Computation of optimal beams in weak turbulence

TL;DR

This paper develops a computational method to find the optimal optical beam that minimizes distortion in weak turbulence, using asymptotic expansion and Fourier space techniques to make the problem tractable.

Contribution

It introduces a novel approach that transforms the eigenvalue problem into a more computationally feasible form using asymptotic and Fourier methods, accommodating general beam shapes.

Findings

The method effectively computes optimal beams in simulated weak turbulence scenarios.

Incorporating turbulence assumptions reduces computational complexity.

Numerical examples demonstrate the practicality of the proposed approach.

Abstract

When an optical beam propagates through a turbulent medium such as the atmosphere or ocean, the beam will become distorted. It is then natural to seek the best or optimal beam that is distorted least, under some metric such as intensity or scintillation. We seek to maximize the light intensity at the receiver using the paraxial wave equation with weak-fluctuation as the model. In contrast to classical results that typically confine original laser beams to be from a special class, we allow the beam to be general, which leads to an eigenvalue problem of a large-sized matrix with each entry being a multi-dimensional integral. This is an expensive and sometimes infeasible computational task in many practically reasonable settings. To overcome this, we utilize an asymptotic expansion and transform the derivation to Fourier space, which allows us to incorporate some optional turbulence assumptions, such as homogeneous-statistics assumption, small-length-scale cutoff assumption, and Markov assumption, to reduce the dimension of the numerical integral. The proposed methods provide a computational strategy that is numerically feasible, and results are demonstrated in several numerical examples.