Simultaneous Observation of Molecular Tilt and Azimuthal Angle Distributions in Spontaneously Modulated Liquid-Crystalline Langmuir Monolayers

We carried out the first quantitative measurements of correlated modulations of molecular tilt and azimuthal angles in two-dimensional smectic- $C$ Langmuir monolayers using simultaneous linear- and circular-polarized reflected light microscopy. For spontaneously formed stripes and higher-order point defects, the tilt angle varies nearly sinusoidally at twice the spatial frequency of the azimuthal rotation. The tilt modulation grows as the second power of the modulation wave number and leads to a large escaped core for the point defect. Our results can be explained by an extended Landau theory of tilted smectics.