volume | PIER Journals

Abstract

We numerically analyze the optical response and nonlinear susceptibilities of fishnet metamaterials with the holes infiltrated by a third-order nonlinear dielectric. Through full-wave simulations and by employing a nonlinear parameter retrieval method, we confirm and quantify the enhanced nonlinearities, showing bulk third-order nonlinear susceptibilities that are up to two orders of magnitude larger than the nonlinear dielectric. We also use the retrieved parameters to calculate the material figure of merits and the conversion efficiencies, showing material figure of merits up to two orders of magnitude larger and conversion efficiencies up to four orders of magnitude larger than the nonlinear dielectric alone. Though these results are calculated using one-unit-cell thick structures, the large magnitude of the enhancement still makes these structures attractive, allowing reasonable conversion efficiencies supported by even subwavelength slabs.

1. Pendry, J. B., D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science, Vol. 312, No. 1780, 1780-1782, 2006.
doi:10.1126/science.1125907

2. Smith, D. R., W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity ," Phys. Rev. Lett., Vol. 84, No. 18, 4184-4187, 2000.
doi:10.1103/PhysRevLett.84.4184

3. Shelby, R. A., D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science, Vol. 292, No. 5514, 77-79, 2001.
doi:10.1126/science.1058847

4. Schurig, D., J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science, Vol. 314, No. 5801, 977-980, 2006.
doi:10.1126/science.1133628

5. Shao, J., H. Zhang, Y. Lin, and H. Xin, "Dual-frequency electromagnetic cloaks enabled by LC-based metamaterial circuits," Progress In Electromagnetics Research, Vol. 119, 225-237, 2011.
doi:10.2528/PIER11052507

6. Shalaev, V. M., "Optical negative-index metamaterials," Nature Photon., Vol. 1, 41-48, 2006.

7. Soukoulis, C. M., S. Linden, and M.Wegener, "Negative refractive index at optical wavelengths," Science, Vol. 315, 47-49, 2007.
doi:10.1126/science.1136481

8. Busch, K., G. von Freymann, S. Linden, S. Mingaleev, L. Tkeshelashvili, and M. Wegener, "Periodic nanostructures for photonics," Phys. Rep., Vol. 444, No. 3, 101-202, 2007.
doi:10.1016/j.physrep.2007.02.011

9. Oraizi, H., A. Abdolali, and N. Vaseghi, "Application of double zero metamaterials as radar absorbing materials for the reduction of radar cross section ," Progress In Electromagnetics Research, Vol. 101, 323-337, 2010.
doi:10.2528/PIER10010603

10. Duan, Z., Y. Wang, X. Mao, W.-X. Wang, and M. Chen, "Experimental demonstration of double-negative metamaterials partially filled in a circular waveguide," Progress In Electromagnetics Research, Vol. 121, 215-224, 2011.
doi:10.2528/PIER11090502

11. Li, J., F.-Q. Yang, and J. Dong, "Design and simulation of L-shaped chiral negative refractive index structure," Progress In Electromagnetics Research, Vol. 116, 395-408, 2011.

12. Canto, J. R., C. R. Paiva, and A. M. Barbosa, "Dispersion and losses in surface waveguides containing double negative or chiral metamaterials," Progress In Electromagnetics Research, Vol. 116, 409-423, 2011.

13. Zhang, S., W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett., Vol. 95, 137404, 2005.
doi:10.1103/PhysRevLett.95.137404

14. Dolling, G., C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Low-loss negative-index metamaterial at telecommunication wavelengths," Opt. Lett., Vol. 31, No. 12, 1800-1802, 2006.
doi:10.1364/OL.31.001800

15. Chettiar, U. K., A. V. Kildishev, H.-K. Yuan, W. Cai, S. Xiao, V. P. Drachev, and V. M. Shalaev, "Dual-band negative index metamaterial: Double negative at 813nm and single negative at 772 nm," Opt. Lett., Vol. 32, No. 12, 1671-1673, 2007.
doi:10.1364/OL.32.001671

16. Li, T., J.-Q. Li, F.-M. Wang, Q.-J. Wang, H. Liu, S.-N. Zhu, and Y.-Y. Zhu, "Exploring magnetic plasmon polaritons in optical transmission through hole arrays perforated in trilayer structures," Appl. Phys. Lett., Vol. 90, No. 25, 251112, 2007.
doi:10.1063/1.2750394

17. Valentine, J., S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Three-dimensional optical metamaterial with a negative refractive index," Nature, Vol. 455, 376-379, 2008.
doi:10.1038/nature07247

18. Minovich, A., D. N. Neshev, D. A. Powell, I. V. Shadrivov, M. Lapine, H. T. Hattori, H. H. Tan, C. Jagadish, and Yu. S. Kivshar, "Tilted response of fishnet metamaterials at near-infrared optical wavelengths ," Phys. Rev. B,, Vol. 81, No. 11, 115109, 2010.
doi:10.1103/PhysRevB.81.115109

