Controlling the Spatial Coherence of an Optical Source Using a Spatial Filter

Milo Hyde

doi:10.3390/app8091465

Abstract

This paper presents the theory for controlling the spectral degree of coherence via spatial filtering. Starting with a quasi-homogeneous partially coherent source, the cross-spectral density function of the field at the output of the spatial filter is found by applying Fourier and statistical optics theory. The key relation obtained from this analysis is a closed-form expression for the filter function in terms of the desired output spectral degree of coherence. This theory is verified with Monte Carlo wave-optics simulations of spatial coherence control and beam shaping for potential use in free-space optical communications and directed energy applications. The simulated results are found to be in good agreement with the developed theory. The technique presented in this paper will be useful in applications where coherence control is advantageous, e.g., directed energy, free-space optical communications, remote sensing, medicine, and manufacturing.

Highlights

Following the nomenclature and notation of Emil Wolf [1], a partially coherent source (PCS) is defined by its autocorrelation function, better known as the mutual coherence function (MCF):Γ (ρ1, ρ2 ; t1, t2 ) = hU (ρ1, t1 ) U ∗ (ρ2, t2 )i, (1)where U (ρ, t) is an instance of a random optical field evaluated at position ρ = xx + ŷy and time t,∗ is the complex conjugate, and hi is the average over the ensemble of U realizations
The technique presented in this paper will be useful in applications where coherence control is advantageous, e.g., directed energy, free-space optical communications, remote sensing, medicine, and manufacturing
The Sout,thy and Sout,sim results noticeably disagree. This occurs because Ssrc is not a fast function compared to T, viz., Criterion 3 is violated

Summary

Introduction

Following the nomenclature and notation of Emil Wolf [1], a partially coherent source (PCS) is defined by its autocorrelation function, better known as the mutual coherence function (MCF):. Where U (ρ, t) is an instance of a random optical field evaluated at position ρ = xx + ŷy and time t,. The first and second moments of many optical sources vary slowly with time such that they can be considered static. This characteristic is referred to as wide-sense stationary and implies that the MCF defined in Equation (1) depends temporally only on the time difference τ = t1 − t2. The temporal Fourier transform of the MCF is the cross-spectral density (CSD) function:.

Objectives

Results

Conclusion