Exact calculation of the optical properties of one-dimensional Nonlinear photonic crystals

We develop a new version of the invariant imbedding theory of wave propagation in arbitrarily-inhomogeneous stratified media made of nonlinear materials. Using this theory, we study electromagnetic wave propagation in one-dimensional nonlinear photonic crystals with and without a defect layer. The invariant imbedding theory allows us to calculate various wave propagation characteristics very efficiently in a numerically exact manner. We calculate the transmission spectra and the electric field distribution inside nonlinear photonic crystals. We find that the electric field inside the defect layer is strongly enhanced. We also observe strong optical bistability near the defect frequency.