Virtual boundary method for the analysis of elliptically cross-sectional photonic-crystal fibers with elliptical pores

This paper introduces a new semianalytical method for the analysis of propagation characteristics of elliptically cross-sectional photonic-crystal fibers (PCFs) with elliptical pores. This method known as a virtual boundary method (VBM) is based on the equivalency between an actual PCF and a three-layered, transversely inhomogeneous waveguide. The complicated refractive-index profile of the PCF is written as a double Fourier series, and an approximate separable wave equation is found in an elliptical coordinate system for the longitudinal field components. The exact solution to the derived equation is expressed in terms of higher order transcendental functions, such as regular and irregular Coulomb-wave functions and Mathieu functions. After having expressed all the field components, boundary conditions are imposed on the boundaries, and then, a transcendental equation for the propagation constant is derived, which is solved numerically. The validity of the method is ensured by comparing various quantities, such as effective indexes, modal birefringences, and electromagnetic field distributions, with those from an accurate full-vector finite-element method (FEM) simulator, showing relatively good agreement between the results. The method correctly confirms some of the unique PCFs´ properties, such as strong localization of light within the fiber and enhancement of modal birefringence as a function of the topology of hole arrangement.