Fluctuations of a homeotropically aligned nematic liquid crystal in the presence of an applied voltage

We determined the refractive-index structure-factor $S_n(\bf k)$ from shadowgraphs of fluctuations in a layer of a homeotropically aligned nematic liquid crystal with negative dielectric anisotropy in the presence of an ac voltage of amplitude $V_0$ applied orthogonal to the layer. $S_n(\bf k)$ had rotational symmetry. Its integral $P(V_0)$ and amplitude $B(V_0)$ increased smoothly through the Fr\'eedericksz transition at $V_0 = V_F$. Its inverse width $\xi(V_0)$ and its relaxation rate $\Gamma_0(V_0)$ had cusps but remained finite at $V_F$. The results are inconsistent with the critical mode at a second-order phase transition.