Analysis of coaxial photonic crystal transmittance by Fourier transform

In this work, we present an analysis of harmonic frequency transmission filters based on one-dimensional photonic crystals using a Fourier transform approach. This approach relates the photonic crystal transmittance with the Fourier transform of the logarithmic derivate of their refraction index profile. We compare this Fourier approach with the exact transmission calculated by means of the transfer matrix method. We study the accuracy of different functions proposed in the literature that relate the Fourier transform of the index profile with the transmittance. This Fourier approach provides a more intuitive understanding of the transmission properties of one-dimensional photonic crystals. We experimentally demonstrate these properties by using coaxial cables of different impedances. This kind of electrical system is easier to perform experimentally and reproduces, in the radio-frequency range, the properties of one-dimensional photonic crystals.