Electro-optic transduction in silicon via GHz-frequency nanomechanics Han Zhao1 2Alkim Bozkurt1 2and Mohammad Mirhosseini1 2 1The Gordon and Betty Moore Laboratory of Engineering

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Electro-optic transduction in silicon via GHz-frequency nanomechanics

Han Zhao,1, 2 Alkim Bozkurt,1, 2 and Mohammad Mirhosseini1, 2, ∗

1The Gordon and Betty Moore Laboratory of Engineering,

California Institute of Technology, Pasadena, California 91125

2Institute for Quantum Information and Matter,

California Institute of Technology, Pasadena, California 91125

(Dated: October 26, 2022)

Interfacing electronics with optical ﬁber networks is key to the long-distance transfer of classical

and quantum information. Piezo-optomechanical transducers enable such interfaces by using GHz-

frequency acoustic vibrations as mediators for converting microwave photons to optical photons

via the combination of optomechanical and piezoelectric interactions. However, despite successful

demonstrations, eﬃcient piezo-optomechanical transduction remains out of reach due to the chal-

lenges 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, mi-

crowave 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 1.8×10−7in a 3.3 MHz bandwidth,

and demonstrate eﬃcient phase modulation with a half-wave voltage of Vπ= 750 mV. 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 adaptable to a wide range of materials for potential applications beyond quantum

technologies.

INTRODUCTION

Bi-directional conversion of electrical and optical sig-

nals is an integral part of telecommunications and is an-

ticipated to play a crucial role in long-distance quantum

information transfer [1]. Direct electro-optic frequency

conversion can be realized via the Pockels eﬀect in non-

linear crystals [2–4]. More recently, the progress in con-

trolling mechanical waves in nano-structures 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 sys-

tems based on this concept have been used for microwave-

optics frequency conversion [6–13] as well as optical mod-

ulation, gating, and non-reciprocal routing [14–16].

A variety of materials such as lithium niobate, gallium

arsenide, gallium phosphide, and aluminum nitride have

been previously used in piezo-optomechanical devices [6–

13]. However, relying on a single material platform for si-

multaneously achieving strong piezoelectric and acousto-

optic responses is challenging. Alternatively, heteroge-

neous integration has been used to combine piezoelectric

materials with silicon optomechanical crystals [17–20].

These devices beneﬁt from the large optomechanical cou-

∗mohmir@caltech.edu; http://qubit.caltech.edu

pling rates facilitated by the large refractive index and

photo-elastic coeﬃcient of silicon [21]. However, they re-

quire sophisticated fabrication processes, which hinder

mass integration with the existing technologies. Addi-

tionally, 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 [18].

Considering this landscape, a monolithic silicon plat-

form for electro-optomechanical transduction is highly

desirable. Beyond providing a large optomechanical cou-

pling, silicon oﬀers an exceptionally low acoustic loss

in cryogenic temperatures [22], which facilitates eﬃcient

microwave-optical transduction. Previous work has pur-

sued capacitive forces, as an alternative to piezoelec-

tricity, for driving mechanical waves in silicon (which

is not a piezoelectric due to its centro-symmetric crys-

talline structure) [23–25]. While eﬃcient electro-optic

transduction has been realized using this approach [26],

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 GHz-frequency acoustic waves

[24], but achieving a large conversion eﬃciency has re-

mained out of reach.

Here, we demonstrate electro-optomechanical trans-

duction via a 5 GHz mechanical mode on a silicon-on-

insulator platform. Our approach relies on a novel ca-

pacitive driving scheme for actuating mechanical vibra-

tions in an extended geometry, where mechanical motion

is shared between an electromechanical resonator and an

arXiv:2210.13549v1 [physics.optics] 24 Oct 2022

FIG. 1. Electro-optomechanical frequency conversion via electrostatic drive. (a) Schematic of the frequency conver-

sion process. (b) The scanning electron microscope image of a fabricated device. The insets show the zoomed-in images of the

optomechanical (OMC) and electromechanical crystal (EMC) resonators, respectively. Partial segments of the metalized ‘wire’

connections and the EMC electrodes are shown in false colors (red and blue, for the two diﬀerent polarities).

optomechanical cavity via a phonon waveguide. By op-

timizing 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 atmo-

spheric pressure, where we achieve a microwave-optical

photon conversion eﬃciency of 1.8×10−7in a 3.3 MHz

bandwidth. Additionally, we employ the transducer de-

vices as resonant phase modulators and quantify their

performance by measuring a modulation half-wave volt-

age of 750 mV. Our platform’s demonstrated eﬃciency

and half-wave voltage are comparable to previous results

in piezo-optomechanical devices. Additionally, we antic-

ipate achieving a signiﬁcantly higher eﬃciency for oper-

ation at cryogenic environments due to the exception-

ally low phonon loss in crystalline silicon. At the same

time, our approach beneﬁts from a signiﬁcantly simpli-

ﬁed fabrication process relying on conventional materials

and techniques. Our work represents an essential ﬁrst

step towards developing piezoelectric-free silicon trans-

ducers for quantum transduction and may have impli-

cations for active RF photonics components, which are

based on electrical actuation of mechanical waves in op-

tomechanical devices [27–29].

