volume | PIER Journals

Abstract

We investigate the electromagnetic wave propagation across a finite inhomogeneous and anisotropic cylindrical metamaterial composite containing both positive and negative effective refractive index parts with linear spatial gradient. Exact analytical solutions for the electric and magnetic field distributions are obtained for a linear variation of effective refractive index across the structure. The model allows for general temporal dispersion and uniform losses within the composite.

1. Veselago, V. G., "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Uspekhi, Vol. 10, 509-514, 1968, Doi: 10.1070/PU1968v010n04ABEH003699.
doi:10.1070/PU1968v010n04ABEH003699 Google Scholar

2. Pendry, J. B., A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low frequency plasmons in thin-wire structures," J. Phys. — Condens. Mat., Vol. 10, 4785-4809, 1998, Doi: 10.1088/0953-8984/10/22/007.
doi:10.1088/0953-8984/10/22/007 Google Scholar

3. Pendry, J. B., A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE T. Microw. Theory, Vol. 47, 2075-2084, 1998, Doi: 10.1088/0953-8984/10/22/007.
doi:10.1109/22.798002 Google Scholar

4. Falcone, F., T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marques, F. Martin, and M. Sorolla, "Babinet principle applied to the design of metasurfaces and metamaterials," Phys. Rev. Lett., Vol. 93, No. 19, 197401-1-197401-4, 2004, Doi: 10.1103/PhysRevLett.93.197401.
doi:10.1103/PhysRevLett.93.197401 Google Scholar

5. Dolling, G., 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., Vol. 30, 3198-3200, 2005, Doi: 10.1364/OL.30.003198.
doi:10.1364/OL.30.003198 Google Scholar

6. 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, No. 13, 137404-1-137404-4, 2005, Doi: 10.1103/PhysRevLett.95.137404.
doi:10.1103/PhysRevLett.95.137404 Google Scholar

7. Kafesaki, M., I. Tsiapa, N. Katsarakis, T. Koschny, C. M. Soukoulis, and E. N. Economou, "Left-handed metamaterials: The fishnet structure and its variations," Phys. Rev. B, Vol. 75, 235114-1-235114-9, 2007, Doi: 0.1103/PhysRevB.75.235114. Google Scholar

8. 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.
doi:10.1038/nature07247 Google Scholar

9. Shelby, R. A., D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science, Vol. 292, 77-79, 2001, Doi: 10.1126/science.1058847.
doi:10.1126/science.1058847 Google Scholar

10. Xiao, S., U. K. Chettiar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, "Yellow-light negative-index metamaterials," Opt. Lett., Vol. 34, 3478-3480, 2009, Doi: 10.1364/OL.34.003478.
doi:10.1364/OL.34.003478 Google Scholar

11. Cai, W. and V. M. Shalaev, "Optical Metamaterials: Fundamentals and Applications," Springer, Dordrecht, 2009, doi:10.1007/978-1-4419-1151-3. Google Scholar

12. Ramakrishna, S. A. and T. M. Grzegorczyk, Physics and Applications of Negative Refractive Index Materials, SPIE Press, Bellingham, WA & CRC Press, Taylor & Francis Group, Boca Raton FL, 2009, Doi: 10.1080/00107510903257459.

13. Pendry, J. B., "Negative refraction makes a perfect lens," Phys. Rev. Lett., Vol. 85, 3966-3969, 2000. Doi: 10.1103/PhysRevLett.85.3966.
doi:10.1103/PhysRevLett.85.3966 Google Scholar

14. Fang, N., H. Lee, C. Sun, and X. Zhang, "Sub-diffraction-limited optical imaging with a silver superlens," Science, Vol. 308, 534-537, 2005, Doi: 10.1126/science.1108759.
doi:10.1126/science.1108759 Google Scholar

15. Engheta, N., "An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability," IEEE Anten. Wirel. Propag. Lett., Vol. 1, 10-13, 2002, Doi: 10.1109/LAWP.2002.802576.
doi:10.1109/LAWP.2002.802576 Google Scholar

16. Pendry, J. B., D. Shurig, and D. R. Smith, "Controlling electromagnetic fields," Science, Vol. 312, 1780-1782, 2006, Doi: 10.1126/science.1126493.
doi:10.1126/science.1125907 Google Scholar

17. Jacob, Z., L. V. Alekseyev, and E. Nerimanov, "Optical hyperlens: Far-field imaging beyond the diffraction limit," Opt. Express, Vol. 14, 8247-8256, 2006, Doi: 10.1364/OE.14.008247.
doi:10.1364/OE.14.008247 Google Scholar

18. Cai, W., U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photonics, Vol. 1, 224-227, 2007, Doi: 10.1038/nphoton.2007.28.
doi:10.1038/nphoton.2007.28 Google Scholar

19. Fung, T. H., L. L. Leung, J. J. Xiao, and K. W. Yu, "Controlling electric fields spatially by graded metamaterials: Implication on enhanced nonlinear optical responses," Opt. Commun., Vol. 282, 1028-1031, 2009, Doi: 10.1016/j.optcom.2008.11.028.
doi:10.1016/j.optcom.2008.11.028 Google Scholar

