Regularization of Mixed-Potential Layered-Media Green's Functions for Efficient Interpolation Procedures in Planar Periodic Structures

The problem of improving the computational efficiency in the numerical analysis of planar periodic structures is investigated here using the mixed-potential integral-equation (MPIE) approach. A new regularization of the periodic Green's functions (PGFs) that are involved in the analysis of multilayered structures is introduced, based on the effective-medium concept. This regularization involves extracting the singularities of the PGFs up to second-order terms. The resulting regularized PGF is very smooth and amenable to interpolation. Thus, optimized interpolation procedures for the PGFs can be applied, resulting in a considerable reduction of computation time without any significant effect on the accuracy. Another benefit of the regularization is that it significantly enhances the convergence of the series for both the vector- and scalar-potential PGFs. The theoretical formulation is fully validated with various numerical results for both two-dimensional (2-D) and one-dimensional (1-D) layered-media periodic structures.

[1]  Chi Hou Chan,et al.  A numerically efficient technique for the method of moments solution for planar periodic structures in layered media , 1994 .

[2]  F. Capolino,et al.  Efficient computation of the 2-D Green's function for 1-D periodic structures using the Ewald method , 2005, IEEE Transactions on Antennas and Propagation.

[3]  G. Valerio,et al.  Methods for the accelerated computation of Green's functions with 2-D periodicity in layered media , 2006, 2006 First European Conference on Antennas and Propagation.

[4]  P. Yla-Oijala,et al.  Calculation of CFIE impedance matrix elements with RWG and n/spl times/RWG functions , 2003 .

[5]  Raed M. Shubair,et al.  Efficient computation of the periodic Green's function in layered dielectric media , 1993 .

[6]  S. Nam,et al.  Rapid calculation of the Green's function in the shielded planar structures , 1997 .

[7]  Sangwook Nam,et al.  Efficient calculation of the Green's function for multilayered planar periodic structures , 1998 .

[8]  H. Rogier,et al.  New Series Expansions for the 3-D Green's Function of Multilayered Media With 1-D Periodicity Based on Perfectly Matched Layers , 2007, IEEE Transactions on Microwave Theory and Techniques.

[9]  Tatsuo Itoh,et al.  Electromagnetic metamaterials : transmission line theory and microwave applications : the engineering approach , 2005 .

[10]  G. Vandenbosch,et al.  Semantics of dyadic and mixed potential field representation for 3-D current distributions in planar stratified media , 2003 .

[11]  A. Borji,et al.  Rapid calculation of the Green's function in a rectangular enclosure with application to conductor loaded cavity resonators , 2004, IEEE Transactions on Microwave Theory and Techniques.

[12]  D. F. Hays,et al.  Table of Integrals, Series, and Products , 1966 .

[13]  G. Valerio,et al.  Comparative Analysis of Acceleration Techniques for 2-D and 3-D Green's Functions in Periodic Structures Along One and Two Directions , 2007, IEEE Transactions on Antennas and Propagation.

[14]  D. Wilton,et al.  Electromagnetic scattering by surfaces of arbitrary shape , 1980 .

[15]  Juan R. Mosig,et al.  Periodic Green's function for skewed 3‐D lattices using the Ewald transformation , 2007 .

[16]  Ding,et al.  On evaluation of the Green function for periodic structures in layered media , 2004, IEEE Antennas and Wireless Propagation Letters.

[17]  R. Singh,et al.  On the use of Shank's transform to accelerate the summation of slowly converging series , 1991 .

[18]  Donald R. Wilton,et al.  Efficient computation of the 2D periodic Green's function using the Ewald method , 2006, J. Comput. Phys..

[19]  L. Felsen,et al.  Radiation and scattering of waves , 1972 .

[20]  G. Ogucu.  A New Spatial Interpolation Algorithm to Reduce the Matrix Fill Time in the Method of Moments Analysis of Planar Microstrip Structures , 2007, IEEE Transactions on Antennas and Propagation.

[21]  Donald R. Wilton,et al.  Efficient computation of the 3D Green's function for the Helmholtz operator for a linear array of point sources using the Ewald method , 2007, J. Comput. Phys..

[22]  P. Wynn,et al.  On a Procrustean technique for the numerical transformation of slowly convergent sequences and series , 1956, Mathematical Proceedings of the Cambridge Philosophical Society.

[23]  D. De Zutter,et al.  A fast converging series expansion for the 2-D periodic Green's function based on perfectly matched layers , 2004, IEEE Transactions on Microwave Theory and Techniques.

[24]  Roberto D. Graglia,et al.  On the numerical integration of the linear shape functions times the 3-D Green's function or its gradient on a plane triangle , 1993 .

[25]  Donald R. Wilton,et al.  Choosing splitting parameters and summation limits in the numerical evaluation of 1-D and 2-D periodic Green's functions using the Ewald method , 2008 .

[26]  P. P. Ewald.  Die Berechnung optischer und elektrostatischer Gitterpotentiale , 1921 .

[27]  K. Michalski,et al.  Electromagnetic scattering and radiation by surfaces of arbitrary shape in layered media. I. Theory , 1990 .

[28]  Krzysztof A. Michalski,et al.  Extrapolation methods for Sommerfeld integral tails , 1998 .

[29]  Krzysztof A. Michalski,et al.  Electromagnetic scattering and radiation by surfaces of arbitrary shape in layered media. II. Implementation and results for contiguous half-spaces , 1990 .

[30]  D. Wilton,et al.  Accelerating the convergence of series representing the free space periodic Green's function , 1990 .

[31]  D. Jackson,et al.  Leaky‐Wave Antennas , 2008 .

[32]  K. Michalski,et al.  Multilayered media Green's functions in integral equation formulations , 1997 .

[33]  Alp Kustepeli,et al.  On the splitting parameter in the Ewald method , 2000 .

[34]  P. Baccarelli,et al.  A full-wave numerical approach for modal analysis of 1-D periodic microstrip structures , 2006, IEEE Transactions on Microwave Theory and Techniques.

[35]  Alejandro Álvarez Melcón,et al.  Two techniques for the efficient numerical calculation of the Green's functions for planar shielded circuits and antennas , 2000 .

[36]  F. Bongard,et al.  Integral-Equation Analysis of 3-D Metallic Objects Arranged in 2-D Lattices Using the Ewald Transformation , 2006, IEEE Transactions on Microwave Theory and Techniques.

[37]  Paolo Baccarelli,et al.  Full-wave analysis of bound and leaky modes propagating along 2d periodic printed structures with arbitrary metallisation in the unit cell , 2007 .