On the Dispersion Relations of Tapered Core Optical Fibers with Liquid Crystal Clad

The paper deals with the case of a three-layer liquid crystal tapered optical fiber (LCTOF) for which the dispersion relations are deduced corresponding to the TE and the TM modes. For the LCTOF under consideration, the outermost clad section is made of liquid crystal material with radial anisotropy whereas the core and the inner clad are homogeneous, non-magnetic and isotropic dielectric regions. Rigorous field expressions corresponding to different LCTOF sections are deduced, and the eigenvalue equations are reported followed by the modal behaviour of the guide in respect of the propagation constants and cutoff situations. Apart from that, a glimpse of the power confinement through the TE and the TM excitations in different fiber sections is also touched upon.