Analysis of Leaky Modes in Photonic Crystal Fibers Using the Surface Integral Equation Method

Jung-Sheng Chiang

doi:10.3390/cryst8040177

Abstract

A fully vectorial algorithm based on the surface integral equation method for the modelling of leaky modes in photonic crystal fibers (PCFs) by solely solving the complex propagation constants of characteristic equations is presented. It can be used for calculations of the complex effective index and confinement losses of photonic crystal fibers. As complex root examination is the key technique in the solution, the new algorithm which possesses this technique can be used to solve the leaky modes of photonic crystal fibers. The leaky modes of solid-core PCFs with a hexagonal lattice of circular air-holes are reported and discussed. The simulation results indicate how the confinement loss by the imaginary part of the effective index changes with air-hole size, the number of rings of air-holes, and wavelength. Confinement loss reductions can be realized by increasing the air-hole size and the number of air-holes. The results show that the confinement loss rises with wavelength, implying that the light leaks more easily for longer wavelengths; meanwhile, the losses are decreased significantly as the air-hole size d/Λ is increased.

Highlights

Leaky modes are modes that propagate in the guide irradiating power and decay exponentially along the direction of propagation
There is proposed a fully vectorial algorithm based on the surface integral equation method that is able to calculate the confinement loss and complex effective refractive index of photonic crystal fibers (PCFs)
As complex root examination is the key technique in the solution, this new algorithm possesses this technique and can be utilized for solving the leaky modes of photonic crystal fibers

Summary

Introduction

Leaky modes are modes that propagate in the guide irradiating power and decay exponentially along the direction of propagation. PCFs exhibit a lot of remarkable properties, such as an endless single-mode, unusual chromatic dispersion effect, design flexibility, supercontinuum generation, an extremely large or small effective core area at the single-mode region, and high nonlinearity [18,19,20,21] These distinctive features of PCFs have promising applications in a variety of fields, from communication fiber links to optoelectronic devices. There is proposed a fully vectorial algorithm based on the surface integral equation method that is able to calculate the confinement loss and complex effective refractive index of PCFs. The new algorithm can model the leaky modes of PCFs with a finite number of air-holes. It can analyze how the confinement loss by the imaginary part of the effective refractive index changes with air-hole size, the number of air-hole rings, and wavelength

Surface Integral Equation Formulation

Dispersion forfor a PCF with twotwo air-hole rings

Diagram

Conclusions