Fluctuations of Power versus Energy for Random Fields Near a Perfectly Conducting Boundary

TL;DR

This paper analyzes the statistical fluctuations of energy and power densities of isotropic random electromagnetic fields near a perfect conductor, revealing decay rates and variability differences based on boundary proximity.

Contribution

It provides a detailed characterization of the standard deviations of energy and power densities near a conducting boundary using quartic plane-wave expansions, highlighting decay behaviors and uncertainty measures.

Findings

Power fluctuations decay faster than mean values with distance.

Standard deviation of power flux increases linearly near the boundary.

Relative uncertainty of scalar power is much smaller than Poynting power.

Abstract

The standard deviations of the energy and Poynting power densities for an isotropic random field near a perfectly conducting planar boundary are characterized, based on quartic plane-wave expansions. For normal and transverse components, different rates of decay exist as a function of electrical distance from the boundary. At large distances, the envelopes for the power are more strongly damped than for the energy, both showing inverse power law decay. The decay for the standard deviation is generally one order faster than for the corresponding mean. For the normally directed power flux, its standard deviation near the boundary increases linearly with distance. The relative uncertainty of the scalar power is much smaller than for the Poynting power. Poynting's theorem for standard deviations is obtained and demonstrates larger standard deviations of the energy imbalance and power flux than their mean values.