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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry van Driel
  • Vol. 29, Iss. 1 — Jan. 1, 2012
  • pp: 79–87

Tunable gradient refractive index optics using graded plasmonic crystals with semiconductor rods

Borislav Vasić and Radoš Gajić  »View Author Affiliations


JOSA B, Vol. 29, Issue 1, pp. 79-87 (2012)
http://dx.doi.org/10.1364/JOSAB.29.000079


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Abstract

Using numerical simulations, we demonstrate the feasibility of tunable gradient refractive index optics at terahertz frequencies based on two-dimensional graded plasmonic crystals (GPCs). They consist of semiconductor rods with spatially dependent radii. In the effective medium approximation, the GPCs can be considered as effective media with a graded effective dielectric permittivity. The semiconductor rods have the Drude-type dispersion. By varying free charge carrier concentration in the rods, it is possible to tune their permittivity. In accordance to effective medium theory, the effective permittivity of the whole GPC is changed at the same time. This property is used for the demonstration of a GPC-based lens with a tunable focus, beam deflector with tunable angle of the beam deflection, and the half Maxwell-fisheye and the Luneburg lens as antennas with tunable radiation patterns. In particular, these GPCs can be made invisible to the incoming radiation by equaling the real part of the rods permittivity to the permittivity of air background.

© 2011 Optical Society of America

OCIS Codes
(080.2710) Geometric optics : Inhomogeneous optical media
(230.4110) Optical devices : Modulators
(260.2065) Physical optics : Effective medium theory
(160.5298) Materials : Photonic crystals

ToC Category:
Materials

History
Original Manuscript: August 15, 2011
Manuscript Accepted: October 18, 2011
Published: December 9, 2011

Citation
Borislav Vasić and Radoš Gajić, "Tunable gradient refractive index optics using graded plasmonic crystals with semiconductor rods," J. Opt. Soc. Am. B 29, 79-87 (2012)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-29-1-79


