Transient electromagnetic pulse propagation in temporally dispersive materials

Sammanfattning: This thesis treats the problem of transient electromagnetic pulse propagation in temporally dispersive media. The analysis is performed using time-domain techniques. In particular, the dispersive wave splitting which decouples the Maxwell equations both in vacuum and inside the medium is utilized. Complex time-dependent electromagnetic fields are introduced. These fields simplify the Maxwell equations to a compact form suitable for an application of time-domain methods. Special attention is paid to the precursors (or forerunners). The presence of forerunners is a characteristic property of pulse propagation in temporally dispersive media. The first (Sommerfeld) and the second (Brillouin) precursors are analyzed in a large class of complex media. The approximations to the first forerunner are obtained in terms of the Bessel functions. The second forerunner approximations are expressed in terms of the hyper-Airy functions. The second forerunner in reflection and transmission data for an isotropic slab is analyzed. Synthetic reflection and transmission data are used to reconstruct the first three susceptibility moments of the material of the slab. Numerical examples confirming the theoretical results are presented. Time-domain fundamental solutions and Green dyadics for temporally dispersive, simple (linear, homogeneous, and isotropic) or bi-isotropic media are introduced. Surface integral representations of the electromagnetic fields in such media are obtained and used to derive surface integral equations. A part of the thesis deals with the propagation of transient pulses in laterally discontinuous dispersive media. A system of coupled integro-differential equations for the propagator kernels is derived.