Study on the Optical Gain of Photonic Crystals with Active Impurity

We have proved the inevitability of the existence of localized field with a defect mode as well as its basic properties with the help of the theory of spontaneous emission from two-level atoms in photonic crystals,which provide a theoretical proof for studying the inherent laws of spontaneous radiation from the doped medium in the paper.On this basis,the inherent laws between the characteristics of localized field,the enhancement of stimulated emission,the phenomenon of transmissivity greater than 1,the abnormality of the group velocity close to the edge of photonic band gap and the negative imaginary component of the complex active refractive index of doped layers in one-dimensional photonic crystals with active impurities or without active impurities were studied by using the method of numerical simulation,which illustrated that the complex active refractive index has a negative imaginary component,and that the dope modes with very high quality factors and great mode density will occur in the photonic forbidden band if an active impurity is introduced into the defect medium in the photonic crystals.Therefore,the enhancement of spontaneous emission can be realized,and the amplification of stimulated emission will be very great and it most probably occurs close to the edge of photonic band gap with the fundamental reason and the group velocity close to the edge of band gap being very small or abnormal.