The design of maxwellian absorbers for numerical boundary conditions and for practical applications using engineered artificial materials

IEEE Transactions on Antennas and Propagation

Volumn 45, Issue 4, 1997, Pages 656-671

  Ziolkowski, Richard W ^a  

^a University of Arizona   (United States)

Author keywords

Absorbing media; Electromagnetic theory; Numerical analysis

Indexed keywords

BANDWIDTH; BOUNDARY CONDITIONS; ELECTRIC CONDUCTIVITY OF SOLIDS; ELECTROMAGNETIC WAVE ABSORPTION; ELECTROMAGNETIC WAVE POLARIZATION; MAXWELL EQUATIONS; NUMERICAL ANALYSIS;

ARTIFICIAL MATERIALS; MAXWELLIAN ELECTROMAGNETIC WAVES;

ELECTROMAGNETIC FIELD THEORY;

EID: 0031117522     PISSN: 0018926X     EISSN: None     Source Type: Journal    
DOI: 10.1109/8.564092     Document Type: Article

References (51)

1. E. Michielssen, J.-M. Sajer, S. Ranjithan, and R. Mittra, "Design of lightweight, broad-band microwave absorbers using genetic algorithms," IEEE Trans Antennas Propagat., vol. 41, pp. 1024-1031, June 1993.
2. I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Vitanen, Electromagnetic Waves in Chiral and Bi-isotropic Media. Boston, MA: Artech House, 1994, pp. 8-14.
3. F. Mariotte, P. Pelet, and N. Engheta, "A review of recent study of guided waves in chiral media," in Bianisotropic Bi-Isotropic Media and Applications, J. A. Kong and A. Priou, Eds. Electromagn. Waves PIER 9, Progress Electromagn. Res., 1994, pp. 311-350.
4. F. Mariotte, "Matériaux chiraux àstructureshétérogènes: modélizations et applications," Ph.D. dissertation, Bordeaux, France, Mar. 1994.
5. F. Mariette, S. A. Tretyakov, and B. Sauviac, "Isotropie chiral composite modeling: Comparison between analytical, numerical, and experimental results," Microwave Opt. Technol. Lett., vol. 7, no. 18, pp. 861-864, Dec. 1994.
6. S. A. Tretyakov and F. Mariotte, "Maxwell Garnett modeling of uniaxial chiral composites with bianisotropic inclusions," J. Electromagn. Waves Applicat., vol. 9, no. 7/8, pp. 1011-1025, 1995.
7. F. Mariotte, F. Guérin, P. Bannelier, and A. Bourgeade, "Numerical computations of the electromagnetic field scattered by complex chiral bodies," J. Electromagn. Waves Applicat., vol. 9, no. 11/12, pp. 1459-1485, NovVDec. 1995.
8. Proc. Chiral'94 Workshop 3rd Int. Workshop Chiral, Bi-isotropic Bianisotropic Media, Le Barp France, May 18-20, 1994, F. Mariotte and J.-P. Parneix, Eds., Pergueux France, C.E.A./C.E.S.T.A.
9. R. E. Raab and J. H. Cloete, "An eigenvalue theory of circular birefringence and dichroism in a nonmagnetic chiral media," J. Electromagn. Waves Applicat., vol. 8, no. 8, pp. 1073-1089, 1994.
10. Z. A. Kaprielian, "Anisotropie effects in geometrically Isotropie lattices," J. Appl. Phys., vol. 29, no. 7, pp. 1053-1063, July 1958.
11. J. Brown, "Artificial dielectrics," in Progress Dielectrics, Heywood, London, vol. 2, pp. 194-225, 1960.
12. M. M. Z. Kharadly and W. Jackson, "The properties of artificial dielectrics comprising arrays of conducting elements," Proc. Inst. Elect. Eng., vol. 100, pp. 199-212, July 1953.
13. G. Estrin, "The effective permeability of an array of thin conducting disks," J. Appl. Phys., vol. 21, no. 7, pp. 667-670, July 1950.
14. Z. A. Kaprielian, "Dielectric properties of a lattice of anisotropic particles," J. Appl. Phys., vol. 27, no. 1, pp. 24-32, Jan. 1956.
