The physical fundamentals of QPM materials and photonic crystals

The behavior of light waves in a homogeneous dielectric crystal is the same as that in a continuous medium, because the wavelength of light is much larger than the period of crystal lattice, or say, the wave vector of light is much smaller than the reciprocal vectors of crystal lattice. However, if some microstructure is introduced into a dielectric crystal, forming a superlattice, and if the periods of the superlattice are comparable with the light wavelength, the situation is quite different. The propagation of light wave in the superlattice (classical system) is similar to the electron motion in a periodic potential of crystal lattice (quantum system). Thus, some ideas in solid-state electronics - for example, the reciprocal space, Brillouin zone, dispersion relation and the like - may be used in light wave processes. Such is the case for photonic crystal. On the other hand the interactions between light wave vectors and reciprocal vectors provided by the superlattice may generate some physical effects. It is the interactions that have led to new frequency generations in the quasi-phase matching materials. The main achievements in the field mentioned are reviewed.