Photonic Bandgaps in Quasiperiodic Multilayer Structures Using Fourier Transform of the Refractive Index Profile

Abstract—In this paper, photonic bandgaps (PBGs) of the quasiperiodic structures is calculated using the Fourier transform of the refractive index profile. Comparing the reflectivity and Fourier spectrum of multilayer structure refractive index, we find that a peak in the Fourier spectrum is equivalent to a sinusoidal term in the refractive index. The wavelength of the peak location in the Fourier spectrum is half the wavelength where a PBG is located. Using Fourier transform analysis of the refractive index of any multilayer structure, we can determine the location of the PBGs of that structure. Peaks in the Fourier spectrum can be used to design reflective band optical filters in optical communication systems. The filtering wavelengths are twice the peaks in the Fourier spectrum.