Independently Controlling Stochastic Field Realization Magnitude and Phase Statistics for the Construction of Novel Partially Coherent Sources

Abstract

In this paper, we present a method to independently control the field and irradiance statistics of a partially coherent beam. Prior techniques focus on generating optical field realizations whose ensemble-averaged autocorrelation matches a specified second-order field moment known as the cross-spectral density (CSD) function. Since optical field realizations are assumed to obey Gaussian statistics, these methods do not consider the irradiance moments, as they, by the Gaussian moment theorem, are completely determined by the field’s first and second moments. Our work, by including control over the irradiance statistics (in addition to the CSD function), expands existing synthesis approaches and allows for the design, modeling, and simulation of new partially coherent beams, whose underlying field realizations are not Gaussian distributed. We start with our model for a random optical field realization and then derive expressions relating the ensemble moments of our fields to those of the desired partially coherent beam. We describe in detail how to generate random optical field realizations with the proper statistics. We lastly generate two example partially coherent beams using our method and compare the simulated field and irradiance moments theory to validate our technique.

Modal Analysis of Pseudo-Schell Model Sources

“…More general sources, though, can be envisaged with different behaviors of the correlation function. In particular, since their coherence properties affect the features of the radiated beam [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], this opens a new way to searching for particular light sources that best fit for specific applications, such as particle trapping [12,19], free space optical communications [20,21], or sub-Rayleigh imaging [22][23][24][25], among others.…”

Introduction to the Special Issue on Structured Light Coherence

“…In [8], the possibility of fine control of the magnitude and the phase of a speckle-field statistics is achieved. Such manipulation is shown to produce entirely new classes or stationary fields with controllable statistical properties of different orders.…”