Theoretical analysis of apertures radiating inside wave chaotic cavities

Abstract

We investigate the mode admittance matrix of an aperture radiating inside a wave-chaotic cavity. The closed electromagnetic system is modeled by a statistical description involving chaotic modes and spectra developed in the framework of random matrix theory. It is shown that the random coupling model, previously derived for modeling port and antenna impedances, is also valid for apertures. The universal fluctuation matrix, expressing the coupling between aperture and cavity modes, is found to be diagonalized by the free-space radiation conductance. We propose a procedure exploiting the Hilbert transform to derive the radiation susceptance, also accounting for the magnetostatic contribution, and thus to compose the full radiation admittance matrix. Wave chaos is found to break aperture orthogonality of certain mode configurations. The model gives a unified picture bridging deterministic theories of aperture radiation, and statistical models necessary for capturing chaotic scattering inside complex cavities. Results are of interest for predicting the field coupled through apertures in complex cavities such as reverberation chambers, and for quantifying interferences inside slotted enclosures containing electronic circuitry, among other practical scenarios.