Zernike polynomials as a phase distortion of Laguerre-Gaussian mode cancellation

Abstract

Laguerre-Gaussian beams and Hermite modes are intrinsically related, even though the first has received most of the attention due to their properties. In this work, we focus on the perturbation of the beams through turbulence. We present an experimental discovery of the decomposition of Laguerre-Gaussian beams due to convective turbulence into Hermite-Gaussian beams. Even though this phenomenon has been observed, mostly using lenses, it was ignored when it was produced by turbulence. We propose an explanation using Zernike Polynomials as a phase distortion. We found that within its randomness, turbulence possesses ordered stages that act as a phase perturbation in the form of a saddle point. These stages coincide with the astigmatic polynomials of the Zernike base.