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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. 8 — Aug. 1, 2010
  • pp: 1671–1679

Second harmonic generation in a generic negative index medium

V. Roppo, C. Ciracì, C. Cojocaru, and M. Scalora  »View Author Affiliations

JOSA B, Vol. 27, Issue 8, pp. 1671-1679 (2010)

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We analyze second harmonic generation in a generic medium composed of Lorentz oscillators for both the electrical permittivity and magnetic permeability. We discuss conditions where a fundamental beam is tuned in a positive index region and generates second and/or third harmonics in a negative index region. Phase matching condition, phase locking, inhibition of absorption at the harmonic wavelengths, and second and third harmonic lenses are also investigated.

© 2010 Optical Society of America

OCIS Codes
(160.4330) Materials : Nonlinear optical materials
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
(190.4400) Nonlinear optics : Nonlinear optics, materials
(350.3618) Other areas of optics : Left-handed materials
(160.3918) Materials : Metamaterials

ToC Category:

Original Manuscript: May 6, 2010
Manuscript Accepted: June 26, 2010
Published: July 30, 2010

V. Roppo, C. Ciracì, C. Cojocaru, and M. Scalora, "Second harmonic generation in a generic negative index medium," J. Opt. Soc. Am. B 27, 1671-1679 (2010)

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  1. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewar, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999). [CrossRef]
  2. V. G. Veselago, “Electrodynamics of substances with simultaneously negative electrical and magnetic permeabilities,” Sov. Phys. Usp. 10, 509–514 (1968). [CrossRef]
  3. R. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001). [CrossRef] [PubMed]
  4. V. M. Shalaev, W. Cai, U. K. Chettiar, H. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30, 3356–3358 (2005). [CrossRef]
  5. G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett. 30, 3198–3200 (2005). [CrossRef] [PubMed]
  6. C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77, 195328 (2008). [CrossRef]
  7. A. K. Popov, V. V. Slabko, and V. M. Shalaev, “Second harmonic generation in left-handed metamaterials,” Laser Phys. Lett. 3, 293–297 (2006). [CrossRef]
  8. A. K. Popov and V. M. Shalaev, “Negative-index metamaterials: Second-harmonic generation, Manley–Rowe relations and parametric amplification,” Appl. Phys. B 84, 131–137 (2006). [CrossRef]
  9. N. M. Litchinitser and V. M. Shalaev, “Photonic metamaterials,” Laser Phys. Lett. 5, 411–420 (2008). [CrossRef]
  10. V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, “Linear and nonlinear wave propagation in negative refraction metamaterials,” Phys. Rev. B 69, 165112 (2004). [CrossRef]
  11. D. A. Powell, I. V. Shadrivov, and Yu. S. Kivshar, “Nonlinear electric metamaterials,” Appl. Phys. Lett. 95, 084102 (2009). [CrossRef]
  12. A. A. Zharov, I. V. Shadrivov, and Yu. S. Kivshar, “Nonlinear properties of left-handed metamaterials,” Phys. Rev. Lett. 91, 037401 (2003). [CrossRef] [PubMed]
  13. I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, “Second-harmonic generation in nonlinear left-handed metamaterials,” J. Opt. Soc. Am. B 23, 529–534 (2006). [CrossRef]
  14. M. Scalora, G. D’Aguanno, M. Bloemer, M. Centini, D. de Ceglia, N. Mattiucci, and Yu. S. Kivshar, “Dynamics of short pulses and phase matched second harmonic generation in negative index materials,” Opt. Express 14, 4746–4756 (2006). [CrossRef] [PubMed]
  15. V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media,” Phys. Rev. A 76, 033829 (2007). [CrossRef]
  16. M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of linear absorption in opaque materials using phase-locked harmonic generation,” Phys. Rev. Lett. 101, 113905 (2008). [CrossRef] [PubMed]
  17. N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606–622 (1962). [CrossRef]
  18. V. Roppo, C. Cojocaru, F. Raineri, G. D’Aguanno, J. Trull, Y. Halioua, R. Raj, I. Sagnes, R. Vilaseca, and M. Scalora, “Field localization and enhancement of phase-locked second- and third-order harmonic generation in absorbing semiconductor cavities,” Phys. Rev. A 80, 043834 (2009). [CrossRef]
  19. 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]
  20. S. O’Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, “Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials,” Phys. Rev. B 69, 241101 (2004). [CrossRef]
  21. M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313, 502–504 (2006). [CrossRef] [PubMed]
  22. Q. Thommen and P. Mandel, “Electromagnetically induced left handedness in optically excited four-level atomic media,” Phys. Rev. Lett. 96, 053601 (2006). [CrossRef] [PubMed]
  23. A. Kussow, A. Akyurtlu, and N. Angkawisittpan, “Optically isotropic negative index of refraction metamaterial,” Phys. Status Solidi B 245, 992–997 (2008). [CrossRef]
  24. G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, “Transmission properties and field localization in a negative index Fabry–Perot etalon,” Laser Phys. 15, 590–593 (2005).
  25. M. Scalora and M. E. Crenshaw, “A beam propagation method that handles reflections,” Opt. Commun. 108, 191–196 (1994). [CrossRef]
  26. Y. R. Shen, Principles of Nonlinear Optics (Wiley, 2003).
  27. E. Fazio, F. Pettazzi, M. Centini, M. Chauvet, A. Belardini, M. Alonzo, C. Sibilia, M. Bertolotti, and M. Scalora, “Complete spatial and temporal locking in phase-mismatched second-harmonic generation,” Opt. Express 17, 3141–3147 (2009). [CrossRef] [PubMed]
  28. N. Akozbek, V. Roppo, M. A. Vincenti, J. V. Foreman, M. J. Bloemer, J. W. Haus, and M. Scalora, “Extraordinary nonlinear optics in ordinary semiconductors,” arXiv:0904.4082.
  29. V. Roppo, M. Centini, D. de Ceglia, M. A. Vicenti, J. W. Haus, N. Akozbeke, M. J. Bloemer, and M. Scalora, “Anomalous momentum states, non-specular reflections, and negative refraction of phase-locked, second-harmonic pulses,” Metamaterials 2, 135–144 (2008). [CrossRef]
  30. A. Zharov, “Subwavelength imaging with opaque nonlinear left-handed lenses,” Appl. Phys. Lett. 87, 091104 (2005). [CrossRef]
  31. C. Ciracì and E. Centeno, “Focusing of second-harmonic signals with nonlinear metamaterial lenses: A biophotonic microscopy approach,” Phys. Rev. Lett. 103, 063901 (2009). [CrossRef] [PubMed]

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