This Demonstration models a photonic crystal that contains alternating layers of two different materials with indices of refraction and , which can be changed. In addition, the number and width of the layers can also be modified, as well as the type of electromagnetic (EM) wave (either transverse magnetic or electric) and the angle at which the EM wave hits the crystal.
Photonic crystals are structures consisting of alternating layers with different indices of refraction and dielectric constants. The way that light travels through such a periodic structure can be solved exactly using Maxwell's equations. Much like the way electrons behave in a periodic potential of a semiconductor, the solutions show that certain wavelengths of electromagnetic waves, or modes, can travel through the photonic crystal, while others cannot. The wavelengths that cannot pass through the crystal are perfectly reflected, thus forming a photonic bandgap. The position of the photonic bandgap can be tuned, by varying the thickness and the index of refraction of each material within the photonic crystal.
 A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation, Hoboken, NJ: John Wiley & Sons, 2003.
 J. D. Jackson, Classical Electrodynamics, Hoboken, NJ: John Wiley & Sons, 1999.