15. J.-P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Computat. Phys., vol. 114, pp. 185-200, Oct. 1994.
16. D. S. Katz, E. T. Thiele, and A. Taflove, "Validation and extension to three dimensions of the Berenger PML absorbing boundary condition for FD-TD meshes," IEEE Microwave Guided Wave Lett., vol. 4, pp. 268-270, Aug. 1994.
17. W. C. Chew and W. H. Weedon, "A 3-D perfectly matched medium from modified Maxwell's equations with stretched coordinates," IEEE Microwave Opt. Technol. Lett., vol. 7, pp. 599-604, Sept. 1994.
18. C. E. Reuter, R. M. Joseph, E. T. Thiele, D. S. Katz, and A. Taflove, "Ultrawideband absorbing boundary condition for termination of waveguiding structures in FD-TD simulations," IEEE Microwave Guided Wave Lett., vol. 4, pp. 344-246, Oct. 1994.
19. C. M. Rappaport, "Perfectly matched absorbing boundary conditions based on anisotropic lossy mapping of space," IEEE Microwave Guided Wave Lett., vol. 5, pp. 90-92, Mar. 1995.
20. R. Mittra and Ü. Pekel, "A new look at the perfectly matched layer (PML) concept for the reflectionless absorption of electromagnetic waves," IEEE Microwave Guided Wave Lett., vol. 5, pp. 84-86, Mar. 1995.
21. W. V. Andrew, C. A. Balanis, and P. A. Tirkas, "A comparison of the Berenger perfectly matched layer and the Lindman higher order ABC's for the FDTD method," IEEE Microwave Guided Wave Lett., vol. 5, pp. 192-194, June 1995.
22. D. C. Wittwer and R. W. Ziolkowski, "How to design the imperfect Berenger PML," Electromagn., vol. 16, pp. 465185, July/Aug. 1996.
23. G. Miir, "Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations," IEEE Trans. Electromagn. Compat., vol. EMC-23, pp. 377-382, Nov. 1981.
24. L. Zhao and A. C. Cangellaris, "A general approach for the development of unsplit-field time-domain implementations of perfectly matched layers for FD-TD grid truncations," IEEE Microwave Guided Wave Lett., vol. 6, pp. 209-211, May 1996.
25. Z. S. Sacks, D. M. Kingsland, R. Lee, and J.-F. Lee, "A perfectly matched anisotropic absorber for use as an absorbing boundary condition," IEEE Trans. Antennas Propagat., vol. 43, pp. 1460-1463, Dec. 1995.
26. M. Gribbons, S.-K. Lee, and A. C. Cangellaris, "Modification of Berenger's perfectly matched layer for the absorption of electromagnetic waves in layered media," in Proc. llth Annu. Rev. Progress Appl. Computat. Electromagn., Monterey, CA, Mar. 1995, pp. 498-503.
27. J. D. Moerloose and M. A. Stuchly, "Behavior of Berenger's ABC for evanescent waves," IEEE Microwave Guided Wave Lett., vol. 5, pp. 344-346, Oct. 1995.
28. B. Chen, D. G. Fang, and B. H. Zhou, "Modified Berenger PML absorbing boundary condition for FD-TD meshes," IEEE Microwave Guided Wave Lett., vol. 5, pp. 399-401, Nov. 1995.
29. J. Fang and Z. Wu, "Generalized perfectly matched layer-An extension of Berenger's perfectly matched layer boundary condition," IEEE Microwave Guided Wave Lett., vol. 5, pp. 451153, Dec. 1995.
30. J.-M. Jin, J. L. Volakis, and V. V. Liepa, "Fictious absorber for truncating finite element meshes in scattering," in Inst. Elect. Eng. Proc. H, vol. 139, pp. 47276, Oct. 1992.
31. A. D. Buckingham, "Permanent and induced molecular moments and long range intermolecular forces," Adv. Chem. Phys., vol. 12, pp. 107-142, 1967.
