Sensitivity of imaging properties of metal-dielectric layered flat lens to fabrication inaccuracies


We characterize the sensitivity of imaging properties of a layered silver-TiO2 flat lens to fabrication inaccuracies. The lens is designed for approximately diffraction-free imaging with subwavelength resolution at distances in the order of a wavelength. Its operation may be attributed to self-collimation with a secondary role of Fabry-Perot resonant transmission, even though the first order effective medium description of the structure is inaccurate. Super-resolution is maintained for a broad range of overall thicknesses and the total thickness of the multilayer is limited by absorption. The tolerance analysis indicates that the resolution and transmission efficiency are highly sensitive to small changes of layer thicknesses.

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  1. 1.

    J.B. Pendry, “Negative refraction makes a perfect lens”, Phys. Rev. Lett. 85, 3966–3969 (2000).

    Article  ADS  Google Scholar 

  2. 2.

    N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens”, Science 308, 534–537 (2005).

    Article  ADS  Google Scholar 

  3. 3.

    D.O.S. Melville and R.J. Blaikie, “Super-resolution imaging through a planar silver layer”, Opt. Express 13, 2127–2134 (2005).

    Article  ADS  Google Scholar 

  4. 4.

    Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens”, Nano Lett. 7, 403–408 (2007).

    Article  ADS  Google Scholar 

  5. 5.

    P. Wróbel, J. Pniewski, T.J. Antosiewicz, and T. Szoplik, “Focusing radially polarized light by concentrically corrugated silver film without a hole”, Phys. Rev. Lett. 102, 183902 (2009).

    Article  ADS  Google Scholar 

  6. 6.

    Z. Liu, S. Durant, H. Lee, Y. Pikus, Y. Xiong, C. Sun, and X. Zhang, “Experimental studies of far-field superlens for sub-diffractional optical imaging”, Opt. Express 15, 6947–6954 (2007).

    Article  ADS  Google Scholar 

  7. 7.

    Y. Xiong, Z. Liu, S. Durant, H. Lee, C. Sun, and X. Zhang, “Tuning the far-field superlens: from UV to visible”, Opt. Express 15, 7095–7102 (2007).

    Article  ADS  Google Scholar 

  8. 8.

    E.A. Ray, M.J. Hampton, and R. Lopez, “Simple demonstration of visible evanescent-wave enhancement with far-field detection”, Opt. Lett. 34, 2048–2050 (2009).

    Article  ADS  Google Scholar 

  9. 9.

    B. Wood, J.B. Pendry, and D.P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system”, Phys. Rev. B74, 115116 (2006).

    ADS  Google Scholar 

  10. 10.

    D.O.S. Melville and R.J. Blaikie, “Experimental comparison of resolution and pattern fidelity in single- and double-layer planar lens lithography”, J. Opt. Soc. Am. B23, 461–467 (2006).

    ADS  Google Scholar 

  11. 11.

    M. Scalora, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, D. Ceglia, M. Centini, A. Mandatori, C. Sibilia, N. Akozbek, M.G. Cappeddu, M. Fowler, and J. Haus, “Negative refraction and sub-wavelength focusing in the visible range using transparent metallo-dielectric stacks”, Opt. Express 15, 508–523 (2007).

    Article  ADS  Google Scholar 

  12. 12.

    X. Li, S. He, and Y. Jin, “Subwavelength focusing with a multilayered Fabry-Perot structure at optical frequencies”, Phys. Rev. B75, 045103 (2007).

    ADS  Google Scholar 

  13. 13.

    D. de Ceglia, M.A. Vincenti, M.G. Cappeddu, M. Centini, N. Akozbek, A. DOrazio, J. Haus, M.J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-IR ranges”, Phys. Rev. A77, 033848 (2008).

    ADS  Google Scholar 

  14. 14.

    M. Conforti, M. Guasoni, and C. De Angelis, “Subwavelength diffraction management”, Opt. Lett. 33, 2662–2664 (2008).

    Article  ADS  Google Scholar 

  15. 15.

    C.P. Moore, M.D. Arnold, P.J. Bones, and R.J. Blaikie, “Analysis and comparison of simulation techniques for silver superlenses”, Proc. Int. Conf. Nanoscience and Nanotechnology, ICONN 2008, 210–213 (2008).

  16. 16.

    C.P. Moore, M.D. Arnold, P.J. Bones, and R.J. Blaikie, “Image fidelity for single-layer and multi-layer silver superlenses”, J. Opt. Soc. Am. A25, 911–918 (2008).

    Article  ADS  Google Scholar 

  17. 17.

    C.P. Moore, R.J. Blaikie, and M.D. Arnold, “An improved transfer-matrix model for optical superlenses”, Opt. Express 17, 14260–14269 (2009).

    Article  ADS  Google Scholar 

  18. 18.

    R. Kotynski and T. Stefaniuk, “Comparison of imaging with sub-wavelength resolution in the canalization and resonant tunnelling regimes”, J. Opt. A-Pure Appl. Op. 11, 015001 (2009).

    Article  ADS  Google Scholar 

  19. 19.

