Linear and nonlinear diffraction gratings in lithium niobate single crystals with a periodic domain structure

An investigation was made of the Bragg diffraction of light by a periodic structure formed by ferroelectric domains in LiNbO$^3$ crystals. The intensities of fifteen Bragg orders were measured at the 633 nm wavelength. The synthesised grating profile had two refractive index peaks ($0.2$ and $0.5$ $\mu$m wide) per period. The peaks were attributed to positively and negatively charged domain walls, revealed by etching a Y-cut crystal. The nonlinear grating profile, i.e. the profile of the spatial modulation of the quadratic nonlinearity $\hat{\chi}^{(2)}$, was determined.