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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry van Driel
  • Vol. 27, Iss. 4 — Apr. 1, 2010
  • pp: 648–659

Loss and gain in metamaterials

Andrey N. Lagarkov, Vladimir N. Kisel, and Andrey K. Sarychev  »View Author Affiliations

JOSA B, Vol. 27, Issue 4, pp. 648-659 (2010)

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Results of studies in the influence of losses on the superresolution achievability are presented. The studies involve modeling and realization of superresolution devices. It is found that rigorous electrodynamic models that are not based on homogenization of composites can be effectively used in modeling devices with metamaterials. The possibilities to compensate losses in near-optic metamaterials by means of active inclusions or active medium are discussed and the active material design is presented. Alternatively, what we believe to be new designs are suggested for applications where losses are desirable.

© 2010 Optical Society of America

OCIS Codes
(100.6640) Image processing : Superresolution
(140.3380) Lasers and laser optics : Laser materials
(350.4010) Other areas of optics : Microwaves
(350.3618) Other areas of optics : Left-handed materials
(160.3918) Materials : Metamaterials

ToC Category:

Original Manuscript: November 2, 2009
Manuscript Accepted: January 11, 2010
Published: March 8, 2010

Andrey N. Lagarkov, Vladimir N. Kisel, and Andrey K. Sarychev, "Loss and gain in metamaterials," J. Opt. Soc. Am. B 27, 648-659 (2010)

