We explore the analogies between a system of coaxial cables with periodicity in the impedance, and a system of dielectric stacks with periodicity in the index of refraction. The latter is a photonic crystal with wave propagation control in the optical range, while the former can be regarded as a "coaxial" photonic crystal for radiofrequency control. We reproduce electrical analogs of widely used thin-film optical devices, such as Bragg reflectors, Fabry-Perot resonators and harmonic transmission filters. Coaxial crystals represent an inexpensive way of teaching multilayer optical coatings. We show also that a simple phasor analysis provides an intuitive technique to describe the transmission properties of optical multilayers.
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 radiofrequency range, the properties of one-dimensional photonic crystals.