Abstract

Abstract. Waveguides play one of the key figures in today's electronics and optics for signal transmission. Corresponding simulations of electromagnetic wave transportation along these waveguides are accomplished by discretization methods such as the Finite Integration Technique (FIT) or the Finite Element Method (FEM). For longitudinally homogeneous and transversely unbounded waveguides these simulations can be approximated by closed boundaries. However, this distorts the original physical model and unnecessarily increases the size of the computational domain size. In this article we present a boundary condition for transversely open waveguides based on the Kirchhoff integral which has been implemented within the framework of FIT. The presented solution is compared with selected conventional methods in terms of computational effort and memory consumption.

Highlights

  • In order to quantify electromagnetic wave propagation in longitudinally homogeneous waveguides, simulations are performed on a two-dimensional domain

  • Unbounded waveguides such as the microstrip-line displayed in Fig. 1 or an on-chip open waveguide are often physically not enclosed by shields

  • The required calculation is performed on a computational domain that consists in the considered case of a face and corresponding boundary conditions, by which the solution is defined

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Summary

Introduction

In order to quantify electromagnetic wave propagation in longitudinally homogeneous waveguides, simulations are performed on a two-dimensional domain. Unbounded waveguides such as the microstrip-line displayed in Fig. 1 or an on-chip open waveguide are often physically not enclosed by shields. For numerical simulations a tailored boundary condition has to be considered. The two-dimensional problem of transversely unbounded waveguide can be calculated in terms of an eigenvalue problem. The required calculation is performed on a computational domain that consists in the considered case of a face and corresponding boundary conditions, by which the solution is defined. In contrary to closed waveguides, numerically efficient and physically correct representations of

Conventional solutions
Closed boundary conditions
Absorbing boundary conditions
Enhanced solution approach
Fundamentals of the Kirchhoff integral
Finite integration technique
Kirchhoff integral used as an open boundary condition for FIT
Computational examples
Investigation of KIR properties
Solution of the nonlinear eigenvalue problem
Distance to the boundary
KIR for symmetrical structures
Reduction of reference sources
Sources of KIR approximations
Numerical derivative of the electric field strength
Numerical integration of the electric field strength
Numerical integration of the Green’s function
Applications of KIR
Transmission line
Optical waveguide
Microstrip line
Conclusions
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