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  1. H. Lamb, “On group velocity,” Proc. London Math. Soc. S2-1, 473-479 (1904). [CrossRef]
  2. L. I. Mandelshtam, “Lectures given on February 26, 1940 and on May 5, 1944” in Complete Issue of Works (Izdatelstvo Trudov AN SSSR, 1950) (in Russian), Vol. 5.
  3. V. M. Agranovich and Yu. N. Gartstein, “Spatial dispersion and negative refraction of light,” Phys. Usp. 49, 1029-1044 (2006). [CrossRef]
  4. D. V. Sivuhin, “About the energy of electromagnetic field in dispersing media,” Opt. Spektrosk. 3, 308-312 (1957) (in Russian).
  5. V. G. Veselago, “Electrodynamics of substances with simultaneously negative electrical and magnetic permeabilities,” Sov. Phys. Usp. 10, 509-514 (1968). [CrossRef]
  6. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000). [CrossRef] [PubMed]
  7. A. N. Lagarkov and V. N. Kissel, “Numerical and experimental investigation of the superresolution in a focusing system based on a plate of 'left-handed' material,” in Proceedings of the 2nd International Conference on Materials for Advanced Technologies, Symposium F: Electromagnetic Materials, L.Hock, O.C.Kim, S.Matitsine, and G.Y.Beng, eds. (World Scientific, 2003), pp. 157-160.
  8. A. N. Lagarkov and V. N. Kissel, “Near-perfect imaging in a focusing system based on a left-handed-material plate,” Phys. Rev. Lett. 92, 077401 (2004). [CrossRef] [PubMed]
  9. S. A. Schelkunoff and H. T. Friis, Antennas: Theory and Practice (John Wiley & Sons, 1952).
  10. A. S. Antonov, V. M. Batenin, A. P. Vinogradov, A. A. Kalachev, A. V. Kulakov, A. N. Lagarkov, S. M. Matitzin, L. V. Panina, K. N. Rozanov, A. K. Sarychev, and Yu. R. Smichkovich, in Electrophysical Properties of Percolation Systems, A.N.Lagarkov, ed. (Institute for High Temperatures, Russian Academy of Sciences, 1990) (in Russian).
  11. A. N. Lagarkov, L. V. Panina, A. K. Sarychev, and Y. R. Smychkovich, in MRS Spring Meeting (1990), paper S 9.3.
  12. A. I. Kolesnikov, A. N. Lagarkov, S. M. Matytsin, L. N. Novogrudskiy, K. N. Rozanov, and A. K. Sarychev, Dielectric Permeability and Conductivity of Polymers Containing Conductive Inclusions, Optical and Electrical Properties of Polymers No. 214, J.A.Emerson and J.M.Torkelson, eds. (Materials Research Society, 1991), p. 119.
  13. A. N. Lagarkov, A. K. Sarychev, Y. R. Smychkovich, and A. P. Vinogradov, “Effective medium theory for microwave dielectric constant and magnetic permeability of conducting stick composites,” J. Electromagn. Waves Appl. 6, 1159-1176 (1992).
  14. A. N. Lagarkov and A. K. Sarychev, “Electromagnetic properties of composites containing elongated conducting inclusions,” Phys. Rev. B 53, 6318-6336 (1996). [CrossRef]
  15. A. N. Lagarkov, V. N. Semenenko, V. A. Chistyaev, D. E. Ryabov, S. A. Tretyakov, and C. R. Simovski, “Resonance properties of bi-helix media at microwaves,” Electromagnetics 17, 213-237 (1997). [CrossRef]
  16. N. Fang and X. Zhang, “Imaging properties of a metamaterial superlens,” Appl. Phys. Lett. 82, 161-163 (2003). [CrossRef]
  17. D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82, 1506-1508 (2003). [CrossRef]
  18. C. K. Ong and X. S. Rao, “Resolution enhancement of a left-handed material superlens,” in Proceedings of the 2nd International Conference on Materials for Advanced Technologies, Symposium F: Electromagnetic Materials, L.Hock, O.C.Kim, S.Matitsine, and G.Y.Beng, eds. (World Scientific, 2003), pp. 123-126.
  19. X. S. Rao and C. K. Ong, “Subwavelength imaging by a left-handed material superlens,” Phys. Rev. E 68, 067601 (2003). [CrossRef]
  20. V. N. Kissel and A. N. Lagarkov, “A study into the possibility of field focusing using 'left-handed' materials,” in Proceedings of the 2nd International Conference on Materials for Advanced Technologies, Symposium F: Electromagnetic Materials, L.Hock, O.C.Kim, S.Matitsine, and G.Y.Beng, eds. (World Scientific, 2003), pp. 145-148.
  21. A. N. Lagar'kov and V. N. Kisel', “Quality of focusing electromagnetic radiation by a plane-parallel slab with a negative index of refraction,” Dokl. Phys. 49, 5-10 (2004). [CrossRef]
