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Planar Gradient Hyperbolic Secant Lens for Subwavelength Focusing and Superresolution Imaging
Optics
Volume 1, Issue 1, December 2012, Pages: 1-10
Received: Dec. 3, 2012; Published: Dec. 30, 2012
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Authors
V. V. Kotlyar, Laser Measurements Laboratory of the Image Processing Systems Institute of the Russian Academy of Sciences, 151 Molodogvardeiskaya street, Samara, Russia
A. A. Kovalev, Laser Measurements Laboratory of the Image Processing Systems Institute of the Russian Academy of Sciences, 151 Molodogvardeiskaya street, Samara, Russia
A. G. Nalimov, Laser Measurements Laboratory of the Image Processing Systems Institute of the Russian Academy of Sciences, 151 Molodogvardeiskaya street, Samara, Russia
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Abstract
Integral relations to describe the propagation of a TE-wave from an external point source through the two-dimensional medium (plane interface) and the plane-parallel plate are proposed. We discuss three types of waves that contribute to the resulting light field, namely, the propagating waves and the first- and second-type surface waves. The comparison of near-field refractive lenses (SIL, NAIL) and a planar hyperbolic secant lens shows their numerical apertures to have close values, with the difference being as small as 5% for the Si-based optical elements. The FDTD-method simulation shows that by combining the gradient-index hyperbolic secant lens with a subwavelength diffraction grating or replacing it with its binary analog, the focal spot size can be made, respectively, 10% and 20% smaller than the diffraction-limited resolution in the 2D medium. We design a Si-based, planar binary microlens to generate a near-surface focal spot of full-width half-maximum size FWHM=0.102λ, where λ is the incident wavelength, which is practically devoid of side-lobes. It is shown that about 10 percent of the total incident beam energy goes to the far-field zone.
Keywords
Superresolution, Gradient-Index Lens, Secant Lens, Near-Field Lenses
To cite this article
V. V. Kotlyar, A. A. Kovalev, A. G. Nalimov, Planar Gradient Hyperbolic Secant Lens for Subwavelength Focusing and Superresolution Imaging, Optics. Vol. 1, No. 1, 2012, pp. 1-10. doi: 10.11648/j.optics.20120101.11
References
[1]
K. Huang, P. Shi, X. Kang, X. Zhang, and Y. Li, "Design of DOE for generating a needle of a strong longitudinally pola-rized field," Opt. Lett., vol. 35, pp. 965–967, 2010.
[2]
E.T.F. Rogers, J. Lindbery, T. Roy, S. Savo, J.E. Chad, M.R. Dennis, N.I. Zheludev, "A super-oscilatory lens optical mi-croscope for subwavelengh imaging," Nat. Mater., vol. 11, pp. 432–435, 2012.
[3]
J.Y. Lee, B.H. Hong, W.Y. Kim, S.K. Min, Y. Kim, M.V. Jouravlev, R. Bose, K.S. Kim, I.-C. Hwang, L.J. Kaufman, C.W. Wong, P. Kim, and K.S. Kim, "Near-field focusing and magnification through self-assembled nanoscale spherical lenses," Nature, vol. 460, pp. 498–501, 2009.
[4]
D.J. Godstein, "Resolution in light microscopy studied by computer simulations," J. Microsc. 166, pp. 185–197, 1992.
[5]
L. Novotny, and B. Hecht, Principles of Nano-Optics, Cam-bridge University Press, 2006.
[6]
A. Bouhelier, J. Renger, M.R. Beversluis, and L. Novotny, "Plasmon-coupled tip-enhanced near-field optical microscopy," J. Microsc., vol. 210, pp. 220–224, 2003.
[7]
K. Karrai, and X. Lorenz, "Enhanced reflectivity contrast in confocal solid immersion lens microscopy," Appl. Phys. Lett., vol. 77, pp. 3459–3461, 2000.
[8]
S.B. Ippolito , B.B. Goldberg, and M.S. Unlu, "High spatial resolution subsurface microscopy," Appl. Phys. Lett., vol. 78, pp. 4071–4073, 2001.
[9]
F.H. Koklu, S.B. Ippolito, B.B. Goldberg, and M.S. Ünlü, "Subsurface microscopy of integrated circuits with angular spectrum and polarization control," Opt. Lett., vol. 34, pp. 1261–1263, 2009.
[10]
D. Karabacak, K. Ekinci, C. Gan, G. Gbur, M. Ünlü, S. Ip-polito, B. Goldberg, and P. Carney, "Diffraction of evanescent waves and nanomechanical displacement detection," Opt. Lett., vol. 32, pp. 1881–1883, 2007.
[11]
D.R. Mason, M.V. Jouravlev, and K.S. Kim, "Enhanced resolution beyond the Abbe diffraction limit with wave-length-scale solid immersion lenses," Opt. Lett., vol. 35, pp. 2007–2009, 2010.
[12]
K. Huang, Y. Li Realization of a subwavelength focused spot without a longitudinal field component in a solid immersion lens-based system Opt. Lett., vol. 36, pp. 3536–3538, 2011.
