The transient reflection from a multilayered material structure is a deep and involved problem, even though closed form representations are available in the frequency domain. This thesis presents a novel approach for evaluating the transient field reflected from a layered material. Here a natural resonance representation is sought for the temporal response in both the late time of the layered structure, and the late time of individual substructures making up the layered material stack. In seeking this representation, a time domain reflection coefficient is defined, such that the convolution with a finite duration incident waveform yields the reflected field in the time domain. Through the definition of this time domain reflection coefficient, a methodology for obtaining the temporal response evolves. Questions on the source of the resonance response during various time periods are answered in this thesis, and the conditions for existence of the natural mode series are developed. It is found that for an n-layered material stack, a natural resonance representation can be found for the transient field if the backing material is either a perfect conductor, or a lossless medium. When the backing layer is lossy, a non-time limited branch cut contribution appears. It is also found that with the addition of a lossless layer, this branch cut contribution can be turned off. This is a valuable result with applications to non-destructive evaluation of materials.
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