Natalie Cartwright, SUNY-New Paltz/CSU
Electromagnetic Wave Propagation in Dispersive Material
An electromagnetic pulse that travels through dispersive material experiences both phase and amplitude change, and each frequency changes at its own rate. For narrowband pulses and short propagation distances, the group velocity approximation may be suitable. For wideband pulses and long propagation distances, uniform asymptotic expansions are capable of providing an accurate approximation. Asymptotic expansions have shown that a pulse propagating through a dielectric material consists of a component whose peak amplitude point decays algebraically with propagation distance, rather than exponentially. Whether or not this slow decay rate can be utilized in detection and imaging is an open question. In this talk, we will review the group velocity approximation and asymptotic expansions of integrals in the context of dispersive pulse propagation. We will show how the aforementioned slow decay rate arises in the context of saddle points and review research on its applicability. We will end with related problems for future work.