Transient analysis of distributed Bragg reflector using wavelet-based implicit TDIE and impedance matrix compression

Summary form only given. A common photonic device is the distributed Bragg reflector (DBR), which is a stack of alternating layers of two materials with different dielectric permittivity. It exhibits high reflectivity at certain frequencies, and is therefore used in state-of-the-art applications, such as mirrors for solid-state lasers and in hollow fibers. We explore a new and efficient approach to analyzing the transient interaction of a wideband electromagnetic pulse with such devices. Transient analysis of a DBR can be formulated in terms of a volume time-domain integral equation (TDIE) and, in turn, solved numerically via the method of moments (MoM) while resorting to the more stable implicit scheme. We seek a representation of the the unknown field within the DBR layers in terms of as compact as possible a set of basis functions. Towards that end, we use a multiresolution basis comprising spatio-temporal wavelet functions. We can effect an automatic selection of the dominant functions needed for the solution via an impedance matrix compression (IMC) procedure. Our results show that the IMC procedure incorporates or omits basis functions automatically, without assuming a priori that the fields are negligible anywhere or at any time. A comparison of the performance of the proposed procedure with that of a standard CG procedure shows that the new procedure is roughly twice its fast.