Method of Moments Simulation of Infinitely Periodic Structures Combining Metal With Connected Dielectric Objects

A method of moments (MoM) technique is described for the simulation of infinitely periodic structures made of complex elements, involving both metal and dielectric parts. A numerical approach based on the MoM was developed, using the EFIE formulation for metallic objects and a modified PMCHWT formulation for the air-dielectric interfaces. The method is also based on an efficient algorithm for the computation of the singly and doubly periodic Green's functions and their gradients. The use of such functions for both inside and outside problems enables the analysis of. structures where the dielectric volumes of successive cells are connected. The accuracy of the MoM approach is assessed in several cases, based on energy conservation checks and on comparisons with analytical models and data available in the literature. Examples are shown for arrays of disconnected and connected dielectric objects, dielectric electromagnetic band-gap (EBG) superstrates and dielectric slabs. Examples with metallic parts embedded in connected dielectric material are given in the case of frequency selective surfaces (FSS) and tapered-slot antennas.

[1]  Jin-Fa Lee,et al.  A symmetric FEM-IE formulation with a single-level IE-QR algorithm for solving electromagnetic radiation and scattering problems , 2004, IEEE Transactions on Antennas and Propagation.

[2]  Weng Cho Chew,et al.  A Coupled PEC-TDS Surface Integral Equation Approach for Electromagnetic Scattering and Radiation From Composite Metallic and Thin Dielectric Objects , 2006, IEEE Transactions on Antennas and Propagation.

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

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

[5]  R. Singh,et al.  On the use of Levin's T-transform in accelerating the summation of series representing the free-space periodic Green's functions , 1993 .

[6]  J. Vardaxoglou,et al.  Artificial magnetic conductor surfaces and their application to low-profile high-gain planar antennas , 2005, IEEE Transactions on Antennas and Propagation.

[7]  P de Maagt,et al.  Linear embedding via Green's operators: a modeling technique for finite electromagnetic band-gap structures. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  W. Merrill,et al.  Artificial versus natural crystals: effective wave impedance of printed photonic bandgap materials , 2000 .

[9]  F. Capolino,et al.  Analysis of directive radiation from a line source in a metamaterial slab with low permittivity , 2006, IEEE Transactions on Antennas and Propagation.

[10]  S. Singh,et al.  Efficient computation of the free-space periodic Green's function , 1991 .

[11]  F. Capolino,et al.  Accelerated computation of the free space Green's function of semi-infinite phased arrays of dipoles , 2006, IEEE Transactions on Antennas and Propagation.

[12]  Constantine A. Balanis,et al.  Analysis of singly and doubly periodic absorbers by frequency-domain finite-difference method , 1996 .

[13]  Gérard Tayeb,et al.  Combined Method for the Computation of the Doubly Periodic Green's Function , 2001 .

[14]  R. Mittra,et al.  Application of electromagnetic bandgap (EBG) superstrates with controllable defects for a class of patch antennas as spatial angular filters , 2005, IEEE Transactions on Antennas and Propagation.

[15]  M. Hakkak,et al.  Design of Compact Dual Band High Directive Electromagnetic Bandgap (EBG) Resonator Antenna Using Artificial Magnetic Conductor , 2007, IEEE Transactions on Antennas and Propagation.

[16]  Andrew J. Poggio,et al.  CHAPTER 4 – Integral Equation Solutions of Three-dimensional Scattering Problems , 1973 .

[17]  Yahya Rahmat-Samii,et al.  The evaluation of MFIE integrals with the use of vector triangle basis functions , 1997 .

[18]  Te-kao Wu,et al.  Scattering from arbitrarily‐shaped lossy dielectric bodies of revolution , 1977 .

[19]  Raj Mittra,et al.  Efficient calculation of the free-space periodic Green's function , 1990 .

[20]  X. Dardenne,et al.  Accelerated Computation of the Free Space Green's Function Gradient of Infinite Phased Arrays of Dipoles , 2006, IEEE Transactions on Antennas and Propagation.

[21]  D. Schaubert,et al.  An efficient computation scheme for the free space Green's function of a two-dimensional semiinfinite phased array , 2003 .

[22]  Lijun Zhang,et al.  Thin frequency-selective lattices integrated in novel compact MIC, MMIC, and PCA architectures , 1998 .

[23]  Hao Ling,et al.  Integral equation modeling of multilayered doubly-periodic lossy structures using periodic boundary condition and a connection scheme , 2004, IEEE Transactions on Antennas and Propagation.

[24]  John L. Volakis,et al.  Doubly periodic volume–surface integral equation formulation for modelling metamaterials , 2007 .

[25]  R. Harrington Time-Harmonic Electromagnetic Fields , 1961 .

[26]  Christophe Craeye,et al.  Finite Array Analysis Through Combination of Macro Basis Functions and Array Scanning Methods , 2008 .

[27]  X. Dardenne,et al.  Element pattern analysis of wide-band arrays with the help of a finite-by-infinite array approach , 2006, IEEE Transactions on Antennas and Propagation.

[28]  D. Schaubert,et al.  Analysis of the tapered slot antenna , 1986 .

[29]  D. Wilton,et al.  Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains , 1984 .

[30]  Christophe Craeye,et al.  On the receiving cross section of an antenna in infinite linear and planar arrays , 2004 .

[31]  C. Holloway,et al.  Reflection and transmission properties of a metafilm: with an application to a controllable surface composed of resonant particles , 2005, IEEE Transactions on Electromagnetic Compatibility.

[32]  John L. Volakis,et al.  Hybrid FE/BI modeling of 3-D doubly periodic structures utilizing triangular prismatic elements and an MPIE formulation accelerated by the Ewald transformation , 1999 .

[33]  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.

[34]  Jukka Sarvas,et al.  Surface Integral Equation Method for General Composite Metallic and Dielectric Structures with Junctions , 2005 .

[36]  G.S. Smith,et al.  An alternative approach for implementing periodic boundary conditions in the FDTD method using multiple unit cells , 2006, IEEE Transactions on Antennas and Propagation.

[37]  Ben A. Munk,et al.  Frequency Selective Surfaces: Theory and Design , 2000 .