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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry M. Van Driel
  • Vol. 24, Iss. 10 — Oct. 1, 2007
  • pp: A53–A61

Creating stable gain in active metamaterials

A. D. Boardman, Yu. G. Rapoport, N. King, and V. N. Malnev  »View Author Affiliations


JOSA B, Vol. 24, Issue 10, pp. A53-A61 (2007)
http://dx.doi.org/10.1364/JOSAB.24.000A53


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Abstract

The question of losses in metamaterials that are based upon magnetic resonances deriving from split-ring arrays is addressed through the use of active inclusions designed from diode arrays. A full discussion of the way in which the current-voltage characteristics of the inclusions are deployed to produce gain is given, and the question of the overall stability of the new material is investigated in a quantitative way that is linked to absolute and convective instability. It is shown that instability associated with the inclusion of negative resistance devices can be avoided through a scheme that is approximately scalable from gigahertz to at least the low terahertz regimes. Furthermore, absolute instabilities that potentially complicate any active gain media can be controlled through a suitable choice of the system parameters. The latter step reduces the working frequency window over which spatial gain is available, leading to the need for compromise. Full numerical details are given with the conclusion that construction of such arrays of diode inclusions is possible and that a practical gain window is accessible.

© 2007 Optical Society of America

OCIS Codes
(140.4480) Lasers and laser optics : Optical amplifiers
(160.0160) Materials : Materials
(160.4670) Materials : Optical materials
(160.4760) Materials : Optical properties
(260.2110) Physical optics : Electromagnetic optics
(260.3090) Physical optics : Infrared, far

History
Original Manuscript: February 12, 2007
Manuscript Accepted: February 23, 2007
Published: August 8, 2007

Virtual Issues
Photonic Metamaterials (2007) JOSA A

Citation
A. D. Boardman, Yu. G. Rapoport, N. King, and V. N. Malnev, "Creating stable gain in active metamaterials," J. Opt. Soc. Am. B 24, A53-A61 (2007)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-24-10-A53


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References

  1. R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001). [CrossRef] [PubMed]
  2. 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]
  3. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996). [CrossRef] [PubMed]
  4. A. D. Boardman, L. Velasco, N. King, and Y. Rapoport, "Ultra-narrow bright spatial solitons interacting with left-handed surfaces," J. Opt. Soc. Am. B 22, 1443-1452 (2005). [CrossRef]
  5. A. D. Boardman, N. King, and L. Velasco, "Negative refraction in perspective," Electromagnetics 25, 365-389 (2005). [CrossRef]
  6. A. D. Boardman, P. Egan, L. Velasco, and N. King, "Control of planar nonlinear guided waves and spatial solitons with a left-handed medium," J. Opt. A, Pure Appl. Opt. 7, S57-S67 (2005). [CrossRef]
  7. A. Boardman, N. King, Y. Rapoport, and L. Velasco, "Gyrotropic impact upon negatively refracting surfaces," New J. Phys. 7, 1-24 (2005). [CrossRef]
  8. D. R. Smith and N. Kroll, "Negative refractive index in left-handed materials," Phys. Rev. Lett. 85, 2933-2936 (2000). [CrossRef] [PubMed]
  9. J. Pendry, "Electromagnetic materials enter the negative age," Phys. World 14, 47-51 (2001).
  10. I. V. Shadrivov, A. A. Sukhorukov, Y. S. Kivshar, A. A. Zharov, A. D. Boardman, and P. Egan, "Nonlinear surface waves in left-handed materials," Phys. Rev. E 69, 016617 (2004). [CrossRef]
  11. R. W. Ziolkowski and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 055625 (2001). [CrossRef]
  12. N. Engheta, "An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability," IEEE Antennas Propag. Mag. 1, 10-13 (2002).
  13. C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell's law," Phys. Rev. Lett. 90, 107401 (2003). [CrossRef] [PubMed]
  14. A. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell's law," Phys. Rev. Lett. 90, 137401 (2003). [CrossRef] [PubMed]
  15. A. Grbic and G. V. Eleftheriades, "Experimental verification of backward-wave radiation from a negative refractive index metamaterial," J. Appl. Phys. 92, 5930-5935 (2002). [CrossRef]
  16. J. O. Dimmock, "Losses in left-handed materials," Opt. Express 11, 2397-2402 (2003). [CrossRef] [PubMed]
  17. A. K. Popov and V. M. Shalaev, "Compensating losses in negative-index metamaterials by optical parametric amplification," Opt. Lett. 31, 2169-2171 (2006). [CrossRef] [PubMed]
  18. M. Lapine, M. Gorkunov, and K. H. Ringhofer, "Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements," Phys. Rev. E 67, 065601 (2003). [CrossRef]
  19. J. Helszajn, Passive and Active Microwave Circuits (Wiley, 1978).
  20. I. V. Shadrivov, S. K. Morrison, and Y. S. Kivshar, "Tunable split-ring resonators for nonlinear negative-index metamaterials," Opt. Express 14, 9344-9349 (2006). [CrossRef] [PubMed]
  21. J. C. M. Garnett, "Colours in metal glasses, in metallic films, and in metallic solutions II," Philos. Trans. R. Soc. London, Ser. A 393, 237-288 (1906).
  22. J. C. Garnett, "Colours in metal glasses and in metallic films," Philos. Trans. R. Soc. London, Ser. A 370, 385-420 (1904).
  23. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).
  24. A. Scott, Active and Nonlinear Wave Propagation in Electromagnetics (Wiley, 1970).
  25. C. Kidner, I. Mehdi, J. R. East, and G. I. Haddad, "Power and stability limitations of resonant tunneling diodes," IEEE Trans. Microwave Theory Tech. 38, 864-872 (1990). [CrossRef]
  26. M. Reddy, R. Y. Yu, H. Kroemer, M. J. W. Rodwell, S. C. Martin, R. E. Muller, and R. P. Smith, "Bias stabilization for resonant tunnel-diode oscillators," IEEE Microw. Guid. Wave Lett. 5, 219-221 (1995). [CrossRef]
  27. Y. Ookawa, S. Kishimoto, K. Maezawa, and T. Mizutani, "Novel resonant tunneling diode oscillator capable of large output power operation," IEICE Trans. Electron. E89C, 999-1004 (2006). [CrossRef]
  28. W. W. Lam, C. F. Jou, H. Z. Chen, K. S. Stolt, N. C. Luhmann, and D. B. Rutledge, "Millimeter-wave diode-grid phase shifters," IEEE Trans. Microwave Theory Tech. 36, 902-907 (1988). [CrossRef]
  29. A. Hurwitz, "On the conditions under which an equation has only roots with negative real parts," in Selected Papers on Mathematical Trends in Control Theory, R.Bellman and R.Kalaba, eds. (Dover, 1964).
  30. E. J. Routh, A Treatise on the Stability of a Given State of Motion, Particularly Steady Motion, Reprinted ed. (Taylor and Francis, 1975).
  31. 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]
  32. D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E 71, 036617 (2005). [CrossRef]
  33. T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz magnetic response from artificial materials," Science 303, 1494-1496 (2004). [CrossRef] [PubMed]
  34. P. A. Sturrock, "Kinematics of growing waves," Phys. Rev. 112, 1488-1503 (1958). [CrossRef]
  35. R. J. Briggs, Electron-Stream Interactions with Plasmas (MIT Press, 1964).
  36. A. L. Pokrovsky and A. L. Efros, "Sign of refractive index and group velocity in left-handed media," Solid State Commun. 124, 283-287 (2002). [CrossRef]

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