Excess Power, Energy, and Intensity of Stochastic Fields in Quasi-Static and Dynamic Environments

The excess power, energy, and intensity of a random electromagnetic field above a high threshold level are characterized based on a Slepian–Kac model for upcrossings. For quasi-static fields, the probability distribution of the excess intensity in its regression approximation evolves from <inline-formula><tex-math notation="LaTeX">$\chi ^2_3$</tex-math></inline-formula> to <inline-formula><tex-math notation="LaTeX">$\chi ^2_2$</tex-math></inline-formula> when the threshold level increases. The excursion area associated with the excess energy exhibits a chi-cubed (<inline-formula><tex-math notation="LaTeX">$\chi ^3_2$</tex-math></inline-formula>) distribution above asymptotically high thresholds, where excursions are parabolic. For dynamic fields, the dependence of the electrical and environmental modulations of the excess power on the hybrid modulation index and threshold level is established. The normalized effective power relative to the quasi-static power increases nonmonotonically when this index increases. The mean and standard deviation of the dynamic excess power are obtained in a closed form and validated by Monte Carlo simulation.