Abstract
We present a multimode Hamiltonian formulation for the problem of opto-acoustic interactions in optical waveguides. We develop a quantised 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 in a particularly transparent manner. The interaction is applied to a Fermi's golden rule calculation of spontaneous Brillouin scattering in uniform waveguides. The Heisenberg equations of motion are then used to obtain coupled mode equations for quantised envelope operators for the optical and acoustic fields. We show that the coupling coefficients obtained coincide with those established earlier. Our formalism provides a new basis for future work involving quantum photon and phonon noise in the low intensity limit, phonon–phonon scattering and anharmonicity effects.
Highlights
Almost a century after it was first proposed [1, 2] and fifty years since the invention of the laser allowed its first observation [3], the phenomenon of stimulated Brillouin scattering (SBS) may only be entering its golden age
The acoustic wave is generated by the process of electrostriction [4, 5], and both the Stokes and acoustic wave grow by a process of positive feedback
Note that while we focus below on the effects associated with material discontinuities, this expression accounts for a bulk contribution to the radiation pressure in graded index materials for which βref(r) varies smoothly in space
Summary
Almost a century after it was first proposed [1, 2] and fifty years since the invention of the laser allowed its first observation [3], the phenomenon of stimulated Brillouin scattering (SBS) may only be entering its golden age. Waveguides in which the acoustic fields are strongly confined can enhance the scattering efficiency of near-stationary quasi-transverse acoustic waves, a requirement for efficient forward SBS where the pump and Stokes wave co-propagate [16, 35] Following this realization there was some variation in the literature as to how best to incorporate the new effects into a coupled mode theory self-consistently. They identify an elegant connection between the opto-acoustic coupling in waveguide SBS and the corresponding coupling in quantum optomechanical systems The latter is treated with a single mode Hamiltonian approach which is appropriate for the optomechanics of a resonator consisting of a single cavity, but limits its application to longer structures with continuous phonon spectra. A comprehensive supplementary materials document provides detailed derivations of many of the results
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