PRINCIPLE OF OPERATION AND DEVICE

DESIGN

Figure 1a shows the conceptual schematic for the chain

of processes in our experiment, which includes 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 optomechanical

crystal cavity, and (iii) creation of sideband optical pho-

tons by modulating the light inside the optomechanical

cavity. We realize the ﬁrst component by taking ad-

vantage of electrostatic actuation. In this approach, a

constant (i.e. ‘DC’) voltage across a parallel-plate ca-

pacitor generates an electrostatic force of attraction. By

perturbing the voltage with a time-varying signal at the

frequency ω(delivered via a microwave waveguide see

ﬁg. 1a), we create an oscillatory component in the at-

traction force F(ω) = (dC/dx)VdcVrf . Here, dC/dxis

the rate of change of the capacitance with respect to

a change in the capacitor’s gap x. This induced time-

varying force resonantly drives a mechanical mode that

is conﬁned to the capacitor’s electrodes. The mechanical

oscillations, in turn, dynamically change the capacitance,

creating an electromagnetic ﬁeld that radiates back into

the microwave waveguide. This electromagnetic radia-

tion results in loss of mechanical energy, which can be

modeled via an electromechanical decay rate (γem) (see

appendix A).

While electrostatic actuation is the standard operation

scheme for micro-electromechanical systems (MEMS)

[30], its application to microwave-optical frequency con-

version has remained relatively limited [23, 24, 31]. This

is partly due to the diﬃculty in simultaneously achiev-

ing a large electromechanical conversion eﬃciency and

conﬁning high-Qmechanical resonances in the GHz fre-

quency band. Additionally, routing acoustic waves be-

tween the electromechanical and optomechanical systems

is challenging due to the often dissimilar form factors

of the mechanical vibrations employed in these distinct

processes. We have recently solved some of these chal-

lenges in developing GHz-frequency electromechanical

crystals and demonstrated operation in the strong cou-

pling regime with large mechanical quality factors (ap-

proximately 10 million) in cryogenic environments [32].

Electromechanical crystal resonators rely on phononic

crystal structures, and here we show that they can be

engineered to interface with optomechanical crystals to

realize eﬃcient microwave-optics transduction.

Figure 1b outlines the main components of our de-

vices. A suspended silicon nanobeam with an array of air

holes contains the electromechanical and optomechanical

components, which are accessed via on-chip microwave

FIG. 2. Device design and modeling. (a) Geometric parameters of the nanobeam’s elliptical hole array. The beam width

w= 530 nm and thickness t= 220 nm are maintained throughout the structure. (b) Mechanical band structures of the phonon

waveguide, and (c) the photon/phonon reﬂector used to terminate the OMC section. Dashed line marks the nominal frequency

of the EMC and OMC resonators. (d) Simulated displacement ﬁeld amplitudes for the two of the hybridized modes with the

largest electro- and optomechanical couplings. The insets show the mode proﬁle of the optical cavity ﬁeld and the electric ﬁelds

from the DC bias voltage and the microwave drive. A nonlinear color map is used to highlight the spatial distribution of the

electric ﬁelds in the EMC. (e) The calculated optomechanical coupling rate of the simulated modes. (f) The electromechanical

dissipation rate of the simulated modes, assuming a bias DC voltage of 10 v. The two dominant peaks correspond to the two

hybridized modes in (d).

and optical waveguides. The nanobeam starts with a

phononic crystal ‘defect’ cavity covered by a thin metal-

lic layer that supports a ‘breathing’ mechanical mode.

Combined with a pair of electrodes that are symmetri-

cally positioned across narrow air gaps, this section forms

the electromechanical crystal (EMC) resonator [32]. The

EMC section is adiabatically tapered to a phonon waveg-

uide, which connects to an optomechanical crystal cav-

ity (OMC, based on the design in [21]) at the opposite

end. The phonon waveguide is designed to be reﬂective

for the TE-polarized optical ﬁelds, but transmissive to

the mechanical breathing mode of interest. Finally, the

OMC cavity is terminated by a photon/phonon mirror

section, which prevents optical and mechanical leakage

into the membrane. The geometric parameters of the el-

liptical hole array deﬁning the diﬀerent sections of the

nanobeam are displayed in ﬁg. 2a. Additionally, we con-

nect the nanobeam to the surrounding membrane via an

array of two-dimensional phononic shields with a wide

band gap for all phonon polarizations at the vicinity of

the operation frequency (see appendix B).

We employ ﬁnite-element-method (FEM) simulations

to model the optical, electrical, and mechanical responses

of the device (see ﬁg. 2 b-f). As evident in ﬁg. 2d, the

termination of the phonon waveguide with the EMC and

OMC resonators creates a mechanical Febry-Perot cav-

ity, which supports extended ‘supermodes’. The degree

of overlap between the mechanical energy density of each

supermode and the electric/optical ﬁelds in EMC/OMC

resonators sets the rates of electromechanical and op-

tomechanical interactions. We numerically calculate the

single-photon optomechanical coupling (g0) and the elec-

tromechanical decay rate (γem) for all the supermodes

in the vicinity of the bare resonance frequency of the

EMC and OMC resonators. As evident in ﬁg. 2e,f, with

careful design of the structure, we can get a pair of dom-

inant supermodes in the spectra, which are identiﬁed as

symmetric and anti-symmetric superpositions of the bare

EMC and OMC resonances. We have numerically stud-

ied the eﬀects of fabrication disorder on the degree of

hybridization of the supermodes and optimized our de-

sign to achieve robustness against percent-level frequency

oﬀsets between the EMC and OMC resonators (see ap-

pendix C).

For each supermode, we have calculated the moving-

boundary and photoelastic contributions to the optome-

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Electro-optictransductioninsiliconviaGHz-frequencynanomechanicsHanZhao,1,2AlkimBozkurt,1,2andMohammadMirhosseini1,2,1TheGordonandBettyMooreLaboratoryofEngineering,CaliforniaInstituteofTechnology,Pasadena,California911252InstituteforQuantumInformationandMatter,CaliforniaInstituteofTechnology,Pasaden...

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Electro-optic transduction in silicon via GHz-frequency nanomechanics Han Zhao1 2Alkim Bozkurt1 2and Mohammad Mirhosseini1 2 1The Gordon and Betty Moore Laboratory of Engineering

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