A DAUBECHIES'-WAVELET-BASED TIME DOMAIN ELECTROMAGNETIC FIELD MODELING TECHNIQUE

Numerical analysis has become an important technique for the modeling of electromagnetic field. However, there still exist many restrictive factors that make numerical analysis difficult to apply to practical problems. The finite-difference time-domain (FDTD) technique [1] and the transmission line matrix method [2] have been applied to many problems and proven to be promising techniques by virtue of their versatility. However for modeling electrically large structures, they are often restricted by memory shortage like other space-discretization methods. The multi-resolution time-domain (MRTD) method based on the Battle-Lemarie wavelets [3] has a highly linear numerical dispersion property. It has been demonstrated that, with this technique, space discretization with only a few cells per wavelength gives accurate results, leading to a reduction of both memory requirement and computation time. Recently, the wavelet-Galerkin scheme based on Daubechies’ compactly supported wavelet with two vanishing moments (D2) was proposed by Cheong et.al. [4]. Although the numerical dispersion of this technique is larger than that of the MRTD method, it has advantages over MRTD in that the Daubechies’ scaling function has compact support, and the stencil size or the number of coefficients in the timeevolution equations is kept to a minimum. Cheong’s method also adopts the so-called “shifted interpolation property”, which enables local field sampling in spite of the asymmetry of the Daubechies’ scaling function and a support larger than unity; with this property, the evaluation of the constitutive equations can be omitted even for inhomogeneous media. The authors have already extended the method to the use of Daubechies’ scaling functions with three and four vanishing moments (denoted as D3 and D4, respectively) [5]. By using basis functions of higher regularity and minimum support, better accuracy and minimum stencil sizes can be expected, resulting in an optimally efficient algorithm. In this paper, a three-dimensional formulation of the wavelet-Galerkin scheme is presented with an implementation of uniaxial perfectly matched layer (UPML) absorbing boundary conditions (ABC) [6]. The accuracy of the present method is first verified, and then it is applied to the analysis of an electricallylarge optical waveguide, which is too expensive to solve with the conventional FDTD method, and the advantage of the present method is demonstrated. This is, to the best of authors’ knowledge, the first attempt to apply the wavelet based approach to the full-wave time-domain analysis of electrically large inhomogeneous structures such as optical waveguides.