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Nonlinear Optics with Metamaterials

Chapter

Abstract

In all the preceding chapters, we studied the linear properties of optical metamaterials, assuming that the effective electric permittivity ε and magnetic permeability μ are independent of the incident light intensity. Indeed, an overwhelming portion of the experimental results on metamaterials reported thus far are exclusively focused on the linear response of metamaterials to external electromagnetic radiation. However, nonlinear effects in metamaterials have become an emerging field of study, particularly among theoretical physicists. A range of nonlinear phenomena in a variety of metamaterials, especially negative-index materials (NIMs), have been theoretically investigated to a considerable extent. The studied topics include general treatments for nonlinear wave propagation and nonlinear Schrödinger equations in NIMs [1, 2], as well as specific nonlinear processes such as second-harmonic generation (SHG) and parametric amplification [3, 4, 5, 6].

Keywords

Nonlinear Medium Fundamental Wave Parametric Amplification Supercontinuum Generation Optical Parametric Amplification 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Agranovich VM, Shen YR, Baughman RH, Zakhidov AA (2004) Linear and nonlinear wave propagation in negative refraction metamaterials. Phys Rev B 69:165112CrossRefADSGoogle Scholar
  2. 2.
    Scalora M, Syrchin MS, Akozbek N, Poliakov EY, D’Aguanno G, Mattiucci N, Bloemer MJ, Zheltikov AM (2005) Generalized nonlinear Schrödinger equation for dispersive susceptibility and permeability: application to negative index materials. Phys Rev Lett 95:013902CrossRefADSGoogle Scholar
  3. 3.
    Popov AK, Shalaev VM (2006) Negative-index metamaterials: second-harmonic generation, Manley–Rowe relations and parametric amplification. Appl Phys B 84:131–137CrossRefADSGoogle Scholar
  4. 4.
    Shadrivov IV, Zharov AA, Kivshar YS (2006) Second-harmonic generation in nonlinear left-handed metamaterials. J Opt Soc Am B 23:529–534CrossRefADSGoogle Scholar
  5. 5.
    Scalora M, D’Aguanno G, Bloemer M, Centini M, de Ceglia D, Mattiucci N, Kivshar YS (2006) Dynamics of short pulses and phase matched second harmonic generation in negative index materials. Opt Express 14:4746–4756CrossRefADSGoogle Scholar
  6. 6.
    Popov AK, Shalaev VM (2006) Compensating losses in negative-index metamaterials by optical parametric amplification. Opt Lett 31:2169–2171CrossRefADSGoogle Scholar
  7. 7.
    Ranka JK, Windeler RS, Stentz AJ (2000) Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm. Opt Lett 25:25–27CrossRefADSGoogle Scholar
  8. 8.
    Zharov AA, Shadrivov IV, Kivshar YS (2003) Nonlinear properties of left-handed metamaterials. Phys Rev Lett 91:037401CrossRefADSGoogle Scholar
  9. 9.
    Lapine M, Gorkunov M, Ringhofer KH (2003) Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements. Phys Rev E 67:065601CrossRefADSGoogle Scholar
  10. 10.
    Gil I, Garcia-Garcia J, Bonache J, Martin F, Sorolla M, Marques R (2004) Varactor-loaded split ring resonators for tunable notch filters at microwave frequencies. Electron Lett 40:1347–1348CrossRefGoogle Scholar
  11. 11.
    Kozyrev AB, Kim H, Karbassi A, van der Weide DW (2005) Wave propagation in nonlinear left-handed transmission line media. Appl Phys Lett 87:121109CrossRefADSGoogle Scholar
  12. 12.
    Klein MW, Enkrich C, Wegener M, Linden S (2006) Second-harmonic generation from magnetic metamaterials. Science 313:502–504CrossRefADSGoogle Scholar
  13. 13.
    Klein MW, Wegener M, Feth N, Linden S (2007) Experiments on second- and third-harmonic generation from magnetic metamaterials. Opt Express 15:5238–5247CrossRefADSGoogle Scholar
  14. 14.
    Simon HJ, Mitchell DE, Watson JG (1974) Optical second-harmonic generation with surface plasmons in silver films. Phys Rev Lett 33:1531–1534CrossRefADSGoogle Scholar
  15. 15.
    Lesuffleur A, Kumar L, Gordon R (2006) Enhanced second harmonic generation from nanoscale double-hole arrays in a gold film. Appl Phys Lett 88:261104CrossRefADSGoogle Scholar
  16. 16.
    van Nieuwstadt JAH, Sandtke M, Harmsen RH, Segerink FB, Prangsma JC, Enoch S, Kuipers L (2006) Strong modification of the nonlinear optical response of metallic subwavelength hole arrays. Phys Rev Lett 97:146102CrossRefADSGoogle Scholar
