Modelling of liquid crystal orientation in capillary tubes

Abstract

Photonic crystal fibers (PCFs) have attracted tremendous interest due to its unique optical properties in guiding the propagation of electromagnetic waves. Recently, liquid crystal (LC), an anisotropic material is infiltrated into the air holes of solid core PCFs in order to increase the tunability of the fibers. The high design flexibility of this fiber provides a lot of possibilities in manipulating the transmission of light.

In this report, the relevant literature review is covered. This part includes the details about the characteristics of both PCFs and LCs together with the numerical simulation method. Subsequently, a simple two-dimensional liquid crystal PCF (LCPCF) with triangular lattice is presented. Plane wave expansion method is th en employed to study the photonic bandgaps effect of this structure. The changing of dielectric tensors of LC due to the alignment of the director (i.e. the value of θc) is included in the study too.

Band structure of LCPCF for various θc is plotted by using Matlab. The matlab codes are attached in the Appendix section. Detailed investigation including the bandgaps shifting, polarization dependent bandgap splitting is discussed.

In addition, the approximate model for x- and y- polarization mode is proposed. It is found that the bandgap splitting occurs because of the high index difference between the extraordinary and ordinary refractive index of LC molecules. Besides, the core line and the radiation line are introduced to explain the propagation of light in LCPCF.