Photonic band structure of Sierpinski waveguide networks

Abstract

The photonic band structure and transmission properties of Sierpinski fractal networks (SNs) made of one-dimensional waveguides are studied with the generalized eigenfunction method. In the absence or presence of dissipation and in different exit situations, we have numerically calculated the transmission coefficient as a function of frequency in the range 0\char21{}500 MHz for the first four generations of SNs. As the number of generations is increased, the structures in the transmission spectra show explicitly the evolution of discrete eigenmodes and the corresponding photonic band gap structures in such fractal networks. The gap structures are not altered by the presence of dissipation and are independent of the exit situation. An interesting anomaly due to dissipation is found at certain frequencies where a resonant peak is split into two peaks with zero transmission in the valley.