  22. A. P. Vinogradov, D. P. Makhnovskii, and K. N. Rozanov, “Effective boundary layer in composite materials,” J. Commun. Technol. Electron. 44, 317-322 (1999).
  23. L. Liu, S. M. Matitsine, Y. B. Gan, and K. N. Rozanov, “The thickness dependence of resonance frequency in anisotropic composites with long conductive fibers,” Electromagnetics 25, 69-79 (2005). [CrossRef]
  24. V. N. Kissel and A. N. Lagarkov, “Superresolution in left-handed composite structures: from homogenization to a detailed electrodynamic description,” Phys. Rev. B 72, 085111 (2005). [CrossRef]
  25. A. N. Lagarkov and V. N. Kisel, “Metamaterials and superresolution: from homogenization to rigorous approach,” Physica B 394, 163-166 (2007). [CrossRef]
  26. T. J. Cui, Z.-C. Hao, X. X. Yin, W. Hong, and J. A. Kong, “Study of lossy effects on the propagation of propagating and evanescent waves in left-handed materials,” Phys. Lett. A 323, 484-494 (2004). [CrossRef]
  27. M. Ricci, N. Orloff, and S. M. Anlage, “Superconducting metamaterials,” Appl. Phys. Lett. 87, 034102 (2005). [CrossRef]
  28. M. I. Stockman, “Criterion for negative refraction with low optical losses from a fundamental principle of causality,” Phys. Rev. Lett. 98, 177404 (2007). [CrossRef]
  29. A. N. Lagarkov and V. N. Kisel, “Electrodynamic properties of simple bodies made of materials with negative permeability and negative permittivity,” Dokl. Phys. 46, 163-165 (2001). [CrossRef]
  30. V. N. Kisel and A. N. Lagarkov, “Electromagnetic wave scattering by the negative refraction index bodies,” Electromagnetic Waves and Electronic Systems 7, 62-65 (2002).
  31. K. J. Vinoy and R. M. Jha, Radar Absorbing Materials: From Theory to Design and Characterization (Kluwer Academic, 1996). [CrossRef]
  32. V. N. Kisel and A. N. Lagarkov, “Near perfect absorption by a flat metamaterial plate,” Phys. Rev. E 76, 065601 (2007). [CrossRef]
  33. A. N. Lagarkov, V. N. Kisel, and V. N. Semenenko, “Wide-angle absorption by the use of a metamaterial plate,” Progress in Electromagnetics Research Letters 1, 35-44 (2008). [CrossRef]
  34. N. Engheta, “An idea for thin, subwavelength cavity resonators using metamaterials with negative permittivity and permeability,” IEEE Antennas Wireless Propag. Lett. 1, 10-13 (2002). [CrossRef]
  35. S. He, Y. Jin, Z. Ruan, and J. Kuang, “On subwavelength and open resonators involving metamaterials of negative refraction index,” New J. Phys. 7, 210 (2005). [CrossRef]
  36. E. F. Knott, J. F. Shaeffer, and M. T. Tuley, Radar Cross Section (Artech House, 1993).
  37. A. Alù, N. Engheta, A. Erontuk, and R. W. Ziolkowski, “Single-negative, double-negative, and low-index metamaterials and their electromagnetic applications,” IEEE Antennas Propag. Mag. 49, 23-36 (2007). [CrossRef]
  38. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999). [CrossRef]
  39. A. Sarychev and V. Shalaev, Electrodynamics of Metamaterials (World Scientific, 2007). [CrossRef]
  40. A. Sarychev and V. Shalaev, “Electromagnetic field fluctuations and optical nonlinearities in metal-dielectric composites,” Phys. Rep. 335, 275-371 (2000). [CrossRef]
  41. V. Batygin and I. Toptygin, Problems in Electrodynamics (Academic, 1978).
  42. V. Shalaev, W. Cai, U. Chettiar, H.-K. Yuan, A. Sarychev, V. Drachev, and A. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30, 3356-3358 (2005). [CrossRef]
  43. V. P. Drachev, W. Cai, U. Chettiar, H.-K. Yuan, A. K. Sarychev, A. V. Kildishev, G. Klimeck, and V. M. Shalaev, “Experimental verification of an optical negative-index material,” Laser Phys. Lett. 3, 49-55 (2006). [CrossRef]
  44. S. Zhang, W. Fan, N. Panoiu, K. Malloy, R. Osgood, and S. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95, 137404 (2005). [CrossRef] [PubMed]
  45. A. Sarychev and V. Shalaev, “Magnetic resonance in metal nanoantennas,” in Complex Mediums V: Light and Complexity, M.McCall and G.Dewar, eds., Proc. SPIE 5508128-137 (2004).
  46. G. Dolling, C. Enkrich, M. Wegener, C. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31, 1800-1802 (2006). [CrossRef] [PubMed]