  17. 17.
    Feth N, Linden S, Klein MW, Decker M, Niesler FBP, Zeng Y, Hoyer W, Liu J, Koch SW, Moloney JV, Wegener M (2008) Second-harmonic generation from complementary split-ring resonators. Opt Lett 33:1975–1977CrossRefADSGoogle Scholar
  18. 18.
    Zeng Y, Hoyer W, Liu J, Koch SW, Moloney JV (2009) Classical theory for second-harmonic generation from metallic nanoparticles. Phys Rev B 79:235109CrossRefADSGoogle Scholar
  19. 19.
    Kim E, Wang F, Wu W, Yu ZN, Shen YR (2008) Nonlinear optical spectroscopy of photonic metamaterials. Phys Rev B 78:113102CrossRefADSGoogle Scholar
  20. 20.
    Shadrivov IV, Sukhorukov AA, Kivshar YS, Zharov AA, Boardman AD, Egan P (2004) Nonlinear surface waves in left-handed materials. Phys Rev E 69:016617CrossRefMathSciNetADSGoogle Scholar
  21. 21.
    Darmanyan SA, Neviere M, Zakhidov AA (2005) Nonlinear surface waves at the interfaces of left-handed electromagnetic media. Phys Rev E 72:036612CrossRefADSGoogle Scholar
  22. 22.
    Li J, Zhou L, Chan CT, Sheng P (2003) Photonic band gap from a stack of positive and negative index materials. Phys Rev Lett 90:083901CrossRefADSGoogle Scholar
  23. 23.
    Hegde RS, Winful HG (2005) Zero-n gap soliton. Opt Lett 30:1852–1854CrossRefADSGoogle Scholar
  24. 24.
    Litchinitser NM, Gabitov IR, Maimistov AI, Shalaev VM (2007) Effect of an optical negative index thin film on optical bistability. Opt Lett 32:151–153CrossRefADSGoogle Scholar
  25. 25.
    Litchinitser NM, Gabitov IR, Maimistov AI (2007) Optical bistability in a nonlinear optical coupler with a negative index channel. Phys Rev Lett 99:113902CrossRefADSGoogle Scholar
  26. 26.
    Maimistov AI, Gabitov IR, Litchinitser NM (2008) Solitary waves in a nonlinear oppositely directed coupler. Opt Spectrosc 104:253–257ADSGoogle Scholar
  27. 27.
    Liu YM, Bartal G, Genov DA, Zhang X (2007) Subwavelength discrete solitons in nonlinear metamaterials. Phys Rev Lett 99:153901CrossRefADSGoogle Scholar
  28. 28.
    Gabitov IR, Indik RA, Litchinitser NM, Maimistov AI, Shalaev VM, Soneson JE (2006) Double-resonant optical materials with embedded metal nanostructures. J Opt Soc Am B 23:535–542CrossRefADSGoogle Scholar
  29. 29.
    Popov AK, Myslivets SA, George TF, Shalaev VM (2007) Four-wave mixing, quantum control, and compensating losses in doped negative-index photonic metamaterials. Opt Lett 32:3044–3046CrossRefADSGoogle Scholar
  30. 30.
    Zharov AA, Zharova NA, Shadrivov IV, Kivshar YS (2005) Subwavelength imaging with opaque nonlinear left-handed lenses. Appl Phys Lett 87:091104CrossRefADSGoogle Scholar
  31. 31.
    Chowdhury A, Tataronis JA (2008) Long wave-short wave resonance in nonlinear negative refractive index media. Phys Rev Lett 100:153905CrossRefADSGoogle Scholar
  32. 32.
    Shen YR (1984) The principles of non-linear optics. Wiley, New YorkGoogle Scholar
  33. 33.
    Boyd RW (2002) Nonlinear optics, 2nd ed. Academic, San DiegoGoogle Scholar
  34. 34.
    Popov AK, Slabko VV, Shalaev VM (2006) Second harmonic generation in left-handed metamaterials. Laser Phys Lett 3:293–297CrossRefADSGoogle Scholar
  35. 35.
    Stockman MI (2007) Criterion for negative refraction with low optical losses from a fundamental principle of causality. Phys Rev Lett 98:177404CrossRefADSGoogle Scholar
  36. 36.
    Kinsler P, McCall MW (2008) Causality-based criteria for a negative refractive index must be used with care. Phys Rev Lett 101:167401CrossRefADSGoogle Scholar
  37. 37.
    Kozyrev AB, Kim H, van der Weide DW (2006) Parametric amplification in left-handed transmission line media. Appl Phys Lett 88:264101CrossRefADSGoogle Scholar
  38. 38.
    Popov AK, Shalaev VM (2007) Nonlinear optical switching from lossy to amplifying negative-index metamaterials. Proceedings of OSA topical meeting “Photonic metamaterials: from random to periodic”, Jackson Hole, WYGoogle Scholar
  39. 39.
    Popov AK, Myslivets SA, Shalaev VM (2009) Resonant nonlinear optics of backward waves in negative-index metamaterials. Appl Phys B 96:315–323CrossRefADSGoogle Scholar
  40. 40.
    Popov AK, Myslivets SA, Shalaev VM (2009) Microscopic mirrorless negative-index optical parametric oscillator. Opt Lett 34:1165–1167CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Stanford UniversityStanfordUSA
  2. 2.Purdue UniversityWest LafayetteUSA

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