Written by Yuhang Jin, AP225 2011 Fall.
Photonic crystals are periodic dielectric nanostructures that can modulate the propagation of light. Usually a photonic crystal contains periodically repeating nano-sized areas of materials with sufficiently different dielectric constants, as displayed in Figure 1. If the absorption of light by these components is small, light can be prevented from propagating in certain directions with certain frequencies due to the Bragg-like reflection. In other words, photonic band gaps are created in photonic crystals, similar to the energy gaps in the motion of electrons in solid state crystals. Here, the macroscopic media with distinct dielectric constants are analogous to the atoms or molecules in a crystal, and the periodic refraction index experienced by the photons is analogous to the periodic Coulomb potential. An example of photonic band gaps is shown in Figure 2.
Categories of photonic crystals
Photonic crystals can be classified based on their dimensions of periodicity, i.e. in how many dimensions the nanostructures repeat themselves. 1D photonic crystals are often alternating sequence of layers with different dielectric constants, for instance Bragg mirrors. 2D photonic crystals usually consist of periodic holes or rods in a dielectric medium, and provide 2D photonic band gaps. 3D photonic crystals are the most difficult to fabricate, and proposed constructions of such 3D periodic nanostructures include spheres in a diamond lattice, Yablonovite, the woodpile crystal, inverse opals and stacks of two-dimensional crystals .
Photonic crystals have vast application thanks to their distinct and engineerable optical properties . For example, 1D photonic crystals can be used as omni-directional reflectors and low-loss optical filters. 2D photonic crystals can serve as logic devices such as optical switches, and be fabricated into photonic crystal fibers and waveguides. The development of 3D photonic crystal is still far from mature due to the difficulty with fabrication, and may have great potential in areas such as optical computation etc .
 J. D. Joannopoulos, S. G. Johnson, J. N. Winn, & R. D. Meade, "Photonic Crystals: Molding the Flow of Light", Princeton University Press, 2008.