Structures in the meniscus of smectic membranes: the role of dislocations?

We report an experimental investigation of the structure of periodic patterns observed in the meniscus of free-standing smectic films. Combination of polarizing optical microscopy and phase shifting interferometry enabled us to obtain new information on the structure of the meniscus, and in particular, on the topography of the smectic-air interface. We investigate the profile of the undulations in the striped structure in the thin part of the meniscus, change of the stripe period with the meniscus thickness and subsequent transition into a two-dimensional structure. It is shown that the two-dimensional structure has an unusual complex profile of "egg-box" type. The striped texture occurs upon cooling from the nontilted smectic-A to the smectic-C* phase, whereas the two-dimensional pattern is present in both phases. We discuss the possible origin of the modulated structures, the role of the dislocations in the meniscus, the elasticity of smectic layers, and the mechanical stress induced by dislocations.