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Theoretical Analysis of Effect of Domain Inversion Shape on Second Harmonic Generation Conversion Efficiencies of Quasi-Phase-Matched Nonlinear Optical Waveguide Devices

The effect of domain inversion shape on the SHG conversion efficiencies of QPM nonlinear waveguide devices is theoretically analyzed. Three domain inversion shapes, namely elliptic, sine and arc, are considered in this analysis. The duty cycle α(x) is derived for each case and the periodic modification of the nonlinear coefficient is taken as a binary square function. To simplify the calculation of the integral overlap between the domain-inverted regions and the guided modes, a highly confined mode and a Gaussian mode are used. The SHG conversion efficiencies are theoretically plotted against the duty cycle α0 for various mode width/waist. The results show that the optimal duty cycle α0 for maximum SHG efficiency is shape-dependent. This implies that, in order to obtain large harmonic intensities, it is necessary to identify the domain inversion shape associated with a particular fabrication process before the QPM structure can be optimized by choosing the appropriate grating duty cycle.