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Generalized multidimensional conservation laws for stimulated Raman and Brillouin scattering in a density gradient

Vijay Patel1, Sarah Chase1, Frank S. Tsung1, John P. Palastro2, Denise E. Hinkel3, and Warren B. Mori1,4

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Phys. Rev. E 114, 045212 – Published 29 October, 2026

DOI: https://doi.org/10.1103/hdkp-2mpm

Abstract

Generalized local and multidimensional conservation laws of action, energy, momentum, and angular momentum are derived for stimulated Raman (SRS) and Brillouin backscattering (SBS) in a density gradient within the paraxial ray approximation. A Lagrangian density is given for which requiring the action be stationary reproduces the well-known envelope equations for SRS and SBS in density gradients in the absence of damping. Using Noether's theorem, the symmetries of the Lagrangian density are used to obtain local conservation laws for quantities that can easily be identified as the wave action, energy, and momentum. These multidimensional conservation laws reduce to the well-known one-dimensional Manley-Rowe relations and frequency and wave number matching conditions. Additional symmetries of the action lead to conservation laws for quantities that are identified as the orbital angular momentum and additional contributions to the energy and momentum of the wave from frequency and wave number shifts. Augmentation of the conservation laws in the presence of damping and extensions of the Lagrangian to include higher order corrections to the paraxial ray equation and nonlinear frequency shifts are also provided.

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Phys. Rev. E 114, 045212– Published 29 October, 2026
  • Received 19 June 2026
  • Accepted 4 September 2026
Article part of CHORUS
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