Stimulated Raman and Brillouin backscattering of collimated beams carrying orbital angular momentum

We study theoretically the exchange of angular momentum between electromagnetic and electrostatic waves in a plasma, due to the stimulated Raman and Brillouin backscattering processes. Angular momentum states for plasmon and phonon fields are introduced for the first time. We demonstrate that these states can be excited by nonlinear wave mixing, associated with the scattering processes. This could be relevant for plasma diagnostics, both in laboratory and in space. Nonlinearly coupled paraxial equations and instability growth rates are derived.

💡 Research Summary

The paper presents a comprehensive theoretical study of how orbital angular momentum (OAM) carried by a collimated laser beam influences stimulated Raman and Brillouin back‑scattering in a plasma. Starting from the well‑established framework of Raman (electron‑plasma wave) and Brillouin (ion‑acoustic wave) scattering, the authors introduce OAM as an additional conserved quantity alongside frequency and linear momentum. They model the incident laser as a Laguerre‑Gaussian mode characterized by an integer topological charge ℓ₀, which determines the helical phase structure of the beam.

A key novelty is the quantization of OAM for the plasma excitations themselves. By applying the azimuthal angular‑momentum operator L̂_z = –i∂/∂φ to the plasma‑wave potentials, the authors define discrete OAM eigenstates for plasmons (ℓₚ) and for ion‑acoustic phonons (ℓₛ). These eigenstates correspond to azimuthal charge‑density or ion‑displacement patterns that rotate around the beam axis, effectively imprinting a vortex‑like motion on the plasma particles.

Using the paraxial approximation for both the electromagnetic field and the plasma waves, the authors derive a set of coupled envelope equations. The electric‑field envelopes A₀ (pump) and A₁ (back‑scattered Stokes) obey

i∂z A₀ + (1/2k₀)∇⊥² A₀ = C_R A₁ B* + C_B A₁ C*,
i∂z A₁ + (1/2k₁)∇⊥² A₁ = C_R A₀ B   + C_B A₀ C,

where B and C are the plasmon and phonon envelopes, respectively, and C_R, C_B are the Raman and Brillouin coupling coefficients. The azimuthal dependence of each envelope is explicitly written as exp(iℓφ), and the nonlinear terms enforce the OAM conservation laws ℓ₀ = ℓ₁ + ℓₚ (Raman) and ℓ₀ = ℓ₁ + ℓₛ (Brillouin).

Linearizing around a strong pump and assuming small Stokes and plasma‑wave amplitudes, the authors obtain analytic expressions for the growth rates:

γ_R = √