of 12
Quasi-two-dimensional optomechanical
crystals with a complete phononic
bandgap
Thiago P. Mayer Alegre,
1
,
2
Amir Safavi-Naeini,
1
,
2
Martin Winger,
1
Oskar Painter
1
,
1
Thomas J. Watson, Sr., Laboratory of Applied Physics, California Institute of Technology,
Pasadena, CA 91125, USA
2
These authors contributed equally to this work.
opainter@caltech.edu
http://copilot.caltech.edu
Abstract:
A fully planar two-dimensional optomechanical crystal
formed in a silicon microchip is used to create a structure devoid of
phonons in the GHz frequency range. A nanoscale photonic crystal
cavity is placed inside the phononic bandgap crystal in order to probe
the properties of the localized acoustic modes. By studying the trends in
mechanical damping, mode density, and optomechanical coupling strength
of the acoustic resonances over an array of structures with varying geo-
metric properties, clear evidence of a complete phononic bandgap is shown.
© 2011 Optical Society of America
OCIS codes:
(220.4880) Optomechanics; (230.5298) Photonic crystals; (230.1040) Acousto-
optical devices.
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1. Introduction
Photonic crystals are periodic dielectric structures in which optical waves encounter strong
dispersion, and in some cases are completely forbidden from propagating within a frequency
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bandgap. Similarly, periodic elastic structures, known as phononic crystals, can be used to con-
trol acoustic waves [1–7] for applications as diverse as the filtering and focusing of sound [8] to
the earthquake proofing of buildings [9]. Recently, microchip structures capable of manipulat-
ing both photons and phonons, dubbed optomechanical crystals (OMCs), have been created to
enhance the interaction of light and mechanics [10–15]. Here we use a planar two-dimensional
(2D) OMC to create a structure devoid of phonons in the GHz frequency range, and use light
to probe its mechanical properties. In addition to being an excellent platform for the study
of radiation pressure and nanomechanics, the 2D-OMC of this work represents an important
step towards more complex devices capable of performing novel classical and quantum optical
signal processing [16, 17].
Interest in cavity-optomechanical systems, in which light is used to sensitively measure and
manipulate the motion of a mechanically compliant optical cavity, has grown rapidly in the last
few years due to the demonstration of micro- and nano-scale systems in which the radiation
pressure force of light is manifest. The physics of these systems is formally equivalent to the
inelastic scattering of light by bulk elastic vibrations (Brillouin scattering), and has been stud-
ied in a variety of settings [18–20]. In cavity optomechanics, the presence of both mechanical
and optical resonances brings about qualitatively new effects, and has been the subject of re-
cent intense study. In its most basic form, the mechanical resonance has been that of movable
end-mirror affixed to a spring (or hung as a pendulum), forming part of a Fabry-Perot cav-
ity. More complex cavity-optomechanical geometries, such as whispering-gallery mode struc-
tures [21, 22], nanomembranes placed within Fabry-Perot cavities, and near-field optical and
microwave devices utilizing the gradient force [23], have also been demonstrated to produce
strong radiation pressure effects. Two structures with particular engineerability of optical and
mechanical properties are the photonic crystal fiber (PCF) [24] and the recently demonstrated
chip-scale optomechanical crystal (OMC) [10]. In the case of the OMC cavity, a patterning of
a silicon (Si) nanobeam is used to create a 200 THz optical cavity simultaneous with a GHz
acoustic cavity.
In the last decade, Si photonics has rapidly developed, in no small part due to the advent
of silicon-on-insulator wafer technology in which a thin Si device layer sits atop a low-index
insulating oxide layer. Planar Si photonic crystal circuits may be formed in the top Si device
layer, which along with the integrability with micro-electronics, has provided an attractive set-
ting for controlling photons. Similarly, in the case of phononics, significant progress has been
made in integrated Si MEMS and NEMS devices for creating RF/microwave filters, oscillators,
and sensors [25–27]. Thin-film OMCs bring together photonic and phononic circuitry, enabling
a new chip-scale platform for delaying, storing, and processing optical and acoustic excita-
tions [16, 17]. Building on our previous work in quasi-1D OMC systems [10], we demonstrate
here a quasi-2D OMC architecture capable of routing photons and phonons around the full
2D plane of a Si chip, and enabling complete localization of phonons via a three-dimensional
acoustic-wave bandgap.