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References

  1. J.-M. Liu, Photonic Devices (Cambridge University, 2005), chapters 5–7. [CrossRef]
  2. T. S. El-Bawab, Optical Switching (Springer, 2005), chapters 2–6.
  3. S. Sato, “Applications of liquid crystals to variable-focusing lenses,” Opt. Rev. 6, 471–485 (1999). [CrossRef]
  4. C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient Index Optics: Fundamentals and Applications (Springer Verlag, 2002), chapter 1.
  5. E. McLeod and C. B. Arnold, “Mechanics and refractive power optimization of tunable acoustic gradient lenses,” J. Appl. Phys. 102, 033104 (2007). [CrossRef]
  6. X. Mao, S.-C. S. Lin, M. I. Lapsley, J. Shi, B. K. Juluri, and T. J. Huang, “Tunable liquid gradient refractive index (L-GRIN) lens with two degrees of freedom,” Lab Chip 9, 2050–2058 (2009). [CrossRef] [PubMed]
  7. Y.-Y. Kao, P. C.-P. Chao, and C.-W. Hsueh, “A new low-voltage-driven GRIN liquid crystal lens with multiple ring electrodes in unequal widths,” Opt. Express 18, 18506–18518 (2010). [CrossRef] [PubMed]
  8. D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E 71, 036609 (2005). [CrossRef]
  9. R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009). [CrossRef] [PubMed]
  10. J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009). [CrossRef] [PubMed]
  11. J. H. Lee, J. Blair, V. A. Tamma, Q. Wu, S. J. Rhee, C. J. Summers, and W. Park, “Direct visualization of optical frequency invisibility cloak based on silicon nanorod array,” Opt. Express 17, 12922–12928 (2009). [CrossRef] [PubMed]
  12. H. Kurt, E. Colak, O. Cakmak, H. Caglayan, and E. Ozbay, “The focusing effect of graded photonic crystals,” Appl. Phys. Lett. 93, 171108 (2008). [CrossRef]
  13. A. Figotin, Y. A. Godin, and I. Vitebsky, “Two-dimensional tunable photonic crystals,” Phys. Rev. B 57, 2841–2848 (1998). [CrossRef]
  14. K. Busch and S. John, “Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum,” Phys. Rev. Lett. 83, 967–970 (1999). [CrossRef]
  15. P. Halevi and F. Ramos-Mendieta, “Tunable photonic crystals with semiconducting constituents,” Phys. Rev. Lett. 85, 1875–1878 (2000). [CrossRef] [PubMed]
  16. C.-S. Kee and H. Lim, “Tunable complete photonic band gaps of two-dimensional photonic crystals with intrinsic semiconductor rods,” Phys. Rev. B 64, 121103 (2001). [CrossRef]
  17. S. W. Leonard, H. M. van Driel, J. Schilling, and R. B. Wehrspohn, “Ultrafast band-edge tuning of a two-dimensional silicon photonic crystal via free-carrier injection,” Phys. Rev. B 66, 161102(2002). [CrossRef]
  18. X. Hu, Q. Zhang, Y. Liu, B. Cheng, and D. Zhang, “Ultrafast three-dimensional tunable photonic crystal,” Appl. Phys. Lett. 83, 2518–2520 (2003). [CrossRef]
  19. D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov, A. B. Pevtsov, and A. V. Sel’kin, “Ultrafast optical switching in three-dimensional photonic crystals,” Phys. Rev. Lett. 91, 213903 (2003). [CrossRef] [PubMed]
  20. C.-S. Kee, J.-E. Kim, H. Y. Park, I. Park, and H. Lim, “Two-dimensional tunable magnetic photonic crystals,” Phys. Rev. B 61, 15523–15525 (2000). [CrossRef]
  21. S. Liu, J. Du, Z. Lin, R. X. Wu, and S. T. Chui, “Formation of robust and completely tunable resonant photonic band gaps,” Phys. Rev. B 78, 155101 (2008). [CrossRef]
  22. S. Kim and V. Gopalan, “Strain-tunable photonic band gap crystals,” Appl. Phys. Lett. 78, 3015–3017 (2001). [CrossRef]
  23. H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444, 597–600 (2006). [CrossRef] [PubMed]
  24. H.-T. Chen, J. F. O’Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrenkenhamer, and W. J. Padilla, “Experimental demonstration of frequency-agile terahertz metamaterials,” Nat. Photon. 2, 295–298 (2008). [CrossRef]
