Propagation of light impulse in aperiodic systems photonic crystals with negative refractive index

We investigate the propagation of light impulse in aperiodic systems including Thue-Morse(TM) and Fibonacci sequence. Both refractive index and optical thickness are considered. At the same time, we calculate the transmission in TM sequence with negative refractive index by using the transfer matrix. We find many completely transparent electromagnetic states appear and the states´ corresponding frequency distribution has a self-similar structure, it is similar to the normal TM photonic crystals, depending on its crystals structure and around a particular center frequency at the midgap frequency of a quarter-wavelength, the transmission is more sensitive to the optical thickness modulation.