Accurate modelling of left-handed metamaterials using a finite-difference time-domain method with spatial averaging at the boundaries

Journal of Optics A: Pure and Applied Optics

Volumn 9, Issue 9, 2007, Pages

  Zhao, Yan ^a   Belov, Pavel ^a   Hao, Yang ^a  

^a QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

Author keywords

Finite difference time domain (FDTD); Left handed metamaterial (LHM)

Indexed keywords

DIFFERENTIAL EQUATIONS; ELECTROMAGNETIC DISPERSION; FINITE DIFFERENCE TIME DOMAIN METHOD; MATHEMATICAL MODELS;

AUXILIARY DIFFERENTIAL EQUATION (ADE); LEFT-HANDED METAMATERIAL (LHM); MATERIAL FREQUENCY DISPERSION;

OPTICAL MATERIALS;

EID: 41649085996     PISSN: 14644258     EISSN: 17413567     Source Type: Journal    
DOI: 10.1088/1464-4258/9/9/S31     Document Type: Article

References (41)

1. Veselago V G 1968 The electrodynamics of substances with simultaneously negative value of ε and μ Sov. Phys.-Usp. 10 509
2. Pendry J B 2000 Negative refraction makes a perfect lens Phys. Rev. Lett. 85 3966
3. Taflove A 2000 Computational Electrodynamics: The Finite-Difference Time-Domain Method 2nd edn (Norwood, MA: Artech House)
4. Luebbers R, Hunsberger F P, Kunz K, Standler R and Schneider M 1990 A frequency-dependent finite-difference time-domain formulation for dispersive materials IEEE Trans. Electromagn. Compat. 32 222-7
5. Gandhi O P, Gao B-Q and Chen J-Y 1993 A frequency-dependent finite-difference time-domain formulation for general dispersive media IEEE Trans. Microw. Theory Tech. 41 658-64
6. Sullivan D M 1992 Frequency-dependent FDTD methods using Z transforms IEEE Trans. Antennas Propag. 40 1223-30
7. Luebbers R J, Hunsberger F and Kunz K S 1991 A frequency-dependent finite-difference time-domain formulation for transient propagation in plasma IEEE Trans. Antennas Propag. 39 29-34
8. Luebbers R J and Hunsberger F 1992 FDTD for Nth-order dispersive media IEEE Trans. Antennas Propag. 40 1297-301
9. Hunsberger F, Luebbers R J and Kunz K S 1992 Finite-difference time-domain analysis of gyrotropic media. I: magnetized plasma IEEE Trans. Antennas Propag. 40 1489-95
10. Melon C, Leveque P, Monediere T, Reineix A and Jecko F 1994 Frequency dependent finite-difference-time-domain formulation applied to ferrite material Microw. Opt. Technol. Lett. 7 577-9
11. Akyurtlu A and Werner D H 2004 BI-FDTD: a novel finite-difference time-domain formulation for modeling wave propagation in bi-isotropic media IEEE Trans. Antennas Propag. 52 416-25
12. Grande A, Barba I, Cabeceira A, Represa J, So P and Hoefer W 2004 FDTD modeling of transient microwave signals in dispersive and lossy bi-isotropic media IEEE Trans. Microw. Theory Tech. 52 773-84
13. Akyurtlu A and Werner D H 2004 A novel dispersive FDTD formulation for modelling transient propagation in chiral metamaterials IEEE Trans. Antennas Propag. 52 2267-76
14. Lee J-Y, Lee J-H, Kim H-S, Kang N-W and Jung H-K 2005 Effective medium approach of left-handed material using a dispersive FDTD method IEEE Trans. Magn. 41 1484-7
15. Kashiwa T, Yoshida N and Fukai I 1990 A treatment by the finite-difference time-domain method of the dispersive characteristics associated with orientation polarization Trans. IEICE E73 1326-8
16. Kashiwa T and Fukai I 1990 A treatment by the FD-TD method of the dispersive characteristics associated with electronic polarization Microw. Opt. Technol. Lett. 3 203-5
17. Goorjian P M and Taflove A 1992 Direct time integration of Maxwell's equations in nonlinear dispersive media for propagation and scattering of femtosecond electromagnetic solitons Opt. Lett. 17 180-2