  25. A. Degiron, J. J. Mock, and D. R. Smith, “Modulating and tuning the response of metamaterials at the unit cell level,” Opt. Express 15, 1115–1127 (2007). [CrossRef] [PubMed]
  26. J.-M. Manceau, N.-H. Shen, M. Kafesaki, C. M. Soukoulis, and S. Tzortzakis, “Dynamic response of metamaterials in the terahertz regime: blueshift tunability and broadband phase modulation,” Appl. Phys. Lett. 96, 021111 (2010). [CrossRef]
  27. N.-H. Shen, M. Massaouti, M. Gokkavas, J.-M. Manceau, E. Ozbay, M. Kafesaki, T. Koschny, S. Tzortzakis, and C. M. Soukoulis, “Optically implemented broadband blueshift switch in the terahertz regime,” Phys. Rev. Lett. 106, 037403 (2011). [CrossRef] [PubMed]
  28. H. Tao, A. C. Strikwerda, K. Fan, W. J. Padilla, X. Zhang, and R. D. Averitt, “Reconfigurable terahertz metamaterials,” Phys. Rev. Lett. 103, 147401 (2009). [CrossRef] [PubMed]
  29. J. Y. Ou, E. Plum, L. Jiang, and N. I. Zheludev, “Reconfigurable photonic metamaterials,” Nano Lett. 11, 2142–2144 (2011). [CrossRef] [PubMed]
  30. I. M. Pryce, K. Aydin, Y. A. Kelaita, R. M. Briggs, and H. A. Atwater, “Highly strained compliant optical metamaterials with large frequency tunability,” Nano Lett. 10, 4222–4227 (2010). [CrossRef] [PubMed]
  31. J. Han, A. Lakhtakia, and C.-W. Qiu, “Terahertz metamaterials with semiconductor split-ring resonators for magnetostatic tunability,” Opt. Express 16, 14390–14396 (2008). [CrossRef] [PubMed]
  32. V. Fedotov, A. Tsiatmas, J. H. Shi, R. Buckingham, P. de Groot, Y. Chen, S. Wang, and N. Zheludev, “Temperature control of Fano resonances and transmission in superconducting metamaterials,” Opt. Express 18, 9015–9019 (2010). [CrossRef] [PubMed]
  33. S. Xiao, U. K. Chettiar, A. V. Kildishev, V. Drachev, I. C. Khoo, and V. M. Shalaev, “Tunable magnetic response of metamaterials,” Appl. Phys. Lett. 95, 033115 (2009). [CrossRef]
  34. A. Minovich, D. N. Neshev, D. A. Powell, I. V. Shadrivov, and Y. S. Kivshar, “Tunable fishnet metamaterials infiltrated by liquid crystals,” Appl. Phys. Lett. 96, 193103 (2010). [CrossRef]
  35. T. Driscoll, H.-T. Kim, B.-G. Chae, B.-J. Kim, Y.-W. Lee, N. M. Jokerst, S. Palit, D. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science 325, 1518–1521 (2009). [CrossRef] [PubMed]
  36. J. Zhu, J. Han, Z. Tian, J. Gu, Z. Chen, and W. Zhang, “Thermal broadband tunable terahertz metamaterials,” Opt. Commun. 284, 3129–3133 (2011). [CrossRef]
  37. A. V. Krasavin and N. I. Zheludev, “Active plasmonics: controlling signals in Au/Ga waveguide using nanoscale structural transformations,” Appl. Phys. Lett. 84, 1416–1418 (2004). [CrossRef]
  38. J. G. Rivas, M. Kuttge, H. Kurz, P. H. Bolivar, and J. A. Sanchez-Gil, “Low-frequency active surface plasmon optics on semiconductors,” Appl. Phys. Lett. 88, 082106 (2006). [CrossRef]
  39. D. Pacifici, H. J. Lezec, and H. A. Atwater, “All-optical modulation by plasmonic excitation of CdSe quantum dots,” Nat. Photon. 1, 402–406 (2007). [CrossRef]
  40. J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: a metal-oxide-Si field effect plasmonic modulator,” Nano Lett. 9, 897–902 (2009). [CrossRef] [PubMed]
  41. R. A. Pala, K. T. Shimizu, N. A. Melosh, and M. L. Brongersma, “A nonvolatile plasmonic switch employing photochromic molecules,” Nano Lett. 8, 1506–1510 (2008). [CrossRef] [PubMed]
  42. K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photon. 3, 55–58 (2009). [CrossRef]
  43. M.-K. Chen, Y.-C. Chang, C.-E. Yang, Y. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, “Tunable terahertz plasmonic lenses based on semiconductor microslits,” Microw. Opt. Technol. Lett. 52, 979–981 (2010). [CrossRef]
