Theoretical Investigation of the Influence of Correlated Electric Fields on Wavefront Shaping

Abstract

Wavefront shaping is a well-known method of restoring a focus deep within scattering media by manipulating the incident light. However, the achievable focus enhancement depends on and is limited by the optical and geometrical properties of the medium. These properties contribute to the number of linearly independent transmission channels for light propagating through the turbid medium. Correlations occur when the number of incident waves coupled into the scattering medium exceeds this finite number of transmission channels. This paper investigates the wavefront shaping of such correlated electric fields. The influence of the observed correlations persists even though the average electric field distribution at positions in the focal plane follows a circular complex Gaussian. We show that correlations of the transmitted electric fields reduce the achievable intensity enhancement, even deep in the turbid medium. The investigations are carried out using a Monte Carlo algorithm. It is based on the speckle statistics of independent waves and introduces correlations of neighbouring electric fields via a Cholesky decomposition of the covariance matrix. Additional investigations include scenarios where the electric fields are not completely randomized, such as for ballistic or insufficiently scattered light. Significant contributions from such little-scattered light are observed to reduce the intensity enhancement further. Data from simulations solving Maxwell’s equations are compared with the results obtained from the Monte Carlo simulations for validation throughout this paper.