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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 21, Iss. 12 — Dec. 1, 2004
  • pp: 2311–2319

Scattering properties of an impedance-matched, ideal, homogeneous, causal “left-handed” sphere

Cesar Monzon, Donald W. Forester, and Louis N. Medgyesi-Mitschang  »View Author Affiliations

JOSA A, Vol. 21, Issue 12, pp. 2311-2319 (2004)

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The plane-wave scattering properties of a sphere of material having an ideal, homogeneous, and causal permittivity ε(f), and permeability μ(f) were investigated through detailed three-dimensional finite-difference time-domain, method-of-moments, and series-solution simulations. A Lorentzian functional form was chosen for ε(f) and μ(f), as it yields causal responses and allows us to study the physics of the left-handed-medium (LHM) regime. Our interest lies mainly in the frequency range where negative refraction [Re(n)<0] is observed. We found that when operating in the LHM regime, an impedance-matched sphere responds with scattering features strikingly different from those found in ordinary materials. In particular, we found zero backscattering and forward scattering that exceeds that of a metal sphere of similar size. The equality of E- and H-plane patterns was proved analytically and numerically, and the possibility of internal subwavelength focusing with a zero index sphere is also reported.

© 2004 Optical Society of America

OCIS Codes
(260.1960) Physical optics : Diffraction theory
(260.2110) Physical optics : Electromagnetic optics
(290.0290) Scattering : Scattering
(290.1350) Scattering : Backscattering
(290.4020) Scattering : Mie theory

Original Manuscript: February 3, 2004
Revised Manuscript: June 3, 2003
Manuscript Accepted: June 3, 2003
Published: December 1, 2004

Cesar Monzon, Donald W. Forester, and Louis N. Medgyesi-Mitschang, "Scattering properties of an impedance-matched, ideal, homogeneous, causal “left-handed” sphere," J. Opt. Soc. Am. A 21, 2311-2319 (2004)

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  1. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968). [CrossRef]
  2. J. B. Pendry, S. A. Ramakrishna, “Near field lenses in two dimensions,” J. Phys. Condens. Matter 14, 8463–8479 (2002). [CrossRef]
  3. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966 (2000). [CrossRef] [PubMed]
  4. F. J. Rachford, D. L. Smith, P. F. Loschialpo, D. W. Forester, “Calculations and measurements of wire and/or split-ring negative index media,” Phys. Rev. E 66, 036613 (2002). [CrossRef]
  5. P. F. Loschialpo, D. L. Smith, D. W. Forester, F. J. Rachford, J. Schelleng, “Electromagnetic waves focused by a negative-index planar lens,” Phys. Rev. E 67, 026502 (2003). [CrossRef]
  6. P. F. Loschialpo, D. W. Forester, D. L. Smith, F. J. Rachford, J. Schelleng, C. Monzon, “Optical properties of an ideal homogeneous, causal ‘left-handed’ material slab,” Phys. Rev. E 70, 036605 (2004). [CrossRef]
  7. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000). [CrossRef] [PubMed]
  8. R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, S. Schultz, “Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial,” Appl. Phys. Lett. 78, 489–491 (2001). [CrossRef]
  9. R. A. Shelby, D. R. Smith, S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77 (2001). [CrossRef] [PubMed]
  10. J. B. Pendry, A. J. Holden, D. J. Robbins, W. J. Stewart, “Magnetism from conductors and Enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999). [CrossRef]
  11. R. W. Ziolkowski, A. D. Kipple, “Causality and double-negative metamaterials,” Phys. Rev. E 68, 026615 (2003). [CrossRef]
  12. J. Pacheco, T. M. Grzegorczyk, B. I. Wu, Y. Zhang, J. A. Kong, “Power propagation in homogeneous isotropic frequency-dispersive left-handed media,” Phys. Rev. Lett. 89, 257401 (2002). [CrossRef] [PubMed]
  13. D. R. Fredkin, A. Ron, “Effectively left-handed (negative index) composite material,” Appl. Phys. Lett. 81, 1753–1755 (2002). [CrossRef]
  14. P. R. Berman, “Goos–Hanchen shift in negatively refractive media,” Phys. Rev. E 66, 067603 (2002). [CrossRef]
  15. I. V. Shadrivov, A. A. Sukhorukov, Y. S. Kivshar, “Beam shaping by a periodic structure with negative refraction,” Appl. Phys. Lett. 82, 3820–3822 (2003). [CrossRef]
  16. M. K. Karkkainen, S. I. Maslovski, “Wave propagation, refraction and focusing phenomena in Lorentzian double-negative materials: a theoretical and numerical study,” Microwave Opt. Technol. Lett. 37, 4–7 (2003). [CrossRef]
  17. S. Foteinopoulou, E. N. Economou, C. M. Soukoulis, “Refraction in media with a negative refractive index,” Phys. Rev. Lett. 90, 107402 (2003). [CrossRef] [PubMed]
  18. A. A. Houck, J. B. Brock, I. L. Chuang, “Experimental observations of a left-handed material that obeys Snell’s law,” Phys. Rev. Lett. 90, 137401 (2003). [CrossRef]
  19. D. R. Smith, D. C. Vier, N. Kroll, S. Schultz, “Direct calculation of permeability and permittivity for a left-handed metamaterial,” Appl. Phys. Lett. 77, 2246–2248 (2000). [CrossRef]
  20. M. Kerker, D.-S. Wang, G. L. Giles, “Electromagnetic scattering by magnetic spheres,” J. Opt. Soc. Am. 73, 765–767 (1983). [CrossRef]
  21. R. Ruppin, “Extinction properties of a sphere with negative permittivity and permeability,” Solid State Commun. 116, 411–415 (2000). [CrossRef]
  22. G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908). [CrossRef]
  23. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  24. The Finite Difference Time Domain simulations were performed with MAXTDA. MAXTDA, written at GTRI, was recently modified by Georgia Tech Research Institute (GTRI) to include causal Lorentzian functional forms for permittivity and permeability.
  25. L. N. Medgyesi-Mitschang, J. M. Putnam, M. B. Gedera, “Generalized method of moments for three-dimensional penetrable scatterers,” J. Opt. Soc. Am. A 11, 1383–1398 (1994). [CrossRef]
  26. J. M. Putnam, M. B. Gedera, “CARLOS-3D: a general-purpose 3-D method of moments scattering code,” IEEE Antennas Propag. Mag., April1993, pp. 69–71.
  27. V. H. Weston, “Theory of absorbers in scattering,” IEEE Trans. Antennas Propag. 11, 578–584 (1963). [CrossRef]
  28. D. S. Jones, The Theory of Electromagnetism (MacMillan, New York, 1964).
  29. R. W. Ziolkowski, E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E 64, 056625 (2001). [CrossRef]
  30. A. Taflove, Computational Electrodynamics, The Finite-Difference Time-Domain Method (Artech House, Norwood, Mass., 1995).
  31. G. T. Ruck, Editor, Radar Cross Section Handbook (Plenum, New York, 1970).
  32. H. M. Nussenzveig, “High-frequency scattering by a transparent sphere—Part I: direct reflection and transmission; Part II: theory of the rainbow and the glory,” J. Math. Phys. 10, 82–177 (1969). [CrossRef]

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