Plasmons with orbital angular momentum. Mendonca

Meaning of some acdemic words

Paraxial photon beams can appropriately be described by a linear superposition of LG functions.

The electric field $\textnormal{E}(r,t)=-\nabla V(r,t)$can be produced by a small perturbation in the electron density, which can lead to the excitation of electron plasma oscillation.
Considering the linearied version of the electron fluid equuation, the wave equation for the electron plasma waves can be given by $$ (\frac {\partial^2} {\partial t^2}-S^2_e\nabla ^2+\omega^2_{pe}) \widetilde{n} = 0 $$
- $\widetilde{n}$ is the perturbed electron density with the equilibrium value $n_0$
- $S_e$ is the electron thermal speed
- $k_B$ is the Boltzmann constant
- $\omega_{pe}$ is the electron plasma frequency
Wave solutions considered in this article are those can be excited by Raman scattering of intense laser pulses, instead of those in the usual plane, which carries no anggular momentum.
This kind of beam solution mentioned in the last point can be taken in the form $\widetilde{n} (r,t)=\widetilde{n}_0(r)\textnormal{exp}(ikz-i\omega t)$, where the amplitude $\widetilde{n}_0(r)$is a slowly function of the spatial coordinates and describes the wave profile
- [My understanding] A wave is composed of myriad wave profile. The prapagation of a wave can be caused by even a small perturbation.
The wave equation can be reduced into a well known paraxial euqation, similar to that usually considered for electromagnetic wave, of the form $$ (\nabla^2_{\perp}+2ik\frac {\partial} {\partial z})\widetilde{n}_0(r)=0 $$