Propagation of light waves in Thue-Morse dielectric multilayers

We investigate the propagation of light waves in an aperiodic multilayer which is composed of dielectric slabs arranged following the Thue-Morse sequence. Both refractive index modulation and optical thickness modulation are considered. The recursion relations of the transfer matrix elements are derived to calculate the transmission. By introducing a localization index we explore the localization properties of light in the aperiodic system. Around a particular center frequency (the midgap frequency of a periodic quarter-wavelength multilayer), the transmission is more sensitive to the optical thickness modulation.