18. Gandhi O P, Gao B Q and Chen J Y 1992 A frequency-dependent finite-difference time-domain formulation for induced current calculations in human beings Bioelectromagnetics 13 543-56
19. Gandhi O P, Gao B Q and Chen J Y 1993 A frequency-dependent finite-difference time-domain formulation for general dispersive media IEEE Trans. Microw. Theory Tech. 41 658-65
20. Lu L, Hao Y and Parini C 2004 Dispersive FDTD characterisation of no phase-delay radio transmission over layered left-handed meta-materials structure IEE Proc. Sci. Meas. Technol. 151 403-6
21. Sullivan D M 1995 Nonlinear FDTD formulations using Z transforms IEEE Trans. Microw. Theory Tech. 43 676-82
22. Demir V, Elsherbeni A Z and Arvas E 2005 FDTD formulation for dispersive chiral media using the Z transform method IEEE Trans. Antennas Propag. 53 3374-84
23. Ziolkowski R W and Heyman E 2001 Wave propagation in media having negative permittivity and permeability Phys. Rev. E 64 056625
24. Loschialpo P F, Smith D L, Forester D W, Rach-ford F J and Schelleng J 2003 Electromagnetic waves focused by a negative-index planar lens Phys. Rev. E 67 025602
25. Cummer S A 2003 Simulated causal subwavelength focusing by a negative refractive index slab Appl. Phys. Lett. 82 1503
26. Feise M W and Kivshar Y S 2005 Sub-wavelength imaging with a left-handed material flat lens Phys. Lett. A 334 326
27. Rao X S and Ong C K 2003 Subwavelength imaging by a left-handed material superlens Phys. Rev. E 68 067601
28. Chen J J, Grzegorczyk T M, Wu B-I and Kong J A 2005 Limitation of FDTD in simulation of a perfect lens imaging system Opt. Express 13 10840
29. Feise M W, Schneider J B and Bevelacqua P J 2004 Finite-difference and pseudospectral time-domain methods applied to backward-wave metamaterials IEEE Trans. Antennas Propag. 52 2955
30. Zhao Y, Belov P and Hao Y 2007 Accurate modelling of the optical properties of left-handed media using a finite-difference time-domain method Phys. Rev. E at press
31. Zhao Y, Belov P and Hao Y 2006 Preprint cond-mat/0610301
32. Mohammadi A, Nadgaran H and Agio M 2005 Contour-path effective permittivities for the two-dimensional finite-difference time-domain method Opt. Express 13 10367-81
33. Mohammadi A and Agio M 2006 Dispersive contour-path finite-difference time-domain algorithm for modelling surface plasmon polaritons at flat interfaces Opt. Express 14 11330-8
34. Podolskiy V A and Narimanov E E 2005 Near-sighted superlens Opt. Lett. 30 75
35. Smith D R, Schurig D, Rosenbluth M, Schultz S, Ramakrishna S A and Pendry J B 2003 Limitations on subdiffraction imaging with a negative refractive index slab Appl. Phys. Lett. 82 1506
36. Hildebrand F B 1956 Introduction to Numerical Analysis (New York: Mc-Graw-Hill)
37. Hwang K-P and Cangellaris A C 2000 Effective permittivities for second-order accurate FDTD equations at dielectric interfaces IEEE Microw. Wireless Compon. Lett. 11 158
38. Berenger J R 1994 A perfectly matched layer for the absorption of electromagnetic waves J. Comput. Phys. 114 185
39. Fang J and Wu Z 1996 Generalised perfectly matched layer for the absorption of propagating and evanescent waves in lossless and lossy media IEEE Trans. Microw. Theory Tech. 44 2216
40. Chen L, He S and Shen L 2004 Finite-size effects of a left-handed material slab on the image quality Phys. Rev. Lett. 92 107404
41. Huang X and Zhou L 2006 Modulating image oscillations in focusing by a metamaterial lens: time-dependent Green's function approach Phys. Rev. B 74 045123