Analysis of the gain effect in one-dimension active photonic crystals

Optical gain-enhancement in active one dimensional photonic crystals is investigated as a function of the characteristic parameters of the system. Using the transfer matrix method, and applying the Bloch theorem, the dispersion relation and the analytical expression relating the gain coefficient to the system parameters (such as the period of the structure, contrast of the refractive indices, geometry of the primitive cell, as well as the number of primitive cells creating the photonic crystal) have been derived. It is shown that the geometry of the primitive cell, as well as the number of primitive cells of which the photonic crystal consists, have a crucial influence on the gain enhancement of the photonic structure.