    N. Mattiucci, G. D’Aguanno, M. Scalora, M.J. Bloemer, and C. Sibilia, “Transmission function properties for multi-layered structures: Application to superresolution”, Opt. Express 17, 17517–17529 (2009).

    Article  ADS  Google Scholar 

  20. 20.

    Q.M. Quan, S.L. Zhu, and R.P. Wang, “Refraction in the fixed direction at the surface of dielectric/silver superlattice”, Phys. Lett. A359, 547–549 (2006).

    ADS  Google Scholar 

  21. 21.

    X. Li and F. Zhuang, “Multilayered structures with high subwavelength resolution based on the metal-dielectric composites”, J. Opt. Soc. Am. A26, 2521–2525 (2009).

    Article  Google Scholar 

  22. 22.

    R. Kotyński and T. Stefaniuk, “Multiscale analysis of subwavelength imaging with metal-dielectric multilayers”, Opt. Lett. 35, 1133–1135 (2010).

    Article  Google Scholar 

  23. 23.

    R. Kotyński, T. Stefaniuk, and A. Pastuszczak, “Sub-wavelength diffraction-free imaging with low-loss metal-dielectric multilayers”, ArXiv:1002.0658. (submitted to J. Appl. Phys. A, 2010)

  24. 24.

    P.A. Belov, C. Simovski, and P. Ikonen, “Canalization of subwavelength images by electro-magnetic crystals”, Phys. Rev. B71, 193105 (2005).

    ADS  Google Scholar 

  25. 25.

    P.A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime”, Phys. Rev. B73, 113110 (2006).

    ADS  Google Scholar 

  26. 26.

    M.A. Vincenti, A. D’Orazio, M.G. Cappeddu, N. Akozbek, M.J. Bloemer, and M. Scalora, “Semiconductor-based superlens for subwavelength resolution below the diffraction limit at extreme ultraviolet frequencies”, J. Appl. Phys. 105, 103103 (2009).

    Article  ADS  Google Scholar 

  27. 27.

    J.W. Goodman, Introduction to Fourier Optics, Roberts & Co Publ., 3rd ed., 2005.

  28. 28.

    B. Saleh and M. Teich, Fundamentals of Photonics, John Wiley & Sons, Inc, 2nd ed., 2007.

  29. 29.

    R. Kotyński, “Fourier optics approach to imaging with sub-wavelength resolution through metal-dielectric multilayers”, Opto-Electron. Rev. 18, 366–375 (2010), (in press, arXiv 1006.3669).

    Article  Google Scholar 

  30. 30.

    A. Taflove and S.C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, Artec House Inc., Boston, 2nd ed., 2000.

    Google Scholar 

  31. 31.

    A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J.D. Joannopoulos, S.G. Johnson, and G. Burr, “Improving accuracy by subpixel smoothing in FDTD”, Opt. Lett. 31, 2972–2974 (2006).

    Article  ADS  Google Scholar 

  32. 32. (an overview of the computation engine implemented in the Crystal Wave tool by the Photon Design Ltd., Oxford).

  33. 33.

    H.V. Baghdasaryan and T.M. Knyazyan, “Problem of plane EM wave self-action in multilayer structure: an exact solution”, Opt. Quant. Electron. 31, 1059–1072 (1999).

    Article  Google Scholar 

  34. 34.

    H.V. Baghdasaryan, T.M. Knyazyan, T.H. Baghdasaryan, and G.G. Eyramjyan, “Development of the method of single expression (MSE) for analysis of plane wave oblique incidence on multilayer structures having complex permittivity and permeability”, Proc. ICTON’2008, Vol. 1, 250–254 (2008).

    Google Scholar 

  35. 35.

    H.V. Baghdasaryan, T.M. Knyazyan, and G.G. Eyramjyan, “Electrodynamical analysis of a transmittive metal-dielectric microstructure by the method of single expression”, Proc. European Microwave Association 4, 76–81 (2008).

    Google Scholar 

  36. 36.

    H.V. Baghdasaryan and T.M. Knyazyan, “Modelling of strongly nonlinear sinusoidal Bragg gratings by the method of single expression”, Opt. Quant. Electron. 32, 869–883 (2000).

    Article  Google Scholar 

  37. 37.

    P. Markos and C. M. Soukoulis, Wave Propagation. From Electrons to Photonic Crystals and Left-handed Materials, Princeton University Press, Princeton and Oxford, 2008.

    Google Scholar 

  38. 38.

    O. Duyar, F. Placido, and H.Z. Durusoy, “Optimization of TiO2 films prepared by reactive electron beam evaporation of Ti3O5”, J. Phys. D. Appl. Phys. 41, 095307 (2008).

    Article  ADS  Google Scholar 

  39. 39.

    P. Johnson and R. Christy, “Optical constants of the noble metals”, Phys. Rev. B6, 4370–4379 (1972).

    ADS  Google Scholar 

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Correspondence to R. Kotyński.

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Kotyński, R., Baghdasaryan, H., Stefaniuk, T. et al. Sensitivity of imaging properties of metal-dielectric layered flat lens to fabrication inaccuracies. Opto-Electron. Rev. 18, 446–457 (2010).

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  • plasmonics
  • nanophotonics
  • nanolenses, super-resolution
  • metal-dielectric multilayers