EM Pulse Transit across a Uniform Dielectric Slab

A fully time dependent electromagnetic field solution describing the transit of a flat pulse of width cT across a uniform dielectric sandwich is obtained herein by use of a Green\´s function technique in the Laplace transform domain. Once the ensuing integral equation has been solved self-consistently within the dielectric sheet, the remainder of field evolution on its exterior follows constructively without any need to cope with boundary conditions or any sort of temporal sequencing on internal pulse bounces. Transform inversion into the temporal plane, relying on a simple development into geometric series at the appropriate steps of analysis, reveals transmitted/reflected pulse trains composed of whole retinues of secondary echo pulses suitably arranged in time and diminished by ascending powers of in/out reflection coefficients. A transcription into computer code verifies that electromagnetic energy content in the transmitted/reflected pulse trains properly sums into that of the impinging pulse, and yields a graphical depiction of the individual, fore/aft pulse trains. Additional work, elsewhere reported, goes on finally to generalize the uniform pulse solution so as to embrace a slab excitation that is profiled [read "carrier modulated by an amplitude/phase signal"] in response to a magnetic amplitude h(tau) extended across a temporal support of width tau = T past the point of first contact.