of 7
790
Vol. 10, No. 6 / June 2023 /
Optica
Research Article
Electro-optic transduction in silicon via
gigahertz-frequency nanomechanics
Han Zhao,
1
,
2
Alkim Bozkurt,
1
,
2
AND
Mohammad Mirhosseini
1
,
2
,
*
1
The Gordon and Betty Moore Laboratory of Engineering, California Institute of Technology, Pasadena, California 91125, USA
2
Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
*mohmir@caltech.com
Received 24 October 2022; revised 22 April 2023; accepted 23 May 2023; published 20 June 2023
Interfacing electronics with optical fiber networks is key to the long-distance transfer of classical and quantum infor-
mation. Piezo-optomechanical transducers enable such interfaces by using gigahertz-frequency acoustic vibrations
as mediators for converting microwave photons to optical photons via the combination of optomechanical and piezo-
electric interactions. However, despite successful demonstrations, efficient quantum transduction remains out of reach
due to the challenges associated with hybrid material integration and increased loss from piezoelectric materials when
operating in the quantum regime. Here, we demonstrate an alternative approach in which we actuate 5-GHz phonons
in a conventional silicon-on-insulator platform. In our experiment, microwave photons resonantly drive a phononic
crystal oscillator via the electrostatic force realized in a charge-biased narrow-gap capacitor. The mechanical vibrations
are subsequently transferred via a phonon waveguide to an optomechanical cavity, where they transform into optical
photons in the sideband of a pump laser field. Operating at room temperature and atmospheric pressure, we measure a
microwave-to-optical photon conversion efficiency of 1.72
±
0.14
×
10
7
in a 3.3 MHz bandwidth. Our results mark
a stepping stone towards quantum transduction with integrated devices made from crystalline silicon, which promise
efficient high-bandwidth operation and integration with superconducting qubits. Additionally, the lack of need for
piezoelectricity or other intrinsic nonlinearities makes our approach applicable to a wide range of materials for poten-
tial applications beyond quantum technologies.
© 2023 Optica Publishing Group under the terms of the Optica Open Access
Publishing Agreement
https://doi.org/10.1364/OPTICA.479162
1. INTRODUCTION
Bidirectional conversion of electrical and optical signals is an
integral part of telecommunications, and is anticipated to play a
crucial role in long-distance quantum information transfer [1].
A direct electro-optic frequency conversion can be realized via
the Pockels effect in nonlinear crystals [2–4]. More recently, the
progress in controlling mechanical waves in nanostructures has
led to a new form of effective electro-optic interaction, which is
mediated via resonant mechanical vibrations [5]. In this approach,
the electrical actuation of mechanical waves in piezoelectric
materials is combined with the acousto-optic effect in cavity
optomechanical systems to modulate the phase of an optical field.
Piezo-optomechanical systems based on this concept have been
used for microwave-optics frequency conversion [6–14] as well as
optical modulation, gating, and nonreciprocal routing [15–17].
A variety of materials such as lithium niobate, gallium arsenide,
gallium phosphide, and aluminum nitride have been previously
used in piezo-optomechanical devices [6–14,18,19]. However,
relying on a single material platform for simultaneously achieving
strong piezoelectric and acousto-optic responses is challenging.
Alternatively, heterogeneous integration has been used to com-
bine piezoelectric materials with silicon optomechanical crystals
(OMCs) [20–23]. These devices benefit from the large optome-
chanical coupling rates facilitated by the large refractive index and
photo-elastic coefficient of silicon [24]. However, they require
sophisticated fabrication processes, which hinder mass integra-
tion with the existing technologies. Additionally, heterogeneous
integration often results in poly-crystalline films and degraded
surface properties, which lead to increased microwave, acoustic,
and optical loss when operating in the quantum regime [21].
Considering this landscape, a monolithic silicon platform for
electro-optomechanical transduction is highly desirable. Beyond
providing a large optomechanical coupling, silicon offers an
exceptionally low acoustic loss in cryogenic temperatures [25–
27], which facilitates efficient microwave-optical transduction.
Previous work has pursued capacitive forces, as an alternative to
piezoelectricity, for driving mechanical waves in silicon (which is
not a piezoelectric due to its centro-symmetric crystalline struc-
ture) [28–30]. While efficient electro-optic transduction has
been realized using this approach [31], the low frequency of the
involved mechanical modes (1–10 MHz) has resulted in a small
electro-optic conversion bandwidth. Conversely, large-bandwidth
operation has been achieved by driving gigahertz-frequency acous-
tic waves [29], but achieving a large conversion efficiency has
remained out of reach.
