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Abstract

Light wave propagation in a periodically stratified medium has many applications in physics, mathematics, and engineering. The subject is of interest to students, teachers, and researchers, as it presents a great opportunity to focus on principles of optics and to understand the basics of mathematical modeling. A complete theory of wave propagation can be derived using Born’s optics theory. We employed that theory to determine the reflectivity of a one-dimensional distributed Bragg reflector (DBR) and do simulations using MATLAB. A DBR is a photonic crystal consisting of alternating layers of materials with different refractive indices. In this study, we modeled theoretical reflectivity of four-period DBR and compared with experimental results previously constructed on a glass substrate and reported by DeSilva et al. (2018). Each period consists of a layer of polyvinyl carbazole and a layer of cadmium sulfide. We used the Cauchy equation for the simulation of the wavelength dependency of the cadmium sulfide refractive index in a wavelength range between 400 and 1000 nm. The theory obtained a center wavelength and a reflectivity for each of the DBR periods in good agreement with the experimental results. Finally, in the appendix, we include a simple MATLAB script that demonstrates the application of the theory to a DBR.

Acknowledgements

The authors would like to thank the University of West Georgia Institutional STEM Excellence program for their financial support for this research. We also acknowledge Jared Thacker who started a simulation for a two-period DBR system as an undergraduate research project while at UWG.

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