Probability Distributions of Local Modal-Density Fluctuations in an Electromagnetic Cavity

Abstract

Results from random-matrix theory are applied to the modeling of random fluctuations in the modal density observed in an electrically large cavity. By starting from results describing the probability distribution of the modal spacing between adjacent frequencies of resonance, or nearest-neighbor spacing, we introduce a simple procedure allowing to pass from the modal spacing to the local modal density as measured over a finite bandwidth. This local definition of the modal density is more consistent with the physics of reverberation chambers, since it has been recently shown that the deviation from asymptotic statistics of field samples is dependent on the number of modes overlapping within a modal bandwidth. It is shown that as opposed to current interpretation, the number of overlapping modes is a strongly fluctuating quantity, and that estimating it by taking the frequency derivative of Weyl's formula can lead to nonnegligible errors and misunderstandings. Regarding these fluctuations as second-order effects is, therefore, not sound from a physical point of view, since the existence of modal-depleted scenarios can easily explain the appearance of local anomalies in the field statistics, particularly, but not exclusively, in the lower frequency range of operation of reverberation chambers.