Characterization of radiation pressure
and thermal effects in a nanoscale
optomechanical cavity
Ryan M. Camacho, Jasper Chan, Matt Eichenfield, and Oskar Painter
Thomas J. Watson, Sr., Laboratory of Applied Physics, California Institute of Technology,
Pasadena, CA 91125
opainter@caltech.edu
http://copilot.caltech.edu
Abstract:
Optical forces in guided-wave nanostructures have recently
been proposed as an effective means of mechanically actuating and
tuning optical components. In this work, we study the properties of a
photonic crystal optomechanical cavity consisting of a pair of patterned
Si
3
N
4
nanobeams. Internal stresses in the stoichiometric Si
3
N
4
thin-film
are used to produce inter-beam slot-gaps ranging from 560-40 nm. A
general pump-probe measurement scheme is described which determines,
self-consistently, the contributions of thermo-mechanical, thermo-optic,
and radiation pressure effects. For devices with 40 nm slot-gap, the optical
gradient force is measured to be 134 fN per cavity photon for the strongly
coupled symmetric cavity supermode, producing a static cavity tuning
greater than five times that of either the parasitic thermo-mechanical or
thermo-optic effects.
© 2009 Optical Society of America
OCIS codes:
(230.5298) Photonic crystals, (230.4685); Optical microelectromechanical
devices, (230.5750); Resonators, (350.4855); Optical tweezers or optical manipulation,
(270.5580); Quantum electrodynamics.
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Radiation pressure forces have recently been studied in the context of mechanically com-
pliant optical microcavities for the sensing, actuation, and damping of micromechanical mo-
tion [1, 2]. A wide variety of cavity geometries have been explored, from Fabry-Perot cavities
with movable internal elements or end-mirrors [3–8], to monolithic whispering-gallery glass
microtoroids [9]. Nanoscale guided-wave devices have also been studied due to their strong op-
tomechanical coupling resulting from the local intensity gradients in the guided field [10–16].
In addition to radiation pressure forces, there exists in each of these cavity geometries com-
peting thermally driven effects [17], a result of optical absorption. Thermally induced pro-
cesses include strain-optical, thermo-optical, and a variety of thermo-mechanical effects (early
measurements of radiation pressure, for instance, were plagued by thermo-mechanical “gas
action” effects [18]). In many cases (but not all [19, 20]), thermal effects can be neglected at
(C) 2009 OSA
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Received 18 Jun 2009; revised 8 Aug 2009; accepted 19 Aug 2009; published 20 Aug 2009
s
l
e
l
b
w
e
h
x
h
y
o
e
a
n
w
-200
-100
0
0
200
400
600
slot-gap,
s
(nm)
e
simulation
experiment
(a)
(b)
gap before undercut
1
μ
m
10
μ
m
50
-50
-150
-250
Fig. 1. (a) Slot width vs. extension offset, simulation and experiment. Support extensions
placed near the outside of the beam width cause outward bowing, but inward bowing when
placed near the inside. (b) Scanning electron microscope images of a device with support
extensions placed just inside of center, causing slight inward bowing resulting in approxi-
mately a slot-gap of
s
=
40 nm at the cavity center. The device parameters that are common
amongst all the devices tested in this work are: nominal lattice constant
a
n
=
590 nm, ex-
tension width
w
e
=
211 nm, hole width
h
x
=
190 nm, hole height
h
y
=
416 nm, beam width
w
=
833 nm, beam length
l
b
=
18
.
4
μ
m, extension length
l
e
=
33
.
1
μ
m. In order to vary the
slot-gap size from 40-560 nm, the extension offset was varied between
o
e
=
70 to
−
235 nm.
the high frequencies associated with micromechanical resonances [9]; however, for static cav-
ity tuning thermal effects may play a significant, if not dominant, role. Calibration of thermal
effects is important not only in identifying the contribution of pure radiation pressure effects,
but also in understanding the parasitic local heating processes, which in the realm of quantum
optomechanics may limit optical cooling methods [21, 22], or for tunable photonics applica-
tions [13,23,24] where deleterious inter-device thermal coupling may arise.
