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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.
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