Nematic bend-splay elasticity near the nematic-smectic-Atransition

Magnetic-field-induced bend-splay deformation experiments are presented which show that the linear Frank-Oseen theory of nematic curvature elasticity is valid near a continuous nematic-smectic-$A$ transition where smectic fluctuations dominate the bend elasticity. The results are compared with the Chu-McMillan criterion for the limit of linear response based on the smectic-$A$ superconductivity analogy. It is shown that the success of the linear theory may be due to the unexpectedly small values of the longitudinal and transverse correlation lengths found in recent x-ray experiments.