When a pump laser shines upon a periodically poled lithium niobate (LN) thin plate nonlinear grating, second-harmonic generation (SHG) and its nonlinear diffraction occurs, with the nonlinear Raman–Nath diffraction (NRND), nonlinear Bragg diffraction (NBD), and nonlinear Cerenkov radiation (NCR) being several prominent examples. In this work we build and present a unified analytical theory to solve SHG for the NRND, NCR, and NBD processes from LN domains, domain walls, and defects. We find that the critical physical entity that governs the nonlinear diffraction is the effective nonlinear coefficient for each Fourier wave component. The analytical theory has a great generality and applicability scope. It allows us to retrieve and analyze everything about the dependence of SHG nonlinear diffraction on a series of physical and geometrical parameters such as the pump laser intensity, polarization, incidence polar and azimuthal angles, the LN thin plate thickness and its crystalline orientation, LN domain size and pitch, domain wall thickness and crystalline configuration, defect size and crystalline configuration, and the SHG diffraction beam angle and polarization. The analytical theory also enables us to analyze deeply the similarities and differences of the three nonlinear diffraction processes NRND, NCR, and NBD, build a smooth and broad connection bridge among these three processes, and construct a unified physical picture to understand, describe, and exploit these three processes of seemingly big difference. Besides, the analytical theory can be applicable to handle nonlinear diffraction by domains, domain walls, and defects in other more complicated 2D and 3D nonlinear gratings made from LN and other nonlinear crystals. Finally, the analytical theory can help to build a bridge connecting the extrinsic SHG nonlinear diffraction properties with the intrinsic domain poling and inversion material and physical properties of LN and other nonlinear crystals and explore novel nonlinear optical devices and technologies.
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