nonlinear and
quantum optics, depends on the ability to create a large op-
tical energy density, either through increased photon number
or photon localization. This may be achieved by creating
optical cavities with large quality factors
Q
and simulta-
neously small modal volumes
V
eff
. The mode volume
V
eff
in
particular can be decreased through the introduction of slots,
increasing the electric field intensity in low-index regions of
the device. As such, slotted photonic crystal cavities
1
and
waveguides
2
have been previously proposed and applied to
create highly sensitive detectors of motion
3
,
4
and molecules.
5
They have also more recently been studied in the context of
Purcell enhancement of spontaneous emission from embed-
ded quantum dots.
6
In the canonical optomechanical system, consisting of a
Fabry-Perot resonator with an oscillating end-mirror,
7
the ra-
diation pressure force per cavity photon is given by
g
OM
o
/
x
=
o
/
L
OM
, where
o
is the cavity resonance fre-
quency,
x
is the position of the end mirror, and
L
OM
is ap-
proximately equal to the physical length of the cavity. In the
quantum realm, one is interested in the zero-point motion
coupling rate, which is given by
g
=
g
OM
/
2
m
eff
m
, where
m
eff
is the effective motional mass and
m
is the mechanical
resonance frequency. Large optomechanical coupling, ap-
proaching
g
OM
=
o
/
, has recently been realized in several
different guided wave optical cavity geometries utilizing
nanoscale slots.
3
,
4
,
8
In this work we design, fabricate, and
measure the optomechanical properties of a slotted two-
dimensional
2D
photonic crystal cavity formed in a Silicon
membrane. Due to the strong optical confinement provided
by a sub-100 nm slot and a 2D photonic band gap, this cavity
structure is demonstrated to have an optical quality factor
Q
10
6
and a coupling rate of
g
/
2
=320 kHz.
A common approach to forming photonic crystal optical
circuits is to etch a pattern of holes into a thin dielectric film
such as the top Silicon device layer in a Silicon-On-Insulator
SOI
microchip. An effective means of forming resonant
cavities in such quasi-2D slab photonic crystal structures is
to weakly modulate the properties of a line-defect
waveguide.
9
–
11
Applying this same design principle to slotted
photonic crystal waveguides,
12
optical cavities with
Q
5
10
4
have been experimentally demonstrated.
5
,
6
A major
source of optical loss in real fabricated structures is light
scattering out of the plane of the slab. One class of optical
states which play an important role in determining scattering
loss are the resonant leaky modes of the slab. These optical
resonances are localized to the slab and yet have wave vector
components which radiate energy into the surrounding clad-
ding. To reduce the effects of these modes it is preferable to
engineer a structure where the photonic crystal waveguide
has no leaky mode bands crossing the localized cavity mode
frequency. For the popular W1 waveguide
9
,
10
with a slot
added in the waveguide center, we have found that the choice
of the slot width is crucial to avoiding coupling to leaky
resonances. Figure
1
a
shows the band structure of a slotted
W1 waveguide with a hole radius
r
=0.285
a
=134 nm, slot
size
s
=0.2
a
=94 nm, thickness
t
=220 nm, and nominal lat-
a
Electronic mail: opainter@caltech.edu.
0 0.1 0.2 0.3 0.4 0.5
150
170
190
210
230
2
5
0
k
(
2
π
/a
)
ν
ο
(
THz
)
(b)
(c)
(d)
(a)
FIG. 1.
Color online
a
Band diagram for a slotted W1 waveguide formed
in a thin
t
=220 nm
silicon layer. The waveguide slot size is
s
=0.2
a
, with
lattice hole radius
r
=0.285
a
for a nominal lattice constant of
a
=470 nm.
The light gray shade indicates the guided mode continua, while the dark
gray represents the unguided continua of radiation modes. The solid curves
are the resonant waveguide bands of the waveguide
the leaky region of the
waveguide bands are indicated by a thicker line
. The photonic quasiband-
gap
for TE-like modes of even vector parity
is highlighted in blue.
b
Electric field intensity,
E
r
2
of the optical mode. The defect region of the
cavity is indicated by the different colored holes corresponding to different
lattice constants.
c
Zoom-in of the slotted region showing strong optical
field confinement.
d
Total displacement field
Q
r
of the simulated fun-
damental mechanical mode at 146.1 MHz.
APPLIED PHYSICS LETTERS
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2010
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tice constant of
a
=470 nm. A large band gap for both guided
and leaky modes
a “quasibandgap”
is clearly present in this
structure for the TE-like
even vector parity
modes of the
waveguide. On the other hand, for slot widths
s
0.25
a
the
quasibandgap of the waveguide closes due to the presence of
leaky resonant bands.
