Doubly periodic volume-surface integral equation formulation for modelling metamaterials

IET Microwaves, Antennas and Propagation

Volumn 1, Issue 1, 2007, Pages 150-157

  Usner, B C ^a   Sertel, K ^a   Volakis, J L ^a  

^a The Ohio State University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPIC MATERIAL; BOUNDARY INTEGRALS; COMPLEX DESIGNS; DOUBLY PERIODIC; FILL TIME; FINITE ELEMENT; GEOMETRICAL MODELLING; HIGH CONTRAST; MATRIX; METALLIC INCLUSIONS; PERIODIC GREEN'S FUNCTION; PIECEWISE HOMOGENEOUS MATERIAL; SURFACE CURRENT; TYPICAL DESIGN; VOLUME INTEGRAL EQUATION; VOLUME SURFACE INTEGRAL EQUATIONS;

DIFFERENTIAL EQUATIONS; GREEN'S FUNCTION; METAMATERIALS; OPTICAL ANISOTROPY; SURFACES;

INTEGRAL EQUATIONS;

EID: 49849094203     PISSN: 17518725     EISSN: 17518733     Source Type: Journal    
DOI: 10.1049/iet-map:20050344     Document Type: Article

References (47)

1. Monk, B.A.: 'Frequency selective surfaces, theory and design', (John Wiley & Sons, New York 2000)
2. Monk, B.A.: Finite antenna arrays and FSS, (John Wiley & Sons, New York 2003)
3. Mittra, R., Chan, C.H., and Cwik, T.: 'Techniques for analyzing frequency selective surfaces - a review', Proc. IEEE, 1988, 76, (12), p. 1593-16150018-9219
4. Tretyakov, S.A.: 'Meta-materials with wideband negative permittivity and permeability', Microw. Opt. Technol. Lett., 2001, 31, (3), p. 163-16510.1002/mop.1387 0895-2477
5. Holloway, C.L., Kuester, E.F., Jarvis, J.B., and Kabos, P.: 'A double negative (DNG) composite medium composed of magnetodielectric spherical particles embedded in a matrix', IEEE Trans. Antennas Propag., 2003, 51, (10), p. 2596-260310.1109/TAP.2003.817563 0018-926X
6. Figotin, A., and Vitebskiy, I.: 'Electromagnetic unidirectionality in magnetic photonic crystals', Phys. Rev. B, 2003, 67, (16), p. 16521010.1103/PhysRevB.67.165210
7. Gedney, S.D., and Mittra, R.: 'Analysis of the electromagnetic scattering by thick gratings using a combined FEM/MM solution', IEEE Trans. Antennas Propag., 1991, 39, p. 1605-161410.1109/8.102776 0018-926X
8. Jin, J.M., and Volakis, J.L.: 'Scattering and radiation analysis of three-dimensional cavity arrays via a hybrid finite-element method', IEEE Trans. Antennas Propag., 1993, 41, (11), p. 1580-158610.1109/8.267360 0018-926X
9. Lucas, E.W., and Fontana, T.P.: 'A 3-d hybrid finite element/boundary element method for the unified radiation and scattering analysis of general infinite periodic arrays', IEEE Trans. Antennas Propag., 1995, 43, (2), p. 145-15310.1109/8.366376 0018-926X
10. Eibert, T.F., and Volakis, J.L.: 'Fast spectral domain algorithms for rapid solution of integral equations', Electron. Lett., 1998, 34, (13), p. 1297-129910.1049/el:19980934 0013-5194
11. Eibert, T.F., Volakis, J.L., Wilton, D.R., and Jackson, D.R.: 'Hybrid FE/BI modeling of 3-D doubly periodic structures utilizing triangular prismatic elements and an MPIE formulation accelerated by the Ewald transformation', IEEE Trans. Antennas Propag., 1999, 47, (5), p. 843-85010.1109/8.774139 0018-926X
12. Eibert, T.F., and Volakis, J.L.: 'Fast spectral domain algorithm for hybrid finite elements/boundary integral modeling of doubly periodic structures', IEE Proc., Microw. Antennas Propag., 2000, 147, (5), p. 329-3341350-2417
13. Poggio, A.J., and Miller, E.K.: 'Integral equation solution of three dimensional scattering problems', (Permagon, Elmsford, NY 1973), 4