In this work we describe the characterization of the low frequency (static) optical and thermal
effects in a nanoscale photonic crystal cavity. This so-called zipper cavity [14,25,26] consists
of a matched pair of Si
3
N
4
nanobeams, placed in the near-field of each other, and patterned
with a one-dimensional (1D) array of air holes. The resonant optical modes of the zipper cav-
ity [25] consist of manifolds of even (bonded) and odd (anti-bonded) symmetry supermodes
of the dual nanobeams, localized along the long-axis of the beams to a central
defect
in the
photonic lattice. The strength of the gradient optical force applied to the beams is exponentially
dependent upon the inter-beam slot gap (
s
) and is described by a dispersive coupling coeffi-
cient,
g
OM
≡
(
∂ω
c
/
∂α
)
, where
ω
c
is the gap-dependent optical cavity resonance frequency and
α
parametrizes the change in the inter-beam slot gap. Utilizing the connection between cavity
mode dispersion and applied optical force, a pump-probe scheme is described below to accu-
rately quantify the optomechanical, thermo-optic, and thermo-mechanical contributions to the
static tuning of the bonded and anti-bonded modes versus internal cavity photon number.
The zipper cavity devices studied here were fabricated from optically thin (
t
=
400 nm)
stoichiometric silicon nitride (Si
3
N
4
), deposited using low-pressure chemical vapor deposition
on a silicon wafer. The deposition process results in residual in-plane stress in the nitride film
of approximately
σ
∼
1 GPa [27]. Electron-beam lithography is used to pattern zipper cavities
with beams of length
l
b
=
33
.
1
μ
m, width of
w
=
833 nm, and an inter-beam spacing of
s
=
120
nm. The beams are clamped at each end using extensions with length equal to
l
e
=
18
.
4
μ
m
and width of
w
e
=
211 nm. The nanobeam and photonic crystal hole pattern are transferred into
the Si
3
N
4
film using a C
4
F
8
/
SF
6
plasma etch. The underlying Si substrate is selectively etched
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Received 18 Jun 2009; revised 8 Aug 2009; accepted 19 Aug 2009; published 20 Aug 2009
VOA
Polarization
Controller
Pump
Dete
c
tor
MUX
Probe
Detector
Pump Laser
VOA
Polarization
Controller
Probe Laser
VOA
DEMUX
Fig. 2. Experimental setup for optical testing. Two separate lasers (pump and probe) with
independent power control, via variable optical attenuators (VOA), and polarization control
are combined into a fiber taper waveguide placed in the near-field of the photonic crystal
cavity. Cavity transmission at both the pump and probe wavelengths are multiplexed and
demultiplexed using a matched set of fiber-based filters and separately monitored using
calibrated photodetectors.
using KOH, releasing the patterned beams. The devices are dried using a critical point CO
2
drying process to avoid surface-tension-induced adhesion of the nanobeams.
The internal stress of the Si
3
N
4
thin-film is used to create a range of slot-gaps. This is
achieved through misalignment of the support extensions and central nanobeams (Fig. 1(b)),
breaking the symmetry of the internal stress along the length of the beams. As shown by the
finite-element-method (FEM) simulations and device measurements plotted in Fig. 1(a), exten-
sions placed near the outside edge of the beams cause outward bowing of the beams, while
extensions placed near the inside edge cause inward bowing. By varying the lateral offset of
the extension (defined as the difference between the center of the main beam and the center
of the extension beam) from
o
e
=
70 to
−
235 nm, zipper cavities with slot-gaps at the cavity
center ranging from 40-560 nm are created. Slot-gaps smaller than 40 nm could not be stably
produced without the nanobeams sticking together at points of nanometer-scale roughness in
the inner sidewall of the beams.
Optical spectroscopy of the zipper cavity modes is performed using the experimental setup
shown in Fig. 2. In this setup, laser light from a bank of tunable external-cavity diode lasers
covering the 1400-1625 nm wavelength band is coupled into an optical fiber taper nanoprobe.