2334-2536/23/060790-07 Journal © 2023 Optica Publishing Group
Research Article
Vol. 10, No. 6 / June 2023 /
Optica
791
Here, we demonstrate electro-optomechanical transduction via
a 5 GHz mechanical mode on a silicon-on-insulator platform. Our
approach relies on a novel capacitive driving scheme for actuating
mechanical vibrations in an extended geometry, where mechanical
motion is shared between an electromechanical resonator and an
optomechanical cavity via a phonon waveguide. By optimizing the
design geometry, we maximize transduction efficiency in structures
with robust performance against frequency disorder. We fabricate
devices based on this concept and test them at room temperature
and atmospheric pressure, where we achieve a microwave-optical
photon conversion efficiency of 1.72
±
0.14
×
10
7
in a 3.3 MHz
bandwidth. Additionally, we employ the transducer devices
as resonant phase modulators and quantify their performance
by measuring a modulation half-wave voltage of 750 mV. Our
platform’s demonstrated efficiency and half-wave voltage are
comparable to previous results in piezo-optomechanical devices.
At the same time, our approach benefits from a significantly sim-
plified fabrication process relying on conventional materials and
techniques. Our work represents an essential first step towards
developing piezoelectric-free silicon transducers for quantum
transduction and may have implications for active RF photonics
components, which are based on electrical actuation of mechanical
waves in optomechanical devices [32–34].
2. PRINCIPLE OF OPERATION AND DEVICE
DESIGN
Figure 1(a) depicts the chain of processes in our experiment, which
consists of three main components: (i) coherent conversion of
radio-frequency signals to mechanical waves, followed by (ii)
routing and delivering of the acoustic wave to an OMC cavity,
and (iii) creation of sideband optical photons by modulating
the light inside the optomechanical cavity. We achieve the first
component through electrostatic actuation, where a constant
DC voltage across a mechanically compliant capacitor generates
an electrostatic force of attraction. Modulating the voltage with
a time-varying signal at the frequency
ω
creates an oscillatory
component in the attraction force,
F
(ω)
=
(
d
C
/
d
x
)
V
dc
V
rf
,
where d
C
/
d
x
is the rate of change of the capacitance with respect
to the capacitor’s gap
x
. This induced time-varying force reso-
nantly drives a mechanical mode that is confined to the capacitor’s
electrodes.
The canonical setting for electro-optomechanical transduc-
tion couples a mechanical oscillator to a pair of microwave and
optical cavities. In the electrostatically driven process under
consideration, electromechanical interaction can be realized by
connecting the DC-biased mechanically compliant capacitor to
a microwave cavity. In this configuration, the electromechanical
interaction rate (
g
em
) determines the electromechanical coopera-
tivity [
C
em
=
4
g
2
em
/(γ
·
κ
mic
)
, where
γ
and
κ
mic
are the intrinsic
mechanical and microwave linewidths], which is a crucial figure of
merit for calculating the transduction efficiency [1]. Alternatively,
the capacitor can be directly attached to a microwave waveguide,
as depicted in Fig. 1(a), without an intermediate microwave cavity.
In this scenario, the electromechanical interaction leads to energy
leakage via electromagnetic radiation into the waveguide. The rate
of energy loss, known as the electromechanical decay rate (
γ
em
),
is related to the cooperativity (
C
em
=
γ
em
). While this direct
connection to the waveguide typically yields lower cooperativies,
it simplifies room-temperature experiments by not requiring a
high-quality-factor microwave cavity (see Supplement 1 for more
details).
While electrostatic actuation is the standard operation scheme
for micro-electromechanical systems (MEMS) [35], its application
to microwave-optical frequency conversion has remained relatively
limited [28,29,36]. This is partly due to the difficulty in simulta-
neously achieving a large electromechanical conversion efficiency
and confining high-
Q
mechanical resonances in the gigahertz-
frequency band. Additionally, routing acoustic waves between
the electromechanical and optomechanical systems is challeng-
ing due to the often dissimilar form factors of the mechanical
vibrations employed in these distinct processes. We have recently
solved some of these challenges in developing gigahertz-frequency
electromechanical crystals
(EMCs) and demonstrated operation in
the strong coupling regime with large mechanical quality factors
(approximately 10 million) in cryogenic environments [37]. EMC
resonators rely on phononic crystal structures, and here we show
that they can be engineered to interface with OMCs for realizing
efficient microwave-optics transduction.
Figure 1(b) outlines the main components of our devices. A
suspended silicon nanobeam with an array of air holes contains
the electromechanical and optomechanical components, which
are accessed via on-chip microwave and optical waveguides. The
nanobeam starts with a phononic crystal “defect” cavity covered
by a thin metallic layer that supports a “breathing” mechanical
mode. Combined with a pair of electrodes that are symmetrically
positioned across narrow air gaps, this section forms the EMC
resonator [37]. The EMC section is adiabatically tapered to a
phonon waveguide, which connects to an OMC cavity (based on
the design in [24]) at the opposite end. The phonon waveguide
Fig. 1.
Electro-optomechanical frequency conversion via electrostatic drive. (a) Schematic of the frequency conversion process. (b) Scanning electron
microscope image of a fabricated device. The insets show the zoomed-in images of the optomechanical (OMC) and electromechanical crystal (EMC) res-
onators, respectively. Partial segments of the metalized “wire” connections and the EMC electrodes are shown in false colors (red and blue, for the two differ-
ent polarities).