Second harmonic generations in aperiodic optical superlattices with finite width and in one-dimensional defective photonic crystals made of nonlinear optical materials

The characteristics of the second harmonic generations (SHGs) in homogeneous and inhomogeneous systems are investigated. We consider two kinds of structures: one is aperiodic optical superlattices (AOSs) with homogeneous linear susceptibility and the modulated second-order nonlinear susceptibility; the second is linear and nonlinear susceptibilities both the system with inhomogeneous. We derive a general solution of SHG for the AOS with finite lateral width and of SHG in considering the depletion of the pump light power. We carry out the design of AOSs by using simulation annealing (SA) algorithm and show that the constructed AOSs can implement multiple wavelength SHGs with identical effective nonlinear coefficient at the preassigned wavelengths of incident light. We observe great enhancement of SHGs in the one-dimensional photonic crystals (PCs) with defects consisting of multiple photonic quantum wells made of nonlinear material when the frequency of fundamental wave aims at one of the defect states. We also propose an effective design approach of aperiodically stacked layers of nonlinear material and air in terms of the SA method. The constructed structure can achieve multiple-wavelength SHGs at the preas-signed wavelengths.