A Hamiltonian treatment of stimulated Brillouin scattering in nanoscale integrated waveguides

J. E. Sipe, M. J. Steel

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36 Citations (Scopus)
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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.

Original languageEnglish
Article number045004
Pages (from-to)1-21
Number of pages21
JournalNew Journal of Physics
Publication statusPublished - 1 Apr 2016

Bibliographical note

Copyright the Author(s) 2016. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.


  • Hamiltonian
  • integrated waveguides
  • nonlinear quantum optics
  • stimulated Brillouin scattering


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