14. Chang, Y., and Harrington, R.F.: 'A surface formulation for characteristic modes of material bodies', IEEE Trans. Antennas Propag., 1997, 25, p. 789-79510.1109/TAP.1977.1141685 0018-926X
15. Wu, T.K., and Tsai, L.L.: 'Scattering from arbitrarily-shaped lossy dielectric bodies of revolution', Radio Sci., 1977, 12, p. 709-7180048-6604
16. Jørgenson, R.E., and Mittra, R.: 'Scattering from structured slabs having 2-dimensional periodicity', IEEE Trans. Antennas Propag., 1991, 39, p. 151-1570018-926X
17. Kuster, E.J., Wang, J.J.H., and Tripp, V.K.: 'Triangular surface-patch modeling for phased-arrays and other planar periodic structures with arbitrary elements', J. Electromagn. Waves Appl., 1992, 26, p. 1607-16190920-5071
18. Kipp, R.A., and Chan, C.H.: 'A numerically efficient technique for the method of moments solution for planar periodic structures in layered media', IEEE Trans. Microw. Theory Tech., 1994, 42, p. 635-64310.1109/22.285070 0018-9480
19. Janaswamy, R.: 'Oblique scattering from lossy periodic surfaces with application to anechoic chamber absorbers', IEEE Trans. Antennas Propag., 1992, 40, p. 162-1690018-926X
20. Moore, J., Ling, H., and Liang, C.S.: 'The scattering and absorption characteristics of material-coated periodic gratings under oblique-incidence', IEEE Trans. Antennas Propag., 1993, 41, p. 1281-128810.1109/8.247755 0018-926X
21. Marly, N., Zutter, D.D., and Pues, H.F.: 'A surface integral equation approach to the scattering and absorption of doubly periodic structures', IEEE Trans. Electromagn. Compat., 1994, 36, (1), p. 14-2210.1109/15.265475 0018-9375
22. Marly, N., Baekelandt, B., Zutter, D.D., and Pues, H.F.: 'Integral equation modeling of the scattering and absorption of multilayered doubly-periodic lossy structures', IEEE Trans. Antennas Propag., 1995, 43, (11), p. 1281-12870018-926X
23. Yang, C.F., Burnside, W.D., and Rudduck, R.C.: 'A periodic moment method solution for TM scattering from lossy dielectric bodies with application to wedge absorber', IEEE Trans. Antennas Propag., 1992, 40, p. 652-66010.1109/8.144599 0018-926X
24. Yang, C.F., Burnside, W.D., and Rudduck, R.C.: 'A doubly periodic moment method solution for the analysis and design of an absorber covered wall', IEEE Trans. Antennas Propag., 1993, 41, p. 600-60910.1109/8.222279 0018-926X
25. Yang, H.D., Diaz, R., and Alexopoulos, N.G.: 'Reflection and transmission of waves from multilayer structures with planar-implanted periodic material blocks', J. Opt. Soc. Am. B, 1997, 14, (10), p. 2513-2521
26. Jordan, K.G., Richter, G.R., and Sheng, P.: 'An efficient numerical evaluation of the Green's function for the helmholtz operator on periodic structures', J. Comp. Phys., 1986, 63, p. 222-235
27. Singh, S., Richards, W.F., Zinecker, J.R., and Wilton, D.R.: 'Accelerating the convergence of series representing the free space periodic Green's function', IEEE Trans. Antennas Propag., 1990, 38, p. 1958-19620018-926X
28. Mathis, A.W., and Peterson, A.F.: 'A comparison of acceleration procedures for the two-dimensional periodic Green's function', IEEE Trans. Antennas Propag., 1996, 44, p. 567-5710018-926X
29. Mathis, A.W., and Peterson, A.F.: 'Efficient electromagnetic analysis of a doubly infinite array of rectangular apertures', IEEE Trans. Microw. Theory Tech., 1998, 46, (1), p. 46-5410.1109/22.654921 0018-9480