[13]
D. Mc Closkey, J.J. Wang, and J.F. Donegan, "Low divergence photonic nanojets from Si3N4 microdisks," Opt. Express, vol. 20, pp. 128–140, 2011.
[14]
A. Di Falco, S.C. Kehr, and U. Leonhardt, "Luneberg lens in silicon photonics," Opt. Express, vol. 19, pp. 5156–5162, 2011.
[15]
T. Zentgrat, Y. Liu, M.N. Mikkelsen, J. Valentine, and X. Zhang, "Plasmonic Luneberg and Eaton lenses," Nat. Nano-techn. 6, pp. 151–155, 2011.
[16]
H. Wu, L.Y. Jiang, W. Jia, and X.Y. Li, "Imaging properties of an annular phtonic crystal slab for both TM-polarization and TE-polarization," J. Opt., vol. 13, pp. 095103, 2011.
[17]
X. Zhang, and Z. Liu, "Superlenses to onercome the diffraction limit," Nat. Mater., vol. 7, pp. 435–441, 2008.
[18]
J. Rho, Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, and X. Zhang, "Spherical hyperlens for two-dimensional sub-diffractional imaging at visible frequencies," Nat. Commun., vol. 1, pp. 143, 2010.
[19]
W. Chen, R.L. Nelson, and Q. Zhan, "Efficient miniature circular polarization analyzer design using hybrid spiral plasmonic lens," Opt. Lett., vol. 37, pp. 1442–1445, 2012.
[20]
S. Huang, H. Wang, K. Ding, and L. Tsang, "Subwavelength imaging enhancement through a tree-dimmensional plasmon superlens with rough surface," Opt. Lett., vol. 37, pp. 1295–1297, 2012.
[21]
J. Martin, J. Proust, D. Gerard, J. Bijcon, and J. Plain, "Intense Bessel-like beams arising from pyramid-shaped microtips," Opt. Lett., vol. 37, pp. 1274–1276, 2012.
[22]
F. De Angelis, F. Gentile, F. Mecarini et al, "Breaking the diffusion limit with super-hydrophobic delivery of molecules to plasmonic nanofocusing SERS structures," Nat. Nanophot., vol. 5, pp. 682–687, 2011.
[23]
F.M. Huang, N. Zheludev, Y. Chen, and F.J. Garcia de Abajo, "Focusing of light by a nanohole array," Appl. Phys. Lett., vol. 90, pp. 091119, 2007.
[24]
V.V. Kotlyar, S.S. Stafeev, L. O’Faolain, and V.A. Soifer, "Tight focusing with a binary microaxicon," Opt. Lett., vol. 36, pp. 3100–3102, 2011.
[25]
X. Li, Y. Cao, and M. Gu, "Superresolution focal-volume induced 3.0 Tbytes/disk capacity by focusing a radially po-larized beam," Opt. Lett., vol. 36, pp. 2510–2512, 2011.
[26]
A. Vainrub, O. Pustovyy, and V. Vodyanov, "Resolution of 90 nm (λ/5) in an optical transmission microscope with an annular condenser," Opt. Lett., vol. 31, pp. 2855–2857, 2006.
[27]
Y. Kuznetsova, A. Neumann, S.R.J. Brueck, "Solid-immersion imaging interferometric nanoscopy to the limits of available frequency space," J. Opt. Soc. Am. A, vol. 29, pp. 772–781, 2012.
[28]
J.W. Goodman, "Introduction to Fourier Optics", Roberts and Company Publishers, 491 p., 2005.
[29]
Radio optics, M.: Sov. Radio, 304 p., 1975 (in Russian).
[30]
M. Born, E. Wolf, "Principles of Optics", 6 ed., Pergamon, 1986.
[31]
Y.R. Triandaphilov, and V.V. Kotlyar, "Photonic Crystal Mikaelian Lens," Optical Memory and Neural Networks (Information Optics), vol. 17, pp. 1–7, 2008.
[32]
V.V. Kotlyar, A.A. Kovalev, and V.A. Soifer, "Subwavelength Focusing with a Mikaelian Planar Lens," Optical Memory and Neural Networks (Information Optics), vol. 19, pp. 273–278, 2010.
[33]
C. Handmer, S. De Sterke, R. McPhedran, L. Botten, M. Steel, and A. Rahmani, "Blazing evanescent gtrating orders: a spectral approach to beating the Rayleigh limit," Opt. Lett., vol. 35, pp. 2846–2848, 2010.
[34]
S. Thongrattanasiri, N.A. Kuhta, M.D. Escarra, A.J. Hoffman, C.F. Gmachl, and V.A. Podolskiy, "Analytical technique for subwavelength far field imaging," App. Phys. Lett., vol. 97, pp. 101103, 2010.
[35]
M.I. Kotlyar, Y.R. Triandafilov, A.A. Kovalev, V.A. Soifer, M.V. Kotlyar, and L. O’Faolain, "Photonic crystal lens for coupling two waveguides," Appl. Opt., vol. 48, pp. 3722–3730, 2009.
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