Study on optical gain of one-dimensional photonic crystals with active impurity

Localized fields in the defect mode of one-dimensional photonic crystals with active impurity are studied with the help of the theory of spontaneous emission from two-level atoms embedded in photonic crystals. Numerical simulations demonstrate that the enhancement of stimulated radiation, as well as the phenomena of transmissivity larger than unity and the abnormality of group velocity close to the edges of photonic band gap, are related to the negative imaginary part of the complex effective refractive index of doped layers. This means that the complex effective refractive index has a negative imaginary part, and that the impurity state with very high quality factor and great state density will occur in the photonic forbidden band if active impurity is introduced into the defect layer properly. Therefore, the spontaneous emission can be enhanced, the amplitude of stimulated emission will be very large and it occurs most probably close to the edges of photonic band gap with the fundamental reason, the group velocity close to the edges of band gap is verv small or abnormal.