Enhancement of second-harmonic generation in helical ferroelectric liquid-crystal cells under oblique incidence

A numerical method was introduced to study the second-harmonic generation (SHG) in helical ferroelectric liquid crystals. The level of approximation is the same as that of the 4 x 4 matrix method and any polarization conditions can be analyzed. A special phase matching of the SHG, which occurs when the fundamental and SH waves are located near the photonic band edges, was analyzed under the oblique incidence condition. For the material used in previous studies, numerical results showed some features at an incidence angle of 30 degrees. (1) Enhanced SHG is possible when the wavelength of SHG matches the dips near the edges of the total-reflection half-pitch band in the linear reflection spectra. (2) The SH peak intensity is expected to show d(3) dependence of cell thickness d.