Meshed index profile method for photonic crystal fibers with arbitrary structures

A meshed index profile method, which is based on the localized function method, is demonstrated for analyzing modal characteristics of photonic crystal fibers with arbitrary air-hole structures. The index profile of PCF, which is expressed as a sum of meshed unit matrix, is substituted to full wave equation. By solving this full wave equation, we obtain the modal characteristics of the PCF such as the mode field distribution, the birefringence and the waveguide dispersion. The accuracy of the proposed meshed index profile method (MIPM) is demonstrated by examining the effective index and the birefringence of the two degenerate fundamental modes in the PCF with a triangular air-hole lattice. The MIPM is not restricted to the PCF structure and will be useful in designing various PCF devices.