  44. C. Min, P. Wang, X. Jiao, Y. Deng, and H. Ming, “Beam manipulating by metallic nano-optic lens containing nonlinear media,” Opt. Express 15, 9541–9546 (2007). [CrossRef] [PubMed]
  45. M. D. Goldflam, T. Driscoll, B. Chapler, O. Khatib, N. M. Jokerst, S. Palit, D. R. Smith, B.-J. Kim, G. Seo, H.-T. Kim, M. Di Ventra, and D. N. Basov, “Reconfigurable gradient index using VO2 memory metamaterials,” Appl. Phys. Lett. 99, 044103 (2011). [CrossRef]
  46. C. Gomez-Reino, M. V. Perez, C. Bao, and M. T. Flore-Arias, “Design of GRIN optical components for coupling and interconnects,” Laser Photonics Rev. 2, 203–215 (2008). [CrossRef]
  47. Z. L. Mei, J. Bai, and T. J. Cui, “Gradient index metamaterials realized by drilling hole arrays,” J. Phys. D 43, 055404 (2010). [CrossRef]
  48. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999), pp. 157–159.
  49. R. K. Lüneburg, The Mathematical Theory of Optics (University of California, 1944), pp. 189–213.
  50. B. Vasić, G. Isić, R. Gajić, and K. Hingerl, “Controlling electromagnetic fields with graded photonic crystals in metamaterial regime,” Opt. Express 18, 20321–20333 (2010). [CrossRef] [PubMed]
  51. B. Vasić and R. Gajić, “Self-focusing media using graded photonic crystals: focusing, Fourier transforming and imaging, directive emission and directional cloaking,” J. Appl. Phys. 110, 053103 (2011). [CrossRef]
  52. P. Halevi, A. A. Krokhin, and J. Arriaga, “Photonic crystal optics and homogenization of 2D periodic composites,” Phys. Rev. Lett. 82, 719–722 (1999). [CrossRef]
  53. J. G. Rivas, C. Janke, P. Bolivar, and H. Kurz, “Transmission of THz radiation through InSb gratings of subwavelength apertures,” Opt. Express 13, 847–859 (2005). [CrossRef]
  54. H. Wallén, H. Kettunen, and A. Sihvola, “Composite near-field superlens design using mixing formulas and simulations,” Metamaterials 3, 129–139 (2009). [CrossRef]
  55. J. G. Rivas, P. H. Bolivar, and H. Kurz, “Thermal switching of the enhanced transmission of terahertz radiation through subwavelength apertures,” Opt. Lett. 29, 1680–1682 (2004). [CrossRef] [PubMed]
  56. C. Janke, J. G. Rivas, P. H. Bolivar, and H. Kurz, “All-optical switching of the transmission of electromagnetic radiation through subwavelength apertures,” Opt. Lett. 30, 2357–2359(2005). [CrossRef] [PubMed]
  57. I. Smolyaninov, “Two-dimensional metamaterial optics,” Laser Phys. Lett. 7, 259–269 (2010). [CrossRef]
  58. E. Devaux, J.-Y. Laluet, B. Stein, C. Genet, T. Ebbesen, J.-C. Weeber, and A. Dereux, “Refractive micro-optical elements for surface plasmons: from classical to gradient index optics,” Opt. Express 18, 20610–20619 (2010). [CrossRef] [PubMed]
  59. B. K. Juluri, S. Chin, S. Lin, T. R. Walker, L. Jensen, and T. J. Huang, “Propagation of designer surface plasmons in structured conductor surfaces with parabolic gradient index,” Opt. Express 17, 2997–3006 (2009). [CrossRef] [PubMed]
  60. T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnol. 6, 151–155 (2011). [CrossRef] [PubMed]
  61. A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011). [CrossRef] [PubMed]
  62. O. Paul, B. Reinhard, B. Krolla, R. Beigang, and M. Rahm, “Gradient index metamaterial based on slot elements,” Appl. Phys. Lett. 96, 241110 (2010). [CrossRef]
  63. J. Neu, B. Krolla, O. Paul, B. Reinhard, R. Beigang, and M. Rahm, “Metamaterial-based gradient index lens with strong focusing in the THz frequency range,” Opt. Express 18, 27748–27757(2010). [CrossRef]
  64. B. Scherger, C. Jördens, and M. Koch, “Variable-focus terahertz lens,” Opt. Express 19, 4528–4535 (2011). [CrossRef] [PubMed]
  65. P. West, S. Ishii, G. Naik, N. Emani, V. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. 4, 795–808 (2010). [CrossRef]

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