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Polarization Studies of 3D Photonic Crystals Using Transmission and Reflection Experiments

We present a polarization study of a 3D photonic crystal suitable for an undergraduate advanced physics laboratory or senior project. The crystal is made of 200-nm diameter polystyrene microspheres which forms a face-centered cubic structure and has a pseudo-bandgap in the [111] direction. We probe this bandgap using polarized light in both transmission and reflection geometries as a function of incident angle. Using the Bragg-Snell law, we derive an effective refractive index of 1.40 for each case, which agrees with the effective medium theory. Application of a new analysis based on the condition of equal heights of primary and secondary reflection peaks in s-polarization, and the collapse of p-polarized reflection for large incident angles, also gives the same effective refractive index. These experiments can be performed by students with a basic knowledge of optics such as use of polarizers, lenses, and spectrometers, and the depth of theory covered can be tailored to meet student needs.