Jupyter notebook simulations of the transmission of radio frequency (RF) waves through periodic coaxial cable configurations with varying impedances and lengths were conducted to model the propagation of bandgaps in one dimensional (1D) photonic crystals. Transmission through each interface and dielectric were modelled and the total reflection of each configuration was calculated as a function of frequency. The data analysis of lab-collected data is also included and compared to the simulations.
Spatially periodic dielectric media such as photonic crystals exhibit bands of frequencies that do not propagate because of multiple reflections and destructive interference. These bandgaps are similar to those observed in semiconductors where the electric potential of the atoms in each crystal creates a bandgap of forbidden energy levels.
Coaxial cable structures can be used to emulate one dimensional (1D) photonic crystals by repeating units of cable combinations with different dielectric properties and known lengths. Each interface between cable segments introduces an impurity into the system as it breaks the crystal symmetry and changes the dielectric impedance. Since coaxial cables create a truly 1D structure, forcing the electromagnetic waves along a single path, quantitative analytical modeling of the cable system is closely representative of wave propagation through a 1D photonic crystal.
Applications of 1D photonic crystals are far-reaching such as being used to increase the sensitivity of substance measurements by tuning the interactions between an analyte and the materials used for the fabrication of the photonic crystal. Furthermore, photonic crystals have been used for laser emission upon a single photon and improving power efficiency in solar cells.