A Hamiltonian treatment of stimulated Brillouin scattering in nanoscale integrated waveguides

TL;DR

This paper develops a Hamiltonian framework for analyzing stimulated Brillouin scattering in nanoscale integrated waveguides, unifying optical and acoustic interactions with a simplified, comprehensive approach.

Contribution

It introduces a multimode Hamiltonian formalism that unifies photoelastic, electrostrictive, radiation pressure, and moving boundary effects in opto-acoustic interactions.

Findings

Coupling coefficients match previous results

Simplifies the connection between radiation pressure and boundary effects

Provides a comprehensive Hamiltonian model for nanoscale waveguides

Abstract

We present a multimode Hamiltonian formulation for the problem of opto-acoustic interactions in optical waveguides. We establish a Hamiltonian representation of the acoustic field and then introduce a full system with a simple opto-acoustic coupling that includes both photoelastic/electrostrictive and radiation pressure/moving boundary effects. The Heisenberg equations of motion are used to obtain coupled mode equations for quantized envelope operators for the optical and acoustic fields. We show that the coupling coefficients obtained coincide with those established earlier, but our formalism provides a much simpler demonstration of the connection between radiation pressure and moving boundary effects than in previous work [C. Wolff et al, Physical Review A 92, 013836 (2015)].