20. Ramakrishna, S. A. and J. B. Pendry, "Spherical perfect lens: Solutions of Maxwell’s equations for spherical geometry," Phys. Rev. B, Vol. 69, 115115-1-115115-7, 2004, Doi: 10.1103/PhysRevB.69.115115. Google Scholar

21. Smith, D. R., J. J. Mock, A. F. Starr, and D. Schurig, "Gradient index metamaterials," Phys. Rev. E, Vol. 71, 036609-1-036609-6, 2005, Doi: 10.1103/PhysRevE.71.036609. Google Scholar

22. Pinchuk, A. O. and G. C. Schatz, "Metamaterials with gradient negative index of refraction," J. Opt. Soc. Am. A, Vol. 24, A39-A44, 2007, Doi: 10.1364/JOSAA.24.000A39.
doi:10.1364/JOSAA.24.000A39 Google Scholar

23. Litchinitser, N. M., A. I. Maimistov, I. R. Gabitov, R. Z. Sagdeev, and V. M. Shalaev, "Metamaterials: Electromagnetic enhancement at zero-index transition," Opt. Lett., Vol. 33, 2350-2352, 2008, Doi: 10.1364/OL.33.002350.
doi:10.1364/OL.33.002350 Google Scholar

24. Dalarsson, M. and P. Tassin, "Analytical solution for wave propagation through a graded index interface between a right-handed and a left-handed material," Opt. Express, Vol. 17, No. 8, 6747-6752, 2009, Doi: 10.1364/OE.17.006747.
doi:10.1364/OE.17.006747 Google Scholar

25. Dalarsson, M., M. Norgren, and Z. Jaksic, "Lossy gradient index metamaterial with sinusoidal periodicity of refractive index: Case of constant impedance throughout the structure," J. Nanophotonics, Vol. 5, No. 1, 051804-1-051804-8, 2011, Doi: 10.1117/1.3590251.
doi:10.1117/1.3590251 Google Scholar

26. Dalarsson, M., M. Norgren, N. Doncov, and Z. Jaksic, "Lossy gradient index transmission optics with arbitrary periodic permittivity and permeability and constant impedance throughout the structure," J. Opt., Vol. 14, No. 6, 065102-1-065102-7, 2012, Doi: 10.1088/2040-8978/14/6/065102.
doi:10.1088/2040-8978/14/6/065102 Google Scholar

27. Dalarsson, M., M. Norgren, T. Asenov, N. Doncov, and Z. Jaksic, "Exact analytical solution for fields in gradient index metamaterials with different loss factors in negative and positive refractive index segments," J. Nanophotonics, Vol. 7, No. 1, 073086-1-073086-1, 2013, Doi: 10.1117/1.JNP.7.073086.
doi:10.1117/1.JNP.7.073086 Google Scholar

28. Dalarsson, M., M. Norgren, T. Asenov, and N. Doncov, "Arbitrary loss factors in the wave propagation between RHM and LHM media with constant impedance throughout the structure," Progress In Electromagnetics Research, Vol. 137, 527-538, 2013.
doi:10.2528/PIER13013004 Google Scholar

29. Mei, , Z. L., J. Bai, and T. J. Cui, "Gradient index metamaterials realized by drilling hole arrays," J. Phys. D, Vol. 43, 055404-1-055404-4, 2010, Doi: 10.1088/0022-3727/43/5/055404. Google Scholar

30. Kildishev, A. V. and V. M. Shalaev, "Engineering space for light via transformation optics," Opt. Lett., Vol. 33, 43-45, 2008, Doi: 10.1364/OL.33.000043.
doi:10.1364/OL.33.000043 Google Scholar

31. Li, J. and J. B. Pendry, "Hiding under the Carpet: A new strategy for cloaking," Phys. Rev. Lett., Vol. 101, No. 20, 203901-1-203901-4, 2008, Doi: 10.1103/PhysRevLett.101.203901.
doi:10.1103/PhysRevLett.101.203901 Google Scholar

32. Valentine, J., J. Li, T. Zentgraf, G. Bartal, and X. Zhang, "An optical cloak made of dielectrics," Nat. Mater., Vol. 8, 568-571, 2009, Doi: 10.1038/nmat2461.
doi:10.1038/nmat2461 Google Scholar

33. Liu, R., X.M. Yang, J. G. Gollub, J. J.Mock, T. J. Cui, and D. R. Smith, "Gradient index circuit by waveguided metamaterials," Appl. Phys. Lett., Vol. 94, 073506-1-073506-3, 2009, Doi: 10.1063/1.3081399. Google Scholar

34. Savini, G., P. A. R. Ade, and J. Zhang, "A new artificial material approach for flat THz frequency lenses," Opt. Express, Vol. 20, 25766-25773, 2012, Doi: 10.1364/OE.20.025766.
doi:10.1364/OE.20.025766 Google Scholar

35. Jain, S., M. Abdel-Mageed, and R. Mittra, "Flat-lens design using field transformation and its comparison with those based on transformation optics and ray optics," IEEE Anten. Wirel. Propag. Lett., Vol. 12, 777-780, 2013, Doi: 10.1109/LAWP.2013.2270946.
doi:10.1109/LAWP.2013.2270946 Google Scholar

Dr. Mariana Dalarsson

Dr. Martin Norgren

Prof. Zoran Jaksic