Applications of the Complex Huygens Principle and Gaussian Pulsed-beam Wavelet Representations in Acoustics and Electromagnetics.

摘要

The original goal was to apply the analytic Huygens representations of EM fields (developed jointly with Dr. Thorkild Hansen in 2009-2011) to scattering, communication and radar. However, in 2012 Dr. Richard Albanese urged me to clarify the concept of electromagnetic inertia which I had defined in 2011, and which posed some conceptual problems since it implied that electromagnetic energy in vacuum generally flows at speeds less than c. Thus I changed my goal to understanding EM inertia and relating it to the reactive field energy. But reactive EM energy is strictly linked to the complex Poynting theorem (CPT), which holds only for time-harmonic fields. Even there, no reactive energy density can be defined because this theorem cannot be interpreted as its conservation law. In 2014 I generalized the CPT to EM fields with arbitrary time dependence and showed that an analytic continuation of the generalized CPT does have an interpretion as a conservation law for reactive EM energy. I further defined a complex radiation impedance density analogous to the impedance Z=R+iX of an RLC circuit. I hope to use this analogy to interpret the real and imaginary parts of the complex impedance density as the radiation resistance and radiation reactance densities of the EM field.