Theory of electrically controllable long-period gratings built in liquid-crystal fibers

A theory of electrically controllable long-period gratings built in a liqui d-crystal fiber has been presented by means of an anisotropic waveguide ana lysis! and the coupled-mode theory with the discretization method. Effectiv e propagation and coupling constants have been found for a circular cross-s ectional fiber with a nematic liquid-crystal core, the optic axis of which is in the direction of the fiber axis. The results show that when uniaxial perturbations of the liquid-crystal director exist in the core, the mode co uplings can occur between modes with different azimuth variations as well a s between modes with the same. Among them, the cross couplings between the fundamental core mode HE11CO and the transverse-magnetic cladding modes TMm cl are most strong compared even to the self-coupling of the fundamental co re mode, and thus the spectral shift with the growth of the director modula tion becomes negligible. Using the derived theoretical results, we discuss numerical examples of long-period liquid-crystal fiber gratings with respec t to the modulation depth of the director and the polarization states of th e fundamental core mode. (C) 2001 Society of Photo-Optical Instrumentation Engineers.