32. A. D. Buckingham and M. B. Dünn, "Optical activity of oriented molecules," J. Chem. Soc. A, pp. 1988-1991, 1971.
33. E. B. Graham and R. E. Raab, "Light propagation in cubic and other anisotropic crystals," in Proc. Royal Soc., London, U.K., 1990, vol. 430, pp. 593-614.
34. _, "Non-reciprocal optical rotation in cubic antiferromagnets," Philosoph. Mag. B, vol. 64, no. 3, pp. 267-274, 1991.
35. D. A. Imrie and R. E. Raab, "A new molecular theory of field gradient induced birefringence used for measuring electric quadrupole moments," Molecular Phys., vol. 74, no. 4, pp. 833-842, 1991.
36. E. B. Graham and R. E. Raab, "Electric dipole effects in magnetic crystals," J. Appl. Phys., vol. 69, no. 4, pp. 2549-2551, Feb. 1991.
37. J. Kong, Electromagnetic Waves. New York: Wiley, 1986, pp. 48-51.
38. R. Luebbers, F. P. Hunsberger, K. S. Kunz, R. B. Standler, and M. Schneider, "A frequency-dependent finite-difference time-domain formulation for dispersive materials," IEEE Trans. Electromagn. Compat., vol. 32, pp. 222-227, Aug. 1990.
39. R. M. Joseph, S. C. Hagness, and A. Taflove, "Direct time integration of Maxwell's equations in linear dispersive media with absorption for scattering and propagation of femtosecond electromagnetic pulses," Opt. Lett., vol. 16, no. 18, pp. 1412-1414, 1991.
40. T. Kashiwa and I. Fukal, "A treatment by the FD-TD method of the dispersive characteristics associated with electronic polarization," Microwave Opt. Technol. Lett., vol. 3, no. 6, pp. 1326-1328, 1990.
41. J. B. Judkins and R. W. Ziolkowski, "Finite-difference time-domain modeling of nonperfectly conducting metallic thin-film gratings," J. Opt. Soc. Amer. A, vol. 12, no. 9, pp. 1974-1983, Sept. 1995.
42. R. W. Ziolkowski and J. B. Judkins, "NL-FDTD modeling of linear and nonlinear corrugated waveguides," J. Opt. Soc. Amer. B, vol. 11, no. 9, pp. 1565-1575, 1994.
43. J. L. Young, "Propagation in linear dispersive media: Finite-difference time-domain methodologies," IEEE Trans. Antennas Propagat., vol. 43, pp. 42226, Apr. 1995.
44. M. Okoniewski and E. Okoniewska, "FDTD analysis of magnetized ferrites: A more efficient algorithm," IEEE Microwave Guided Wave Lett., vol. 4, pp. 169-171, June 1994.
45. C. Melon, Ph. Leveque, T. Monediere, A. Reineix, and F. Jecko, "Frequency dependent finite-difference-time-domain [(FD)2 TD] formulation applied to ferrite material," IEEE Microwave Opt. Tech. Lett., vol. 7, pp. 577-579, Aug. 1994.
46. R. W. Ziolkowski, "The design of Maxwellian absorbers for numerical boundary conditions and for practical applications using engineered artificial materials," Univ. Arizona, Tucson, AZ, Electromagn. Lab. Rep. EM-0014, May 1996.
47. F. Mariotte, private communications, Aug. 1995.
48. R. W. Ziolkowski, J. A. Arnold, and D. M. Gogny, "Ultrafast pulse interactions with two-level atoms," Phys. Rev. A, vol. 52, no. 4, pp. 3082-3094, Oct. 1995.
49. K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell's equations," IEEE Trans. Antennas Propagat., vol. AP-14. pp. 302-307, May 1966.
50. R. W. Ziolkowski, "Time-derivative Lorentz-material model based absorbing boundary condition," IEEE Trans. Antennas Propagat., to be published.
51. _, "Time-derivative Lorentz-materials and their utilization as electromagnetic absorbers," Phys. Rev. A, to be published.