Optical analysis of spatially periodic patterns in nematic liquid crystals: diffraction and shadowgraphy.

Optical methods are most convenient for analyzing spatially periodic patterns with wave vector q in a thin layer of a nematic liquid crystal. In the standard experimental setup a beam of parallel light with a “short” wavelength λ � 2π/q passes the nematic layer. Recording the transmitted light the patterns are either directly visualized by shadowgraphy or characterized more indirectly by the diffraction fringes due to the optical-grating effects of the pattern. In this work we present a systematic short-wavelength analysis of these methods for the commonly used planar orientation of the optical axis of liquid crystal at the confining surfaces. Our approach covers general three-dimensional experimental geometries with respect to the relative orientation of q and of the wave vector k of the incident light. In particular, we emphasize the importance of phase-grating effects, which are not accessible in a pure geometric optics approach. Finally, as a by-product we present also an optical analysis of