  47. G. Dolling, C. Enkrich, M. Wegener, C. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312, 892-894 (2006). [CrossRef] [PubMed]
  48. G. Dolling, M. Wegener, C. Soukoulis, and S. Linden, “Negative-index metamaterial at 780 nm wavelength,” Opt. Lett. 32, 53-55 (2007). [CrossRef]
  49. T. Klar, A. Kildishev, V. Drachev, and V. Shalaev, “Negative-index metamaterials: going optical,” IEEE J. Sel. Top. Quantum Electron. 12, 1106-1115 (2006). [CrossRef]
  50. V. M. Shalaev, Nat. Photonics 1, 41-48 (2007). [CrossRef]
  51. J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avil, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455, 376-379 (2008). [CrossRef] [PubMed]
  52. A. Grigorenko, A. Geim, H. Gleeson, Y. Zhang, A. Firsov, I. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438, 335-338 (2005). [CrossRef] [PubMed]
  53. A. Kildishev, V. Drachev, U. Chettiar, V. Shalaev, D. Werner, and D. Kwon, “Comment on 'Negative refractive index in artificial metamaterials',” Opt. Lett. 32, 1510-1511 (2007). [CrossRef] [PubMed]
  54. J. O. Dimmock, “Losses in left-handed materials,” Opt. Express 11, 2397-2402 (2003). [CrossRef] [PubMed]
  55. J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005). [CrossRef] [PubMed]
  56. V. Podolskiy and E. Narimanov, “Near-sighted superlens,” Opt. Lett. 30, 75-77 (2005). [CrossRef] [PubMed]
  57. A. Sarychev, G. Shvets, and V. Shalaev, “Magnetic plasmon resonance,” Phys. Rev. E 73, 036609 (2006). [CrossRef]
  58. A. Sarychev and G. Tartakovsky, “Magnetic plasmonic metamaterials in actively pumped host medium and plasmonic nanolaser,” in Complex Photonic Media, G.Dewar, M.McCall, M.Noginov, and N.Zheludev, eds., Proc. SPIE 6320, 63200A (2006).
  59. A. Sarychev and G. Tartakovsky, “Magnetic plasmonic metamaterials in actively pumped host medium and plasmonic nanolaser,” Phys. Rev. B 75, 085436 (2007). [CrossRef]
  60. A. K. Sarychev, A. A. Pukhov, and G. Tartakovsky, “Metamaterial comprising plasmonic nanolasers,” in Progress in Electromagnetics Research Symposium (PIERS) (2007), pp. 95-98.
  61. D. Bergman and M. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90, 027402 (2003). [CrossRef] [PubMed]
  62. B. Kogan, V. Volkov, and S. Lebedev, “Superluminescence and generation of stimulated radiation under internal-reflection conditions,” JETP Lett. 16, 100-105 (1972).
  63. G. Plotz, H. Simon, and J. Tucciarone, “Enhanced total reflection with surface plasmons,” J. Opt. Soc. Am. 69, 419-421 (1979). [CrossRef]
  64. A. Sudarkin and P. Demkovich, “Excitation of surface electromagnetic waves on the boundary of a metal with an amplifying medium,” Sov. Phys. Tech. Phys. 34, 764-766 (1989).
  65. A. Tredicucci, C. Gmachl, F. Capasso, A. Hutchinson, D. Sivco, and A. Cho, “Single-mode surface-plasmon laser,” Appl. Phys. Lett. 76, 2164-2166 (2000). [CrossRef]
  66. I. Avrutsky, “Surface plasmons at nanoscale relief gratings between a metal and a dielectric medium with optical gain,” Phys. Rev. B 70, 155416 (2004). [CrossRef]
  67. S. Ramakrishna and J. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B 67, 201101(R) (2003). [CrossRef]
  68. M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110-1112 (2009). [CrossRef] [PubMed]
  69. E. Plum, V. A. Fedotov, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Towards the lasing spaser: controlling metamaterial optical response with semiconductor quantum dots,” Opt. Express 17, 8548-8551 (2009). [CrossRef] [PubMed]
  70. M. Wegener, J. L. García-Pomar, C. M. Soukoulis, N. Meinzer, M. Ruther, and S. Linden, “Toy model for plasmonicmetamaterial resonances coupled to two-level system gain,” Opt. Express 16, 19785-19798 (2008). [CrossRef] [PubMed]
  71. A. Fang, Th. Koschny, M. Wegener, and C. M. Soukoulis, “Self-consistent calculation of metamaterials with gain,” Phys. Rev. B 79, 241104(R) (2009). [CrossRef]
  72. D. B. Li and C. Z. Ning, “Giant modal gain, amplified surface plasmon-polariton propagation, and slowing down of energy velocity in a metal-semiconductor-metal structure,” Phys. Rev. B 80, 153304 (2009). [CrossRef]

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