In order to form a localized cavity resonance, we begin
with the slotted cavity waveguide structure of Fig.
1
a
.A
localized resonance is created from the lower frequency
waveguide band by reducing smoothly the local lattice con-
stant from a nominal value of
a
=470 nm to a value of
a
=450 nm in the center of the cavity. Three-dimensional
finite-element-method
FEM
simulations of the optical and
mechanical properties of the resulting cavity structure were
performed. The simulated electric field intensity of the fun-
damental confined optical mode is shown in Fig.
1
b
. This
mode has a resonance wavelength of
o
1550 nm, a theo-
retical radiation-limited
Q
10
6
and an effective optical
mode volume of
V
eff
=0.04
o
3
.
To allow for mechanical motion of the structure, three
rectangular holes of dimensions 4.9
1.0
m
2
are cut on
each side of cavity device as shown in Fig.
1
d
. FEM simu-
lations show that this allows for a fundamental in-plane
mechanical mode of motion with frequency
m
/
2
=146.1 MHz and an effective motional mass of
m
eff
=20 pg. The optomechanical coupling between the localized
optical and mechanical modes is computed using a
variation
13
of the Hellmann-Feynman perturbation theory
adopted for optomechanical systems,
14
yielding an optom-
echanical coupling of
g
OM
=2
480 GHz
/
nm, or a zero-
point motion rate of
g
=2
800 kHz.
Slotted cavities with the dimensions stated above are
fabricated using a Silicon-On-Insulator wafer from SOITEC
=4–20
cm, device layer thickness
t
=220 nm, buried-
oxide layer thickness 2
m
. The cavity geometry is defined
by electron beam lithography followed by reactive-ion etch-
ing to transfer the pattern through the 220 nm silicon device
layer. The cavities are undercut using HF:H
2
O solution to
remove the buried oxide layer, and cleaned using a
piranha/HF cycle.
15
A scanning electron microscope
SEM
micrograph of a final device is shown in Fig.
2
a
. Figures
2
b
and
2
c
show the local waveguide defect and slotted
region of the cavity, respectively.
The resulting devices are placed in a nitrogen purged
box at standard temperature and pressure and characterized
optically using a swept-wavelength external-cavity laser
=1510–1590 nm,
300 kHz
via a dimpled fiber-taper
probe.
16
A broadband cavity transmission spectrum is shown
in Fig.
3
a
, with the first and second order optical cavity
modes separated by roughly by 10 nm, in agreement with
simulations. For the first-order mode, optical
Q
on the order
of 10
6
is measured consistently in these devices. A narrow-
band optical transmission spectrum
calibrated using a fiber
Mach–Zender interferometer
for one such device is shown
in the inset of Fig.
3
a
, with a measured intrinsic optical
Q
i
=1.2
10
6
.
The mechanical properties of the slotted photonic crystal
cavity are measured by driving the system with the laser
frequency locked to a detuning of a half-linewidth
blue or
red
from the cavity resonance. The transmitted cavity laser
light is sent through an erbium doped fiber amplifier and then
onto a high-speed photodetector. The photodetected signal is
sent to an oscilloscope
2 GHz bandwidth
where the elec-
tronic power spectral density
PSD
is computed. An ex-
2
m
(a)
(b)
(c)
a
slot
500nm
FIG. 2.
Color online
a
SEM image of the fabricated sample.
b
Zoom-in
SEM image of the cavity region, with the heterostructure defect cavity re-
gion highlighted in false color, and
c
SEM image showing the etched
sidewalls of the slot and holes.
-10
0
1
0
0.6
1
1550
1560
1570
1580
0.7
0.8
0.9
1
-90
-88
-86
-84
-82
-80
-78
-76
-74
0
100
200
300
ν
m
(MHz)
ν
m
(MHz)
λ
o
(nm)
Δν
m
(Hz)
(
a
)
(b)
(
c
)
(d)
10
-8
10
5
10
6
10
-7
10
-6
RF PSD (dBm)
P
dropped
(W)
Q
i
= 1.2x10
6
Δλ
o
(pm)
P
dropped
=
149 150 151 152 153
Normalized RF PSD
Normalized Optical Transmission
393.6 nW
196.8 nW
98.4 nW
49.2 nW
29.6 nW
59.2 nW
118.4 nW
x1
x 1.6
x 7.7
x16
x1
x 1.2
x 1.9
mag.
red side
blue side
o
o
i
i
FIG. 3.
Color online
a
Normalized optical transmission spectrum show-
ing the first and second order optical cavity modes.
inset
Transmission
spectrum for the first order mode showing an intrinsic quality factor of
Q
i
=1.2
10
6
.
b
rf-PSD of the photodetected signal, indicating a series of
resonance peaks corresponding to mechanical motion of the patterned slab.
