Modeling random screens for predefined electromagnetic Gaussian–Schell model sources

Abstract

In a previous paper [Opt. Express22, 31691 (2014)] two different wave optics methodologies (phase screen and complex screen) were introduced to generate electromagnetic Gaussian Schell-model sources. A numerical optimization approach based on theoretical realizability conditions was used to determine the screen parameters. In this work we describe a practical modeling approach for the two methodologies that employs a common numerical recipe for generating correlated Gaussian random sequences and establish exact relationships between the screen simulation parameters and the source parameters. Both methodologies are demonstrated in a wave-optics simulation framework for an example source. The two methodologies are found to have some differing features, for example, the phase screen method is more flexible than the complex screen in terms of the range of combinations of beam parameter values that can be modeled. This work supports numerical wave optics simulations or laboratory experiments involving electromagnetic Gaussian Schell-model sources.

A Simplified Model for Optical Systems with Random Phase Screens

“…Consequently, we chose the transfer function simulation approach and not the impulse response approach to better simulate the free-space propagation (Ch.5 in [ 24 ]). The Gaussian RPSs were simulated by convolving an uncorrelated random signal with a Gaussian function in a similar way to the Gaussian Schell-model beam simulations [ 3 , 24 , 25 ].…”

“…Because and are independent random functions, and are also independent, and we may calculate the expected value of their involved terms separately (the third line). Assuming , then , and assuming that the spatial statistics of the RPSs are WSS, then the expected value is independent of the dummy variable and can be factored outside the integral (Ch.8 in [ 21 ], [ 25 ]), where we use the statistical AC definition (fourth line). Now we need to calculate the left term in Equation (A5).…”