30. Wallinga, G.S., Rothwell, E.J., Chen, K.M., and Nyquist, D.P.: 'Efficient computation of the two-dimensional periodic Green's function', IEEE Trans. Antennas Propag., 1999, 47, (5), p. 895-8970018-926X
31. Trintinalia, L.C., and Ling, H.: 'Integral equation modeling of multilayered doubly-periodic lossy structures using periodic boundary condition and a connection scheme', IEEE Trans. Antennas Propag., 2004, 52, (9), p. 2253-226110.1109/TAP.2004.834147 0018-926X
32. Wang, T.M., and Ling, H.: 'Electromagnetic scattering from 3-dimensional cavities via a connection scheme', IEEE Trans. Antennas Propag., 1991, 39, p. 1505-151310.1109/8.97382 0018-926X
33. Cwik, T.A., and Mittra, R.: 'Scattering from periodic array of free standing arbitrarily shaped perfectly conducting or resistive patches', IEEE Trans. Antennas Propag., 1987, 35, p. 1226-123410.1109/TAP.1987.1143999 0018-926X
34. Usner, B.C., Sertel, K., Carr, M., and Volakis, J.L.: 'Generalized volume-surface integral equation for modeling inhomogeneities within high contrast composite structures', IEEE Trans. Antennas Propag., 2006, 54, (1), p. 68-7510.1109/TAP.2005.861579 0018-926X
35. Ewald, P.P.: 'Die berechnung optischer und elektrostatischen gitterpotentiale', Ann. Phys., 1921, 64, p. 253-258
36. Kolundžija, B.M.: 'Electromagnetic modeling of composite metallic and dielectric structures', IEEE Trans. Microw. Theory Tech., 1999, 47, (7), p. 1021-103210.1109/22.775434 0018-9480
37. Carr, M., Topsakal, E., and Volakis, J.L.: 'A procedure for modeling material junctions in 3-D surface integral equation approaches', IEEE Trans. Antennas Propag., 2004, 52, (5), p. 1374-137910.1109/TAP.2004.827247 0018-926X
38. Shin, J., Glisson, A.W., and Kishk, A.A.: 'Generalization of surface junction modeling for composite objects in an SIE/MoM formulation using a systematic approach', ACES J., 2005, 20, (1), p. 1-12
39. Antilla, G.E., and Alexopoulos, N.G.: 'Scattering from complex three-dimensional geometries by a curvilinear hybrid finite-element-integral equation approach', J. Opt. Soc. Am. A, 1994, 11, p. 1445-1457
40. Sertel, K., and Volakis, J.L.: 'Method of moments solution of volume integral equations using parametric geometry modeling', Radio Sci., 2002, 37, (1), p. 101-1070048-6604
41. Song, J.M., and Chew, W.C.: 'Moment method solutions using parametric geometry', J. Electromagn. Waves Appl., 1995, 9, (1), p. 71-830920-5071
42. Usner, B.C., Sertel, K., and Volakis, J.L.: 'Conformal Galerkin testing for VIE using parametric geometry', Electron. Lett., 2004, 40, (15), p. 926-92710.1049/el:20045004 0013-5194
43. Milton, G.: 'The theory of composites', (Cambridge University Press 2002)
44. Lewin, L.: 'The electrical constants of a material loaded with spherical particles', Proc. Inst. Elec. Eng., 1947, 94, p. 65-68
45. Veselago, V.G.: 'The electrodynamics of substances with simultaneously negative values of ε and μ', Usp. Fiz. Nauk., 1967, 92, p. 517-5260042-1294
46. Jylha, L., Kolmakov, I., Maslovski, S., and Tretyakov, S.: 'Modeling of isotropic backward-wave materials composed of resonant spheres', 2005 July), arXiv:cond-mat/0507324v1
47. Eleftheriades, G.V., and Balmain, K.G.: 'Negative refraction metamaterials: fundamental principles and applications', (Wiley-IEEE Press 2005)