Modeling and Simulation of Photonic Crystal Fibers and Distributed Feedback Photonic Crystal Fiber Lasers

A photonic crystal fiber (PCF) is comprised of a solid or air core surrounded by periodically arranged air holes running along the length of the fiber, which guides light in a fundamentally new way compared to conventional optical fibers, affecting almost all areas of optics and photonics. To analyze the dispersion and loss properties of PCFs, a two-dimensional (2D) finite-difference frequency-domain (FDFD) method combined with the technique of perfectly matched layer (PML) is developed. The propagation constant and loss can be obtained with accuracies in the orders of ∼10-6 and ∼10 -3, respectively. The Bragg fiber is a kind of PCF with alternate layers surrounding a solid or air core. To improve the performance of the above algorithm, a 1D FDFD method in the cylindrical coordinates is proposed to fully utilize the rotational symmetry property of the Bragg fiber. In addition to improving the accuracy, this method reduces the computation region from 2D to a straight line, significantly relieving the computation burden. A second method, called Galerkin method, is also developed under cylindrical coordinates. The mode fields are expanded using orthogonal Laguerre-Gauss functions; and the method is accurate and stable. However, it cannot do the loss analysis. For photonic-band-gap-guiding PCFs, the properties of the confined modes are closely related to the band structures of the cladding photonic crystals. Therefore, a third FDFD method using periodic boundaries is developed in a generalized coordinate system. Various lattice geometries are analyzed in the same manner, and the results are comparable to those obtained by the plane wave expansion method which is commonly used in the literature. Finally, a theoretical model for analyzing distributed feedback (DFB) PCF lasers has been presented. Two structures are investigated: PCFs with triangular lattice (TPCF) and PCFs made of capillary tube (CPCF). The modeling and simulation of erbium-doped and erbium/ytterbium (Er/Yb) co-doped DFB lasers are aimed at finding suitable PCF geometry to achieve low threshold and high output power. Various steps involved in this model are: (1) the properties of PCFs are analyzed by the FDFD method; (2) the Bragg grating is investigated by coupled mode theory; (3) the coupled wave equations are solved by transfer matrix method; and (4) Er atom is modeled as a three-level medium while energy transfer between Yb and Er atoms is considered for Er/Yb co-doped fiber. It is found that a CPCF laser with a smaller mode area is useful for lower-threshold applications and both of CPCF and TPCF lasers with larger mode areas are suitable for high-power operation