Tunable diffraction gratings and phase filters are important functional devices in optical communication and sensing systems. Polarization gratings, in particular, capable of redirecting an incident light beam completely into the first diffraction orders may be successfully fabricated in liquid crystalline cells assembled from substrates coated with uniform transparent electrodes and orienting layers that force a specific molecular distribution. In this work, the diffraction properties of liquid crystal (LC) cells characterized by a continually rotating cycloidal director pattern at the cell substrates and in the bulk, are studied theoretically by solving a relevant set of the Euler-Lagrange equations. The electric tunability of the gratings is analyzed by estimating the changes in liquid crystalline molecular distribution and thus in effective birefringence, as a function of external voltage. To the best of our knowledge, such detailed numerical calculations have not been presented so far for liquid crystal polarization gratings showing a cycloidal director pattern. Our theoretical predictions may be easily achieved in experimental conditions when exploiting, for example, photo-orienting material, to induce a permanent LC alignment with high spatial resolution. The proposed design may be for example, used as a tunable passband filter with adjustable bandwidths, thus allowing for potential applications in optical spectroscopy, optical communication networks, remote sensing and beyond.
Second-order integrable Lagrangians and WDVV equations
