Photonic crystal fibers: Characterization and supercontinuum generation

Photonic crystals are periodic; dielectric structures that exhibit photonic bandgaps (PBGs), spectral regions within which light is forbidden to propagate inside the medium. As an exciting area in photonic crystals and fiber optics, photonic crystal fibers (PCFs, both index-guiding and PBG-guiding) have brought us many new opportunities by enabling new photonic devices for a range of applications. In this thesis, I investigated index-guiding PCFs in two respects: modeling their optical properties and studying supercontinuum (SC) generation in them.; As the first part of my research, I developed and/or applied several efficient methods in modeling and characterization of index-guiding PCFs, some of which can be easily applied in studying PBG-guiding PCFs. Based on a plane-wave expansion approach, I proposed a method by which one can obtain the effective cladding indices by solving the full-vector wave equation for a periodic cladding structure. This work improves the effective index model for the characterization of PCFs, which can provide insights into some of the interesting properties of PCFs, including "endlessly single mode operation" and novel dispersion properties. In order to rigorously model PCFs, however. one needs to solve the full-vector wave equation because the complex structures and high-index contrast make the scalar wave equation insufficient. To this end, I investigated two methods: multipole scattering method and full-vector finite-difference frequency-domain (FDFD) method. Both methods were demonstrated to be efficient and can accurately characterize linear optical properties of PCFs, including propagation constants, modal fields, dispersion, birefringence and modal area. I also studied birefringent properties of PCFs under squeezing or twisting by using a finite element, method. This study shows that, stress-induced linear birefringence in a PCF is reduced when compared to a standard fiber, and that twist-induced circular birefringence is enhanced in a PCF having small air-filling fraction in the cladding.; In the second part of the thesis research. I studied SC generation in PCFs. The high effective nonlinearity of a PCF due to the small core size can be combined with a shifted zero-dispersion wavelength (shifted to a wavelength region where high-power laser sources---Ti:sapphire femtosecond lasers---are available). This combination facilitates the generation of broadband SC spanning more than 2 octaves. Using a generalized scalar nonlinear Schrodinger equation, I first numerically studied the effect of input pulse frequency chirping on SC generation in PCFS. The simulations show that the SC bandwidth increases with linear chirping, and that the coherence of SC improves as linear chirping increases. Most interestingly, an optimal positive linear chirp is identified that maximizes the SC bandwidth, corresponding to the formation of only one red-shifting Raman soliton. Next I numerically investigated the polarization properties of SC spectra, generated in birefringent PCFs, by solving the generalized coupled nonlinear Schrodinger equations. The simulations illustrate the complicated polarization behavior across the SC spectrum and quantify the pulse-to-pulse polarization fluctuations in the presence of input noise. Finally I carried out an experimental study of the polarization properties in a birefringent PCF, achieving qualitative agreements with numerical simulations.