A computational study on the efficient second-harmonic generation (SHG) in one-dimensional nonlinear photonic crystals (PhCs) is presented. The design requirements are specified in terms of the corresponding fundamental wavelength of the incident wave, at which the maximum conversion efficiency of SHG occurs. The computational approach has developed a Newton-type local optimization method to optimize the fill factor and the period of a PhC. An optimal structure can be determined by controlling the band structure such that the frequencies of the fundamental and second-harmonic waves are precisely located at the lower edges of photonic bandgaps. The results of our numerical experiments show the optimal design problem can be solved efficiently based on crucial initial data given by some useful engineering intuitions. The SHG with high conversion efficiency is achieved by choosing the geometrical parameters of the elementary cell optimally and controlling the band structure of the PhC precisely.
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