Mode Classification and Calculation in All-Solid Photonic Bandgap Fibers

• Published in: Journal of lightwave technology Vol. 30; no. 6; pp. 821 - 828
• Main Authors: Xing, Wenquan, Bai, Jinxu, Li, Yanfeng
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 15.03.2012; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; Circuit properties; Effective index model; Electric, optical and optoelectronic circuits; Electronics; Equations; Exact sciences and technology; finite difference method; Frequency conversion; Frequency division multiplexing; Fundamental areas of phenomenology (including applications); Indexes; Information, signal and communications theory; Integrated optics. Optical fibers and wave guides; Mathematical model; mode analysis; Multiplexing; Optical and optoelectronic circuits; optical fiber design; Optical fibers; Optical materials; Optics; phase matching; photonic bandgap fiber; Photonic bandgap materials; photonic crystal fiber; Physics; second harmonic generation; Signal and communications theory; Telecommunications and information theory; Integrated optics; Similarity; phase matching; Microstructured fiber; Boundary condition; Frequency division multiplexing; Implementation; photonic bandgap fiber; Fiber core; Optical fiber; photonic crystal fiber; Second harmonic generation; Step index; mode analysis; Phase tuning; Guided wave; Vector method; Waveguide; Cylindrical coordinate; Photonic crystal; Second harmonic; Analytical method; Effective index model; optical fiber design; Finite difference method
• ISSN: 0733-8724; 1558-2213
• DOI: 10.1109/JLT.2011.2179791

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 degenerate 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 μm. The phase matching condition is achieved between an index-guided fundamental HE 11 mode for the IR and a bandgap-guided higher-order HE 12 mode for the second harmonic. The fiber parameters determined by the EIM are confirmed by the FDM.