2. Sample structure
The phononic crystal used in this work is the recently proposed [14] “cross” structure shown in
Fig. 1(a). Geometrically, the structure consists of an array of squares connected to each other
by thin bridges, or equivalently, a square lattice of cross-shaped holes. The phononic bandgap
in this structure arises from the frequency separation between higher frequency tight-binding
bands, which have similar frequencies to the resonances of the individual squares, and lower
frequency effective-medium bands with frequencies strongly dependent on the width of the con-
necting bridges,
b
=
a
h
[14]. A typical band diagram for a nominal structure (
a
=
1
.
265
μ
m,
h
=
1
.
220
μ
m,
w
=
340 nm) is shown in Fig. 1(c). Blue (red) lines represent bands with even
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5660
50
100
150
(c)
(b)
(a)
(d)
Γ
XM
Γ
0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
k
ν
m
(GHz)
b(nm)
X
Γ
M
k
y
k
x
(
c
)
(
a
)
Hz
)
h
a
y
x
x
x
x
x
y
d
w
Fig. 1. (a) Real space crystal lattice of the cross crystal with lattice constant
a
, cross length
h
, cross width
w
, and membrane thickness
d
. The bridge width is defined as
b
=
a
h
. (b)
Reciprocal lattice of the first Brillouin zone for the cross crystal. (c) Phononic band diagram
for the nominal cross structure with
a
=
1
.
265
μ
m,
h
=
1
.
220
μ
m,
w
=
340 nm. Dark blue
lines represent the bands with even vector symmetry for reflections about the
x
y
plane,
while the red lines are the flexural modes which have odd vector mirror symmetry about
the
x
y
plane. (d) Tuning of the bandgap with bridge width,
b
. Light grey, dark grey,
and white areas indicate regions of a symmetry-dependent (i.e., for modes of only one
symmetry) bandgap, no bandgap, and full bandgap for all acoustic modes, respectively.
(odd) vector symmetry for reflections about the
x
y
plane. The lowest frequency bandgap for
the even modes of the simulated cross structure extends from 0
.
91 GHz to 3
.
6 GHz. Within
this bandgap, there are regions of full phononic bandgap (shaded blue) where no mechanical
modes of any symmetry exist, and regions of partial symmetry-dependent bandgap (shaded red)
where out-of-plane flexural modes with odd symmetry about the
x
y
plane are allowed. As the
bridge width is increased, the lower frequency effective-medium bands become stiffer, causing
an increase in their frequency, while the higher frequency tight-binding band frequencies re-
main essentially constant. A gap-map show in in Fig. 1(d), showing how the bandgaps in the
structure change as a function of phononic crystal bridge width, illustrates this general feature.
As shown in Figs. 2(a)-(c), the cross crystal is used as a phononic cage (cavity) for an em-
bedded optical nanocavity [28] (highlighted in a green false color) consisting of a quasi-2D
photonic crystal waveguide with a centralized “defect” region for localizing photons. This em-
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(
a)
(d)
-20
-10
0
10
20
0.97
0.98
0.99
1.00

(pm)
Transmission (arb. units)

1.0pm
Q
i
=1.5x10
6
(e
)
(c)
1
m
2
m
-2
-2
-20
-2
y
x
b
a
w
h
400nm
(b)
Fig. 2. (a) Scanning electron micrograph (SEM) of one of the fabricated 2D-OMC struc-
tures. The photonic nanocavity region is shown in false green color. In (b), Zoom-in SEM
image of the cross crystal phononic bandgap structure. (c) Zoom-in SEM image of the op-
tical nanocavity within embedded in the phononic bandgap crystal. Darker (lighter) false
colors represents larger (smaller) lattice constant in the optical cavity defect region. (d)
FEM simulation of
E
y
electrical field for the optical cavity. (e) Typical measured transmis-
sion spectra for the optical nanocavity, showing a bare optical
Q
-factor of
Q
i
=
1
.
