Comparison of Techniques for Predicting Statistical Distribution of Fields in Chaotic Enclosures

Here we explore a key difference between statistical techniques for estimating electric fields in chaotic, overmoded cavities. The Stochastic Power Balance, the Random Coupling Model, and the Stochastic Green's Function are all based on expanding field parameters in statistical cavity eigenfunctions approximated by a sum over random plane waves where eigenmode spacing is given by random matrix theory. They differ, however, in how they evaluate the statistics of fields over an ensemble. Power balance, initially developed by the acoustics community, first averages the field energy over the cavity and then notes that this average energy varies over an ensemble of such cavities, empirically characterizing this variation with a lognormal distribution. Then, noting that for each value of average cavity energy the field is Rayleigh distributed, they get field statistics from a convolution integral over the two distributions. Both the Random Coupling Model and Stochastic Green's Function calculate the point-to-point coupling for each member of the ensemble and calculate field statistics using a Monte Carlo approach. In this paper we compare the two approaches, finding that for high modal overlap they are identical and differ only modestly at lower modal overlap.