19. Dolling, G., M. Wegener, C. M. Soukoulis, and S. Linden, "Design-related losses of double-fishnet negative-index photonic metamaterials," Opt. Express, Vol. 15, No. 18, 11536-11538, 2007.
doi:10.1364/OE.15.011536

20. Ku, Z. and S. R. J. Brueck, "Comparison of negative refractive index materials with circular, elliptical and rectangular holes," Opt. Express, Vol. 15, No. 8, 4515-4522, 2007.
doi:10.1364/OE.15.004515

21. Zhang, S., W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, "Near-infrared double negative metamaterials," Opt. Express, Vol. 13, No. 12, 4922-4930, 2005.
doi:10.1364/OPEX.13.004922

22. Minovich, A., D. N. Neshev, D. A. Powell, and I. V. Shadrivov, "Tunable fishnet metamaterials infiltrated by liquid crystals," Appl. Phys. Lett., Vol. 96, No. 19, 193103, 2010.
doi:10.1063/1.3427429

23. Wang, X., D.-H. Kwon, D. H.Werner, I.-C. Khoo, A. V. Kildishev, and V. M. Shalaev, "Tunable optical negative-index metamaterials employing anisotropic liquid crystals," Appl. Phys. Lett., Vol. 91, No. 14, 143122, 2007.
doi:10.1063/1.2795345

24. Pendry, J. B., A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory, Vol. 47, No. 11, 2075-2084, 1999.
doi:10.1109/22.798002

25. Zharov, A. A., I. V. Shadrivov, and Y. S. Kivshar, "Nonlinear properties of left-handed metamaterials," Phys. Rev. Lett., Vol. 91, No. 3, 037401, 2003.
doi:10.1103/PhysRevLett.91.037401

26. Klein, M. W., C. Enkrich, M. Wegener, and S. Linden, "Second-harmonic generation from magnetic metamaterials," Science, Vol. 313, No. 5786, 502-504, 2006.
doi:10.1126/science.1129198

27. Shadrivov, I. V., A. B. Kozyrev, D. W. van der Weide, and Y. S. Kivshar, "Tunable transmission and harmonic generation in nonlinear metamaterials," Appl. Phys. Lett., Vol. 93, No. 16, 161903, 2008.
doi:10.1063/1.2999634

28. Popov, A. and V. Shalaev, "Negative-index metamaterials: Second-harmonic generation, Manley-Rowe relations and parametric amplification," Appl. Phys. B, Vol. 84, No. 1, 131-137, 2006.
doi:10.1007/s00340-006-2167-4

29. Poutrina, E., S. Larouche, and D. R. Smith, "Parametric oscillator based on a single-layer resonant metamaterial," Opt. Commun., Vol. 283, No. 8, 1640-1646, 2010.
doi:10.1016/j.optcom.2009.11.037

30. Powell, D. A., I. V. Shadrivov, Y. S. Kivshar, and M. V. Gorkunov, "Self-tuning mechanisms of nonlinear split-ring resonators," Appl. Phys. Lett., Vol. 91, No. 14, 144107, 2007.
doi:10.1063/1.2794733

31. Shadrivov, I. V., A. B. Kozyrev, D. W. van der Weide, and Y. S. Kivshar, "Nonlinear magnetic metamaterials," Opt. Express, Vol. 16, No. 25, 20266-20271, 2008.
doi:10.1364/OE.16.020266

32. Rose, A., D. Huang, and D. R. Smith, "Controlling the second harmonic in a phase-matched negative-index metamaterial," Phys. Rev. Lett., Vol. 107, No. 6, 063902, 2011.
doi:10.1103/PhysRevLett.107.063902

33. Larouche, S. and D. R. Smith, "A retrieval method for nonlinear metamaterials," Opt. Commun., Vol. 283, No. 8, 1621-1627, 2010.
doi:10.1016/j.optcom.2009.10.107

34. Rose, A., S. Larouche, D. Huang, E. Poutrina, and D. R. Smith, "Nonlinear parameter retrieval from three-and four-wave mixing in metamaterials," Phys. Rev. E, Vol. 82, No. 3, 036608, 2010.
doi:10.1103/PhysRevE.82.036608

35. Rose, A., S. Larouche, and D. R. Smith, "Quantitative study of the enhancement of bulk nonlinearities in metamaterials," Phys. Rev. A, Vol. 84, No. 5, 053805, 2011.
doi:10.1103/PhysRevA.84.053805

36. Smith, D. R., S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from re°ection and transmission coefficients," Phys. Rev. B, Vol. 65, No. 19, 195104, 2002.
doi:10.1103/PhysRevB.65.195104

37. Smith, D. R., D. C. Vier, T. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamate rials," Phys. Rev. E, Vol. 71, No. 3, 036617, 2005.
doi:10.1103/PhysRevE.71.036617

Dr. Jun Guo

Dr. Yuanjiang Xiang

Dr. Xiaoyu Dai

Dr. Shuangchun Wen