Insets: FEM-simulated mechanical modes matching the frequency of the
strongest few peaks in the spectra
“o”
“i”
labels out-of-plane
in-plane
motion
.
c
rf-PSD around the frequency of the fundamental in-plane me-
chanical resonance for various optical powers dropped into the cavity. The
bottom
top
three spectra represent spectrum taken with red
blue
detuning
of the input laser from the cavity resonance. Denoted for each spectrum is
the optical power dropped into the cavity and a scale factor used to normal-
ize the peak height in each spectrum to a common value.
d
Linewidth of
the fundamental in-plane mechanical mode extracted from the spectra in
c
.
=blue detuning, o=red detuning.
181106-2
Safavi-Naeini
etal.
Appl. Phys. Lett.
97
, 181106
2010
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ample of the measured rf-spectrum from a typical slotted
cavity device is shown in Fig.
3
b
. The fundamental in-
plane mode, corresponding to the largest peak in the
spectrum, is found to occur at a frequency of
m
/
2
=151 MHz, very close to the simulated value of 146 MHz.
rf spectra for various dropped optical powers into the cavity
are shown in Fig.
3
c
. The corresponding mechanical line-
width is plotted in Fig.
3
d
. The effects of the retarded com-
ponent of the dynamical back-action
7
of the light field on the
mechanical resonance are clear in both plots, with red
blue
detuning resulting in a reduction
amplification
in the me-
chanical resonance peak height and a broadening
narrow-
ing
of the mechanical linewidth. One curious aspect of the
measured mechanical spectra, however, are the two smaller
resonance peaks around the main resonance line. The higher
frequency resonance is a result of the splitting of the in-plane
differential slab mode into two independent half-slab modes
due to loading by the fiber taper which is placed in partial
contact on one side of the slab
, while the lower frequency
resonance believed to be due to a nearby flexural
out-of-
plane
resonances of the slab. FEM simulations show the
presence of a flexural mode within a few megahertz of the
fundamental in-plane mode, and SEM images show that the
membranes are subject to weak stress-induced bowing which
can lead to in-plane and out-of-plane mode mixing, resulting
in the enhanced optical transduction of the flexural reso-
nance.
The optomechanical coupling of the fundamental in-
plane mechanical resonance can be estimated using two dif-
ferent methods. The first method involves calibration of the
optical powers and electronic detection system, and uses the
fact that the transduced thermal Brownian motion of the me-
chanical resonator is proportional to
g
2
.
17
The second method
compares the ratio of the rf power in the first and second
harmonic of the mechanical frequency. This method is inde-
pendent of the absolute optical power and detection effi-
ciency, and relies only on accurate knowledge of the optical
linewidth. Both of these methods were found to yield an
experimental optomechanical coupling rate of
g
=2
320 kHz
g
OM
=2
140 GHz
/
nm
for the fundamental
in-plane mechanical resonance, roughly a factor of 2.5 times
smaller than the FEM-estimated value. As alluded to above,
this discrepancy likely results from the splitting of the in-
plane motion into two separate slab-halves and the mixing of
in-plane motion with the weakly coupled flexural modes of
the patterned slab.
In summary, the slotted photonic crystal cavity described
here reduces optical scattering loss through the avoidance of
resonant leaky modes of the structure while simultaneously
allowing for large electric field enhancement in the cavity
slot region. The demonstrated optical loss rate of the cavity
is
/
2
160 MHz, which in conjunction with the high me-
chanical frequency
m
/
2
=151 MHz
of the fundamental
in-plane mechanical resonance, puts this system in the re-
solved sideband limit of cavity optomechanics
/
2
m
1
.
The resolved sideband limit is important for a variety of
applications, including optical cooling of the mechanical mo-
tion to the quantum mechanical ground-state.
18
,
19
The zero-
point motion coupling rate is estimated to be
g
/
2
=320 kHz for the slotted cavity, due largely to the electric
field enhancement in the slot and corresponding to one of the
largest values measured to date.
20
The estimated
Q
/
V
eff
ratio
for the measured devices is 3
10
7
−3
, indicating that
these slotted cavities may also find use in other applications
such as Silicon-based cavity-QED
Ref.
6
and sensing.
5
A.S.N. and T.P.M.A. contributed equally to this work.
This work was supported by the DARPA/MTO ORCHID
program through a grant from AFOSR, and the Kavli Nano-
science Institute at Caltech. A.S.N. gratefully acknowledges
support from NSERC.
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181106-3
Safavi-Naeini
etal.
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, 181106
2010
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