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Second harmonic generation in nematic liquid crystals

Due to inversion symmetry, uniform nematic liquid crystals do not show second harmonic generation (SHG) in the bulk. The inversion symmetry may be broken by spatial variation of the director field. We have studied SHG in nematic cells with spatially periodic distortions of the director field. Cells were constructed with optically patterned alignment layers on the cell walls, and filled with the liquid crystal E7. Using 35 ps pulses from a mode-locked Nd:YAG laser at 1.06 microns, we observed bulk SHG, and measured the intensity and polarization of the SH signal as a function of angle, pump polarization and temperature. We propose a simple model for the symmetry breaking polarization and the resulting SHG, and consider phase matching in inhomogeneous periodic birefringent media.