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Analysis of Dielectric Layer PBG Structure Using Precise Integration

In: Computational Mechanics

Author

Listed:
  • H. W. Yang

    (Beijing University of Technology, College of Applied Sciences)

  • W. X. Zhong

    (Dalian University of Technology, State Key Laboratory of Structural Analysis for Industrial Equipment)

  • Y. K. Sui

    (Beijing University of Technology, College of Applied Sciences)

Abstract

PBG structure is a periodic dielectric structure designed to have photonic band gaps. The PBG structure was first studied in optical field and it is presently developed for use at microwave and millimeter-wave frequencies because the PBG is an electromagnetic band-gap. The analytical method of such structures is not always available. Thus the Finite-Difference Time-Domain (FDTD) method has been widely used. Unfortunately, when FDTD method is employed for the PBG filter structures, the curve of parameter S 21 (stop-band characteristics) would greatly oscillate. A huge number of iteration time steps are needed to attain a convergence solution of S 21 curve [1]. The precise integration algorithm [2, 3] is an effective arithmetic for matrix Riccati differential equations. In this paper, the precise integration algorithm is used to analyze the stop-band characteristic of dielectric layer PBG structure in waveguide as shown in Figure. This kind of PBG filter was widely studied since it is easy to design and manufacture. First, a dielectric layer and an air layer are treated as sub-structure respectively. Then transverse section is discretized by regular edge element. The longitudinal variables are eliminated and mixed energy is introduced. The stiff matrices of a dielectric layer and an air layer can be calculated by the precision integration based on Riccati equations in Hamilton system. The stiff matrices of a period can be obtained by the combination of substructures, and then the whole structure can be solved with boundary conditions. This method can dramatically reduce the unknown variables of the equations because of only needing transverse discretization for the problem. Examples show its precision and efficiency. The precise integration, finite element method and Hamilton system are introduced to the field of PBG structure successfully.

Suggested Citation

  • H. W. Yang & W. X. Zhong & Y. K. Sui, 2007. "Analysis of Dielectric Layer PBG Structure Using Precise Integration," Springer Books, in: Computational Mechanics, pages 414-414, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-75999-7_214
    DOI: 10.1007/978-3-540-75999-7_214
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