Transient electromagnetic scattering from a dielectric sphere

The mathematical solution for the time-dependent interaction of a polarized electromagnetic wave with a dielectric sphere is the subject of this dissertation. The work was motivated by the increasing use of ultrashort laser pulses and the observable differences compared to continuous wave lasers. Single frequency solutions assume that internally reflected light has built up within the sphere over an infinite amount of time and that waves traveling inside and outside of the sphere can interact with one another. This assumption is not valid when the incident excitation is a short pulse containing a wide spectrum of frequencies. The transient problem is solved by the application of transformation methods to obtain a complex frequency solution. After a frequency domain solution for the scattering problem is determined, the result is then transformed back to the time domain. The transient scattered fields are shown for several short pulses and compared with the continuous wave results