Calculation Of Transmission Modes In Photonic Crystal Fibers Containing Metamaterials

This thesis focuses on the numerical analysis for the transmission modes in photonic crystal fibers(PCFs),which are known as multi-hole fiber and micro-structure fiber.A special PCF with metamaterials,a kind of medium with different dielectric constant and permeability from ordinary materials,is investigated in our work.For the numerical research on PCFs,the finite element method is used to study the band structure of photonic crystals and transmission loss of PCFS,which are composed of ordinary materials and metamaterials.The mathematical model and numerical simulation method for efficient calculation of the photonic crystal bandgap are studied firstly.The main difficulties in this research include the solution of large-scale eigenvalue problems and the design of finite element algorithms for nano-structures with metamaterials.Based on the wave equation derived from Maxwell's equations,a finite element method is designed to solve the wave equation numerically and obtain the bandgap for photonic crystal structures.Our work includes physical model,mathematical analysis,finite element algorithm,optic property analysis and so on.Also,based on our numerical method,the negative refractive index range of photonic crystals is obtained by calculating the equal frequency surface.By solving the wave equation when the dielectric constant and permeability dependent on frequency,we also get the bandgap of a special photonic crystal structure.Furthermore,an optimal structure is proposed for the further application of photonic crystal structures.The numerical simulation of the transmission modes and loss of PFCs and the structural optimization design of PFCs are studied secondly.The main works of this part include designing numerical methods for the numerical solution of vector wave equations,dealing with the unbounded problem by PML techniques,and the optimal design of fiber structure with metamaterials.By using the vector finite element method to solve the vector wave equations,the confinement loss of photonic crystal fibers is calculated.For the unbounded problem,adding PML around the fiber makes the domain of such problem is bounded.The implement of the numerical simulation uses Comsol software,which is simple for transmission modes simulation and design based on the finite element methods.At a specific frequency of 1.55 microns,an optimal filling ratio range of optical fiber is obtained by analyzing the bandgap.The simulation results show that a better fiber structure is obtained compared with the original structure.Furthermore,the loss of fibers containing metamaterials at different filling rates is obtained by using our proposed methods.A simple and efficient method is presented to calculate transmission modes in photonic crystal fibers containing metamaterials.The simulation process also is a new approach to find an optimal PCF structure.