Electromagnetic Multi–Gaussian Speckle

Milo W Hyde,Olga Korotkova

doi:10.3390/opt3010003

Abstract

Generalizing our prior work on scalar multi-Gaussian (MG) distributed optical fields, we introduce the two-dimensional instantaneous electric-field vector whose components are jointly MG distributed. We then derive the single-point Stokes parameter probability density functions (PDFs) of MG-distributed light having an arbitrary degree and state of polarization. We show, in particular, that the intensity contrast of such a field can be tuned to values smaller or larger than unity. We validate our analysis by generating an example partially polarized MG field with a specified single-point polarization matrix using two different Monte Carlo simulation methods. We then compute the joint PDFs of the instantaneous field components and the Stokes parameter PDFs from the simulated MG fields, while comparing the results of both Monte Carlo methods to the corresponding theory. Lastly, we discuss the strengths, weaknesses, and applicability of both simulation methods in generating MG fields.

Highlights

We find the moments of partially polarized MG speckle, including the speckle contrast, before concluding the theoretical analysis with derivations of the instantaneous Stokes parameter probability density functions (PDFs)
We found the coefficients of the following fourth-order polynomial that resulted in the best fit to the speckle contrast: C( M, P ) ≈
We generalized our prior work on stochastic scalar MG fields to the electromagnetic domain

Summary

Introduction

Light speckle is one of the classic areas of study in statistical optics manifesting itself via spatial intensity randomization and being the consequence of field interference. In the past few years, there has been interest in engineered, non-Gaussian speckle for use in microscopy and imaging applications [21,22,23] With these potential applications in mind, we recently presented a new random variable [termed multi-Gaussian (MG)] for modeling stochastic optical fields, whose PDF was an alternating series of weighted Gaussian PDFs [24]. This feature of the MG PDF, being a suitable sum of Gaussian PDFs, made it possible and, very affordable, to derive, in closed form, the PDF of intensity for scalar MG-distributed fields and determine speckle moments such as the contrast. We find the moments of partially polarized MG speckle, including the speckle contrast, before concluding the theoretical analysis with derivations of the instantaneous Stokes parameter PDFs. To validate our analysis, we generate, in simulation, realizations of a generic electromagnetic MG speckle field using two different approaches. We conclude our paper with a brief summary of the key results

Bivariate Complex MG PDF

The MG Polarization Matrix and Speckle Contrast

Instantaneous Stokes Parameter PDFs for MG Speckle

S2 and S3

Simulation

Conclusions