Numerical analysis for three-dimensional optical waveguides with periodic structure using Fourier series expansion method

• Published in: Electronics & communications in Japan. Part 2, Electronics Electronics, 2003-12, Vol.86 (12), p.22-31
• Main Authors: Miyamoto, Tokuo, Momoda, Michiko, Yasumoto, Kiyotoshi
• Format: Article
• Language: English
• Subjects: fiber grating; numerical analysis; three-dimensional periodic optical waveguide
• ISSN: 8756-663X; 1520-6432
• DOI: 10.1002/ecjb.10171

Three‐dimensional optical waveguides with an arbitrary cross section and a periodic configuration have been important as optical IC elements. However, it is not always easy to obtain highly accurate solutions for them without respect to the number of periods. In this paper, the Fourier series expansion method, improved for accurate numerical analysis independently of the number of periods introducing Floquet's theorem, is applied to a fiber grating and various thin‐film optical waveguides with index‐modulation‐type periodic structures and rectangular cross sections. The wavelength characteristics of the transmitted and reflected powers of the guided mode and the radiation field are derived at each period (40 to 1000). As a result, the wavelength characteristics of the power are made clear for periodic optical waveguides of embedded type and raised type with a glass or semiconductor substrate, including inhomogeneous cases. The algorithm thus proves to be useful for detailed analysis of various three‐dimensional periodic optical waveguides. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 86(12): 22–31, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.10171