Optical-field-enhanced and static-field-induced first-order Fréedericksz transitions in a planar parallel nematic liquid crystal

It is shown that the purely static (magnetic or electric) field-induced Fréedericksz transition in a planar parallel oriented nematic-liquid-crystal cell is always second order. But with an additional optical field, the magnetic-field-induced Fréedericksz transition can become first order and bistable. For the electric field, if 9ν/4>w>0, the electric-field-induced first-order transition can be enhanced by the optical field, where ν=($n_c$/$n_o$ ${)}^2$-1, w=${\epsilon }_{?}$/${\epsilon }_{\perp }$-1, $n_o$ and $n_c$ are the ordinary and extraordinary indices of refraction, ${\epsilon }_{\perp }$ and ${\epsilon }_{?}$ are the dielectric constants perpendicular and parallel to the local nematic director. The exact and small-angle approximate solutions describing the nematic’s orientation are obtained. The first-order transition enhancement tricritical optical field intensity and criterion are also given.