Inferring the time-dependent complex Ginzburg-Landau equation from modulus data

TL;DR

This paper introduces a method to infer the evolution equation of a complex wave field from modulus data over three planes, retrieving phase non-interferometrically and determining all terms of the complex Ginzburg-Landau equation.

Contribution

A novel formalism that infers the time-dependent complex Ginzburg-Landau equation solely from magnitude data, including phase retrieval and term determination.

Findings

Successfully tested with simulated data

Can be extended to multi-component fields

Determines all evolution terms from modulus data

Abstract

We present a formalism for inferring the equation of evolution of a complex wave field that is known to obey an otherwise unspecified (2+1)-dimensional time-dependent complex Ginzburg-Landau equation, given field moduli over three closely-spaced planes. The phase of the complex wave field is retrieved via a non-interferometric method, and all terms in the equation of evolution are determined using only the magnitude of the complex wave field. The formalism is tested using simulated data for a generalized nonlinear system with a single-component complex wave field. The method can be generalized to multi-component complex fields.