Multiple-beam optical interferometry of anisotropic soft materials nanoconfined with the surface force apparatus

Soft anisotropic materials that change their macroscopic properties in response to external stimuli such as light, electric field, or pressure are central to several new directions of technology, including optics, micro-mechanics, and bioengineering. Responsiveness is fundamentally connected to the anisotropic ordering of the material's building blocks at the nanometer scale. Here we propose the surface force apparatus as a powerful tool for investigating optically anisotropic materials at the nanometer scale using multiple-beam optical interference, allowing for simultaneous determination of film thickness, alignment, and chiral rotation of the optical axis. We present a method based on 4 × 4 matrices for calculating the exact transmission and reflection coefficients for light incident normal to a planar optical multilayer comprising an arbitrary number of chiral anisotropic layers with the helical axis normal to the layer. The multilayer can also include uniform birefringent media, optical adsorbing (e.g., metals) and isotropic materials. We introduce a technique to analyze and interpret the complex multiple-beam interference patterns arising from such multilayers and demonstrate it for the case of a twisted nematic liquid crystal confined to nanoscale thickness with the surface force apparatus. The analysis opens the prospect of studying the effect of strong confinement on the structure and response of a wide class of anisotropic materials.