5
×
10
6
.
bedding of an optical cavity within an acoustic cavity enables, through the strong radiation-
pressure-coupling of optical and acoustic waves, the probing of the properties of the bandgap-
localized phonons via a light field sent through the optical nanocavity. The theoretical electric
field mode profile and the measured high-
Q
nature of the optical resonance of the photonic
crystal cavity are shown in Figs. 2(d) and (e), respectively. Such a phonon-photon heterostruc-
ture design allows for completely independent tuning of the mechanical and optical properties
of our system, and in what follows, we use this feature to probe arrays of structures with dif-
ferent geometric parameters. In particular, by varying the bridge width
b
of the outer phononic
bandgap crystal, the lower bandgap edge can be swept in frequency and the resulting change in
the
lifetime
,
density of states
, and
localization
of the trapped acoustic waves interacting with the
central optical cavity can be monitored. Two different phonon cavity designs,
S
1
and
S
2
, were
fabricated in this study. First, in Sec. 5.1, we focus on the lower acoustic frequency
S
1
struc-
ture, for which an array of devices with bridge width varying from
b
=
53 nm to 173 nm (in
6 nm increments) was created. Similar results are also shown for the high acoustic frequency
S
2
structure in Sec. 5.2.
3. Fabrication
The phononic-photonic cavities were fabricated using a Silicon-On-Insulator wafer from
SOITEC (
ρ
=
4-20
Ω
·
cm, device layer thickness
t
=
220 nm, buried-oxide layer thickness
2
μ
m). The cavity geometry is defined by electron beam lithography followed by inductively-
coupled-plasma reactive ion etching (ICP-RIE) to transfer the pattern through the 220 nm sili-
con device layer. The cavities were then undercut using HF:H
2
O solution to remove the buried
oxide layer, and cleaned using a piranha/HF cycle [29].
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4. Experimental setup
The experimental setup used to measure the phononic-photonic crystal cavity properties is
shown in Fig. 3(a). A fiber-coupled tunable near-infrared laser, (New Focus Velocity, model
TLB-6328) spanning approximately 60 nm, centered around 1540 nm, has its intensity and po-
larization controlled respectively by a variable optical attenuator (VOA) and a fiber polarization
controller (FPC). The laser light is coupled to a tapered, dimpled optical fiber (Taper) which
has its position controlled with nanometer-scale precision. The transmission from the fiber is
passed through another VOA before being detected.
To measure the optical properties, a photodetector (PD, New Focus Nanosecond Photodetec-
tor, model 1623) is used. The detected optical transmission signal is recorded while sweeping
the laser frequency. By controlling the distance between the fiber taper and the sample, the ex-
ternal coupling rate (
κ
e
) is changed. Figure 3(c) shows the change in the coupling rate for two
different positions of the fiber taper. In the limit where the external coupling rate is zero we
can measure the intrinsic coupling rate (
κ
i
). The total optical loss is then
κ
=
κ
e
+
κ
i
. A typical
fiber taper transmission spectrum is shown in Fig. 2(e), with a measured intrinsic optical quality
factor of
Q
i
=
1
.
5
×
10
6
. Usually, after touching, the external coupling rate was on the order of
tens of MHz (
κ
e
/
2
π
70 MHz) which corresponds to a transmission dip of
70%.
EDFA
FPC
Taper
Phononic-Photonic Crystal
5μm
(a)
(b)
(c)
Sample
Hovering
Sample
Touching
-40
-30
-20
-10
0
20
4030
10
60
70
80
90
100
Delta (pm)
Norm. Transmission (%)
PD
BS
PR
D
D
A
PR
Laser
Scope
BS
BS
VOA
VOA
Lock
Box
FPC
Fig. 3. (a) Experimental setup for measuring the PSD. (b) Optical micrograph of the ta-
pered fiber coupled to the device while performing experiments. (c) Optical spectra for two
different positions of the taper relative to the device are shown.
To measure the mechanical properties, the transmitted signal is sent through an erbium doped
fiber amplifier (EDFA) and sent to a high-speed photoreceiver (PR, New Focus model, 1554-B)
with a maximum transimpedance gain of 1
,
000 V/A and a bandwidth (3 dB rolloff point) of
12 GHz. The RF voltage from the photoreceiver is connected to the 50
Ω
input impedance of
the oscilloscope. The oscilloscope can perform a Fast Fourier Transform (FFT) to yield the RF
power spectral density (RF PSD). The RF PSD is calibrated using a frequency generator that
outputs a variable frequency sinusoid with known power.
Our devices are in the sideband resolved limit, i.e. the total optical loss rate is smaller than the
mechanical frequency,
κ
<
Ω
M
. Therefore the largest transduced signal is achieved when the
laser frequency is detuned from the optical cavity resonance by the mechanical frequency [10].
The probe laser is locked to approximately 1 GHz (2
.
5 GHz) on the blue side of the cavity
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