Abstract
We introduce a finite-difference frequency-domain algorithm for coupled acousto-optic simulations. First-principles acousto-optic simulation in time domain has been challenging due to the fact that the acoustic and optical frequencies differ by many orders of magnitude. We bypass this difficulty by formulating the interactions between the optical and acoustic waves rigorously as a system of coupled nonlinear equations in frequency domain. This approach is particularly suited for on-chip devices that are based on a variety of acousto-optic interactions such as the stimulated Brillouin scattering. We validate our algorithm by simulating a stimulated Brillouin scattering process in a suspended waveguide structure and find excellent agreement with coupled-mode theory. We further provide an example of a simulation for a compact on-chip resonator device that greatly enhances the effect of stimulated Brillouin scattering. Our algorithm should facilitate the design of nanophotonic on-chip devices for the harnessing of photon-phonon interactions.
Highlights
We have presented a numerically efficient, first-principles method for simulating stimulated Brillouin scattering (SBS) in optical devices. Both devices simulated here consisted of two-dimensional structures with a transverse electric polarization operating using the backwards SBS configuration, the theory underlying the acousto-optic finite-difference frequency-domain (FDFD) algorithm is completely general to acousto-optic and optomechanic wave phenomena, and this algorithm can be extended to three dimensions, as well as to other forms of acousto-optic interactions, such as the forward SBS process or an on-chip acousto-optic modulator
The concept behind this algorithm is not restricted by the method with which we discretize the simulation domain, so it can be formulated for other firstprinciples frequency-domain techniques such as the finite element method (FEM), where a different discretization scheme is used.[50]
Since FEM is formulated as the solution to boundary value problems and is superior to FDFD in modeling curved surfaces, we should expect the equivalent
Summary
There has been increasing interest in acousto-optic devices, with an emphasis on the design of on-chip structures to efficiently harness various photon and phonon interaction mechanisms such as the stimulated Brillouin scattering (SBS).[1,2,3,4] As SBS yields an extremely strong nonlinear interaction with narrow resonances, it has found applications in many important areas of optics and acoustics.[1,2,3] Traditionally, SBS has been studied extensively in fiber-optic devices in order to inhibit undesired nonlinear effects induced by SBS.[1,2,3,4] More recently, SBS has been tailored for micron-scale on-chip devices,[2,3,5,6,7,8,9,10] where it is considered to be an attractive candidate in the creation of lasers with ultra-narrow bandwidths,[11,12,13,14] gigahertz frequency combs,[15,16] slow light,[17] and on-chip signal processing devices such as the microwave photonic filter[18,19] and optical isolators.[20,21,22,23]. The physics of the acousto-optic system can be rigorously formulated as a system of coupled nonlinear equations, whose solution provides the steady-state dynamics of the acousto-optic systems With such a frequency-domain solver, we bypass the need to compute field values at every time step and can directly simulate a general class of acoustooptic devices without the limitations in time-domain simulations as imposed by the vastly differing time scales between optical and acoustic waves. The remainder of this manuscript is structured as follows.
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