Mode Classification and Calculation in All-Solid Photonic Bandgap Fibers

Abstract—The classification and calculation of the core modes of all-solid photonic bandgap fibers (ASPBFs) are addressed. The first 12 modes of a multimode ASPBF are calculated by a full-vector finite difference method (FDM) using a Yee’s cell in cylindrical coordinates. The modes of the ASPBFs are labeled in analogy with step-index fibers based on their mode profile similarities, and are classified into nondegenerate modes or degen-erate pairs according to the minimum waveguide sectors and the associated boundary conditions based on results from symmetry analysis. Furthermore, an analytical effective index model (EIM) for ASPBFs can be formulated, which yields highly accurate results in calculating the effective indices of those 12 modes. The advantages of simple and fast implementation of the EIM are demonstrated by designing ASPBFs that can be used in second harmonic generation for a source wavelength of 1.06 m. The phase matching condition is achieved between an index-guided fundamental mode for the IR and a bandgap-guided higher-order mode for the second harmonic. The fiber parameters determined by the EIM are confirmed by the FDM. Index Terms—Effective index model, finite difference method, mode analysis, optical fiber design, phase matching, photonic bandgap fiber, photonic crystal fiber, second harmonic generation. I