ˇ
C
Microwave-to-optical conversion using lithium
niobate thin-film acoustic resonators
LINBO SHAO
1,6
, MENGJIE YU
1
, SMARAK MAITY
1
, NEIL SINCLAIR
1,2
, LU ZHENG
3
,
CLEAVEN CHIA
1
, AMIRHASSAN SHAMS-ANSARI
1
, CHENG WANG
1,4
, MIAN
ZHANG
1,5
, KEJI LAI
3
, AND MARKO LON AR
1,7
This document provides supplementary information to "Microwave-to-optical conversion using
lithium niobate thin-film acoustic resonators," https://doi.org/10.1364/OPTICA.6.001498. It provides
details of numerical simulations of acousto-optic interactions, dynamics of the acousto-optic cavity,
and calculations of the acousto-optic coupling and conversion efficiencies.
1. NUMERICAL SIMULATION OF THE ACOUSTO-OPTIC
INTERACTION
We perform a 2D numerical simulation of our device cross-
section (Fig. S1(a)) using COMSOL Multiphysics. Optical and
acoustic modes are simulated independently and the acousto-
optic interactions are then calculated by the integral of acoustic
and optical fields using corresponding nonlinear coefficient ma-
trices.
A. Simulation of optical and acoustic modes
The single-mode optical waveguide of our device supports fun-
damental TE and TM modes (Fig. S1). The electric field profiles
of the optical modes are used in the calculation of the acousto-
optic interaction.
The simulation of the acoustic mode includes strain, elec-
tric field, and the piezoelectric effect. Multiple acoustic modes
with gigahertz resonant frequencies are found in the eigenmode
simulation. We plot only a few acoustic modes in Fig. S2. The
electrical excitation of these acoustic modes are enabled by the
interdigital transducers (IDTs).
B. Calculation of acousto-optic interactions
The acousto-optic interactions are calculated by integrating the
optical and acoustic modes with matrices that describe moving
boundary, photoelastic and electro-optic effects. Calculations
here are based on theory formulated in previous works [1–4].
Lithium niobate thin film
Metal electrodes
Optical
waveguide
(a)
(b)
(c)
TE mode
TM mode
Fig. S1.
(a) Device structure for 2D numerical simulation. (b),
(c) Optical electric field of the fundamental TE and TM modes,
respectively.
In our work, the acousto-optic interactions are described by
the change of optical mode index due to the acoustic mode.
The acoustic mode amplitude
α
, defined by the maximum dis-
placement, is normalized to a single phonon occupation of the
acoustic resonator using
¯hΩ =
1
2
m
eff
Ω
2
α
2
, where
Ω
is the acous-
tic frequency. The effective mass
m
eff
of the acoustic mode is
1
John A. Paulson School of Engineering and Applied Sciences, Harvard University, 29 Oxford Street, Cambridge, Massachusetts 02138,
USA
2
Division of Physics, Mathematics and Astronomy, and Alliance for Quantum Technologies (AQT), California Institute of Technology,
1200 E. California Blvd., Pasadena, California 91125, USA
3
Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA
4
Department of Electrical Engineering & State Key Laboratory of THz and Millimeter Waves, City University of Hong Kong, Kowloon, Hong
Kong, China
5
HyperLight Corporation, 501 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
6
e-mail: shaolb@seas.harvard.edu
7
e-mail: loncar@seas.harvard.edu
Published 2 December 2019