Electro-optic response of a ferroelectric liquid crystal in thick free-standing films

We study the electro-optic response of a ferroelectric liquid crystal in free-standing films as thick as the helical pitch. In the films thicker than about one pitch, two relaxation modes are observed in the frequency spectra. The relaxation frequency of the slower mode decreases when increasing the film thickness, while that of the faster mode, which appears at approximately 1 kHz, is almost independent of the film thickness. In thinner films, a single relaxation mode is observed at several hundred Hz. The obtained relaxation spectra are discussed in comparison to the theoretical spectra of the phase mode in a system of finite length along the helical axis calculated by Urbanc and Žekš [Phys. Rev. E 52, 3892 (1995)].