of 4
Optimized optomechanical crystal cavity with acoustic radiation shield
Jasper Chan, Amir H. Safavi-Naeini, Jeff Hill, Se ́an Meenehan, and Oskar Painter
Thomas J. Watson, Sr., Laboratory of Applied Physics,
California Institute of Technology, Pasadena, CA 91125
(Dated: June 12, 2012)
We present the design of an optomechanical crystal nanobeam cavity that combines finite-element
simulation with numerical optimization, and considers the optomechanical coupling arising from
both moving dielectric boundaries and the photo-elastic effect. Applying this methodology results
in a nanobeam with an experimentally realized intrinsic optical
Q
-factor of 1
.
2
×
10
6
, a mechanical
frequency of 5
.
1 GHz, a mechanical
Q
-factor of 6
.
8
×
10
5
(at
T
= 10 K), and a zero-point-motion
optomechanical coupling rate of
g
= 1
.
1 MHz.
The use of radiation pressure forces to control and
measure the mechanical motion of engineered micro- and
nanomechanical objects has recently drawn significant
attention in fields as diverse as photonics [1], precision
measurement [2], and quantum information science [3].
A milestone of sorts in cavity circuit- and optomechan-
ics is the recent [4, 5] cooling of a mechanical resonator
to a phonon occupancy
n
<
1 using cavity-assisted ra-
diation pressure backaction [6, 7]. Backaction cooling
involves the use of an electromagnetic cavity with reso-
nance frequency
ω
o
sensitive to the mechanical displace-
ment,
x
, of the mechanical resonator. The canonical sys-
tem is a Fabry-Perot cavity of length
L
with one end
mirror fixed and with the other end mirror of mass
m
eff
mounted on a spring with resonance frequency
ω
m
. The
coupling between the electromagnetic field and mechan-
ics is quantified by the frequency shift imparted by the
zero-point motion of the mechanical resonator, given by
g
=
g
OM
̄
h/
2
m
eff
ω
m
, where
g
OM
=
∂ω
o
/∂x
=
ω
o
/L
.
One of many technologies recently developed to make
use of radiation pressure effects are optomechanical crys-
tals (OMCs) [8, 9]. Optomechanical crystals, in their
most general form, are quasi-periodic nanostructures in
which the propagation and coupling of optical and acous-
tic waves can be engineered. In this work we present the
comprehensive design, fabrication, and characterization
of a quasi-1D OMC cavity formed from the silicon de-
vice layer of a silicon-on-insulator (SOI) microchip. Our
design incorporates both moving-boundary and photo-
elastic (electrostriction) radiation pressure contributions,
and simultaneously optimizes for optical and acoustic pa-
rameters.
The nominal unit cell of a nanobeam OMC, geomet-
rically a silicon block with an oval hole in it, is shown
schematically in Fig. 1a. The corresponding optical and
mechanical bandstructure diagrams are shown in Figs. 1c
and d, respectively. As indicated by the gray shaded re-
gion in the photonic bandstructure, the continuum of un-
guided optical modes above the light line precludes the
existence of a complete photonic band gap (only a quasi-
bandgap exists for the guided modes of the beam). The
physical dimension of the unit cell block (see caption of
Fig. 1a) are chosen to yield a photonic quasi-bandgap sur-
rounding a wavelength
λ
1550 nm. The corresponding
mechanical bandstructure has a series of acoustic bands
in the GHz frequency range (the ratio of the optical fre-
quencies to that of the mechanical frequencies is roughly
the ratio of the speed of light to sound in silicon). By
classifying the acoustic bands by their vector symmetry,
we can again define a quasi-bandgap for the mechanical
system in terms of modes of common symmetry (modes
of different symmetry may couple weakly due to sym-
metry breaking introduced by the fabrication process, an
issue we discuss and mitigate later in the design process).
Using previously developed design intuition [9], we
choose to focus on the optical “dielectric” band at the
X
-point and the mechanical “breathing mode” band at
the Γ-point (these bands emphasized by thicker lines in
Figs. 1c and e). Fig.1d and f shows the optical dielectric
band
X
-point and the breathing mode Γ-point frequency
as the unit cell is transformed smoothly from that in
Fig. 1a to that in Fig. 1b. We see that such a transition—
simultaneously reducing the lattice constant
a
and de-
creasing the hole aspect ratio,
r
h
h
y
/h
x
—causes an
increase in the
X
-point optical frequency and a reduction
in the Γ-point mechanical frequency, pushing both opti-
cal and mechanical modes into the quasi-bandgap of their
respective bands (shown as shaded regions in Figs. 1c and
e).
An optomechanical cavity can be formed by transi-
tioning from the nominal unit cell in Fig. 1a, forming the
“mirror” region, to the defect unit cell of Fig. 1b. This
cavity can be parameterized by the maximum change in
a
(defined as
d
max
{
1
a/a
nominal
}
), the number of
holes in the defect region, the maximum curvature of
a/a
nominal
(plotted in Fig.2a) and the
r
h
of the center
hole. Including the unit cell geometric parameters
a
,
w
,
h
x
, and
h
y
(
t
is fixed to 220 nm), an entire nanobeam de-
sign is specified by these 8 values. Finite-element-method
(FEM) simulations of a complete structure are used to
determine the fundamental cavity mode frequencies (
ω
o
and
ω
m
), motional mass
m
eff
[10], and radiation-limited
optical
Q
-factor,
Q
o
. To quantify the coupling rate, we
consider both the frequency shift due to the moving di-
electric boundary [11] and the photo-elastic effect [12],
so that
g
OM
=
g
OM,MB
+
g
OM,PE
. The moving boundary
arXiv:1206.2099v1 [physics.optics] 11 Jun 2012