Using precision motorized stages, the tapered fiber can be controllably placed into the near-field
of a zipper cavity [28], allowing for evanescent excitation and detection of resonant modes.
Polarization of the laser field is adjusted using a fiber polarization controller, and optimized
for coupling to the high-
Q
TE-like modes of the zipper cavity [25] (i.e., dominant electric field
polarization in the plane of the device).
Figure 3(a) shows a series of wavelength scans from an array of nominally identical zipper
cavities, each with slightly differing slot-gap due to variation in the lateral extension alignment.
Scanning electron microscope images of the central region of each zipper cavity, from which
the slot-gap is measured, are shown to the right of each wavelength scan. Even (bonded) and
odd (anti-bonded) parity supermodes are identified by stepping the taper across the width of the
zipper cavity and noting the lateral spatial symmetry of the mode coupling [14]. Three distinct
pairs of modes are identified in the wavelength scans, with the fundamental longtitudinal cavity
(C) 2009 OSA
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Received 18 Jun 2009; revised 8 Aug 2009; accepted 19 Aug 2009; published 20 Aug 2009
modes (TE
±
,
0
) occurring at shorter wavelengths and the higher-order modes shifted to longer
wavelengths (this is a result of the negative curvature of the photonic band-edge from which
the modes originate [25]). Radio frequency (RF) spectra of the optical transmission intensity
(see Fig. 3(b)) were performed to verify the presence of micromechanical oscillation and free
movement of the nanobeams even for the smallest of slot-gaps.
Overlayed on the wavelength scan plots of 3(a) are theoretical dispersion curves generated
using FEM simulations of the optical properties of the zipper cavity (a single in-plane scaling
factor of 5% was used to match the TE
+
,
0
resonant wavelength for the largest (560 nm) slot-gap,
which is within the accuracy of our SEM calibration). Figure 3(c) shows a plot of the measured
and simulated splitting of the fundamental bonded and anti-bonded modes versus the SEM-
measured slot gap. Good correspondence is found for all but the smallest (40 nm) slot gap,
in which the theoretical curve shows significantly more dispersion for the bonded modes. The
source of this discrepancy is not fully understood, but may be due to other effects such as the
dispersive nature of the refractive index of the Si
3
N
4
material itself (the frequency separation
of the even and odd supermodes is more than 10 THz for the smallest slot-gap). As discussed
below, the local sensitivity of each mode to beam displacement is consistent with the measured
40 nm slot gap.
In order to understand the various actuation methods of the zipper cavity, it is useful to con-
sider the dispersive nature of the two supermode mode types, and their relation to the magni-
tude and direction of the optical force. In an adiabatic limit [10,29], the radiation pressure force
can be related to the gradient of the internal optical cavity energy,
F
OM
=
−
∂
(
N
̄
h
ω
c
)
/
∂α
=
−
N
̄
hg
OM
, where
N
is the stored photon number and
α
is a displacement factor related to the
movement of the nanobeams (here we choose
α
to be equal to one half the slot-gap size to be
consistent with previous work in Refs. [14,25]). As can be seen in the measured and simulated
dispersion curves of Figure 3(c), the symmetric bonded modes with large field strength in be-
tween the beams, tunes to the red with shrinking slot-gap (i.e.,
g
OM
for the bonded mode is
positive for
α
=
s
/
2). The direction of the optical force for photons stored in a bonded mode
thus tends inwards, pulling the beams together (this is a result of the fact that in order to per-
form mechanical work on the beams, the stored photons must lose energy through a reduction
in their frequency). In the case of the odd parity anti-bonded cavity modes, the resonance fre-
quency decreases with increasing slot-gap, resulting in a negative
g
OM
and an optical force that
pushes the beams apart.
Owing to the different dispersive character of the bonded and anti-bonded cavity modes,
and the different directions in which cavity photons of each mode type apply forces to the two
beams, pure radiation pressure effects actuate and tune the cavity modes in a unique and dis-
tinctive manner. This should be contrasted with thermo-optic and thermo-mechanical effects.
