A phase-space approach for propagating field–field correlation functions

Abstract

We show that radiation from complex and inherently random but correlated wave sources can be modelled efficiently by using an approach based on the Wigner distribution function. Our method exploits the connection between correlation functions and the Wigner function and admits in its simplest approximation a direct representation in terms of the evolution of ray densities in phase space. We show that next leading order corrections to the ray-tracing approximation lead to Airyfunction type phase space propagators. By exploiting the exact Wigner function propagator, inherently wave-like effects such as evanescent decay or radiation from more heterogeneous sources as well as diffraction and reflection can be included and analysed. We discuss in particular the role of evanescent waves in the near-field of non-paraxial sources and give explicit expressions for the growth rate of the correlation length as a function of the distance from the source. The approximations are validated using full-wave simulations of model sources. In particular, results for the reflection of partially coherent sources from flat mirrors are given where the influence of Airy function corrections can be demonstrated. We focus here on electromagnetic sources at microwave frequencies and modelling efforts in the context of electromagnetic compatibility.

Near-Field Scanning and Propagation of Correlated Low-Frequency Radiated Emissions

“…This momentum variable is associated with ray direction in the short-wavelength limit but in the reactive near field dominating the measurements we report, it instead dictates the rate of evanescent decay away from the source. This extends previous work [15,Sec 3. ] in which a phase-space propagator has been used to transport weakly evanescent components.…”

“…In a full 3D simulation, x = (x, y) and d = 2, but we also discuss a simplified analysis in which x is represented by a single component x and d = 1. Both the CF and WF of propagating [7] and weakly evanescent [15] wave densities have been studied extensively for a planar source. …”

Wigner-Function-Based Propagation of Stochastic Field Emissions From Planar Electromagnetic Sources

“…ACFs of scalar fields radiated from arbitrary complex sources can be propagated efficiently in free-space through the WF approach [38], [14]. In this paper we extend the method to a tensorial setting appropriate to EM radiation.…”

“…The aim of this work is to demonstrate that an approach introduced in [14] based on propagating ACFs from NFS measured field data using the so-called Wigner transformation is a viable alternative for stochastic field modelling. Near-toFar Field (NFF) propagation is a delicate task as its computation, whether deterministic [15] or stochastic [16], [17], is computationally intensive.…”

“…The proposed method allows for analysing the spatial ACF of a spatially continuous source or a set of discrete sources. The latter may be a wire array, for example, driven by voltages radiating partially correlated field components [14]. The knowledge of the ACF within planar surfaces at different distances from the source can be useful to assist source reconstruction methods [28], [29], [30], [31], far-field estimation [32], [33], as well as recently introduced phase-resolved scanning [34] and Emission Source Microscopy (ESM) methods [35].…”