The thermo-optic tuning of the cavity modes is related to the change in refractive index of the
cavity material with temperature. For the Si
3
N
4
zipper cavity studied here, the thermo-optic
coefficient is known to be positive (and of magnitude
∂
n
/
∂
T
≈
1
.
9
×
10
−
5
K
−
1
[14]). The man-
ifold of bonded and anti-bonded cavity modes thus tend to uniformly red shift with increasing
temperature due to the thermo-optic effect (differences between modes in resonance frequency
and modal overlap with the Si
3
N
4
beams are insignificant). Increased temperature in the local
cavity region of the beams, due to optical absorption, not only increases the refractive index of
the clamped beams, but may also produce non-uniform thermal expansion and significant strain
in the structure. Unlike the radiation pressure force, the resulting thermo-mechanical force is
only dependent upon the temperature rise, and thus actuates the zipper cavity beams in the same
manner independent of which cavity mode is being driven. Owing to the different dispersive
nature of the cavity modes, however, the sign of the thermo-mechanical tuning will depend
upon the type of supermode being considered.
(C) 2009 OSA
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Received 18 Jun 2009; revised 8 Aug 2009; accepted 19 Aug 2009; published 20 Aug 2009
1480
1500
1520
1540
1560
1580
1600
1620
0
100
200
300
400
500
600
wavelength (nm)
slot-gap,
s
(nm)
(a)
mode splitting (nm)
100
200
300
400
500
0
20
40
60
80
100
120
35
150
5
slot-gap (nm)
−20
λ
/(d
λ
/d
α
) (
μ
m)
0
−15
−10
−5
slot-gap,
s
(nm)
(c)
0
20
40
60
-80
-60
-40
frequency (MHz)
Power Spectral Density (dB)
t
TE
-, 0
TE
+, 0
TE
-, 1
TE
+, 1
TE
-, 2
TE
+, 2
-10
-5
0
0.8
0.9
1
Detuning (GHz)
Transmission
m
ν
= 2.5 MHz
*
(b)
1
μ
m
Fig. 3. (a) Experimentally measured optical transmission as a function of wavelength in an
array of six devices (SEM images of the central cavity region on right), each with a different
slot-gap. Overlayed are FEM simulations of the cavity mode dispersion versus gap size,
where solid curves are for the bonded modes, dashed curves for the anti-bonded modes,
and the color of the curve matches the highlighting applied to the different mode orders
(red=TE
±
,
0
, green=TE
±
,
1
, blue=TE
±
,
2
). (b) Measured RF spectrum of the TE
+
,
0
mode
for the largest gap (
s
=
560 nm) zipper cavity. Inset shows the optical transmission as a
function of detuning as the pump laser is swept across the cavity resonance (dashed vertical
line indicates detuning for RF spectrum measurement). (c) Plot of the FEM-simulated and
experimentally measured bonded and anti-bonded mode splitting versus slot-gap. The inset
shows the effective optomechanical coupling length (
L
OM
≡
λ
/
(
d
λ
/
d
α
) in the small slot-
gap region (solid curve for bonded mode, dashed curve for anti-bonded mode).
We perform measurements of the different cavity mode tuning mechanisms using a two laser
pump and probe scheme. In this scheme, a strong pump beam is coupled into either the funda-
mental bonded (TE
+
,
0
) or anti-bonded (TE
−
,
0
) cavity mode. In order to measure the self-mode
tuning of a given mode the pump laser frequency is swept across the cavity mode resonance
producing a bistability curve such as that shown in Fig. 3(b). A fit to the bistability curve yields
the self-mode resonance tuning versus dropped power into the cavity for a fixed input power.
The dropped cavity power is then converted into an internal photon number via the intrinsic
Q
-
factor of the cavity mode [30] (measured to be
Q
i
≈
6
×
10
4
for both the fundamental bonded
and anti-bonded modes using a calibrated fiber Mach-Zender interferometer). In order to ob-
(C) 2009 OSA
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#113057 - $15.00 USD
Received 18 Jun 2009; revised 8 Aug 2009; accepted 19 Aug 2009; published 20 Aug 2009