Optical Memory and Neural Networks

, Volume 20, Issue 1, pp 23–42

Influence of vortex transmission phase function on intensity distribution in the focal area of high-aperture focusing system

  • S. N. Khonina
  • N. L. Kazanskiy
  • S. G. Volotovsky
Article

Abstract

An analysis of the possibility of reducing lateral size and increasing longitudinal size of high-aperture focal system focus using vortex transmission phase function for different types of input polarization including the general vortex one was carried out.

We have shown both analytically and numerically that subwavelength localization for separate components of the vector field is possible at any polarization type. This fact can be important when considering the interaction between laser radiation and materials that are selectively sensitive to different components of electromagnetic field.

In order to form substantially subwavelength details in total intensity, specific polarization types and additional apodization of pupil function such as masking by a narrow annular slit, are necessary. The optimal selection of the slit radius allows to balance the tradeoff between focus depth and focal spot size.

Keywords

high-aperture focusing system Debye approximation vector electric field subwavelength light localization focus length extension vortex transmission phase function generalized vortex polarization 

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References

  1. 1.
    Karman, G.P., Beijersbergen, M.W., van Duijl, A., Bouwmeester, D., and Woerdman, J.P., Airy Pattern Reorganization and Subwavelength Structure in a Focus, J. Opt. Soc. Am., Ser. A, 1998, vol. 15, no. 4, pp. 884–899.CrossRefGoogle Scholar
  2. 2.
    Quabis, S., Dorn, R., Eberler, M., Glockl, O., and Leuchs, G., Focusing Light to a Tighter Spot, Opt. Commun., 2000, vol. 179, pp. 1–7.CrossRefGoogle Scholar
  3. 3.
    Kant, R., Superresolution and Increased Depth of Focus: An Inverse Problem of Vector Diffraction, J. Mod. Opt., 2000, vol. 47, no. 5, pp. 905–916.Google Scholar
  4. 4.
    Dorn, R., Quabis, S., and Leuchs, G., Sharper Focus for a Radially Polarized Light Beam, Phys. Rev. Lett., 2003, vol. 91, p. 233901.CrossRefGoogle Scholar
  5. 5.
    Davidson, N. and Bokor, N., High-Numerical-Aperture Focusing of Radially Polarized Doughnut Beams with a Parabolic Mirror and a Flat Diffractive Lens, Opt. Lett., 2004, vol. 29, no. 12, pp. 1318–1320.CrossRefGoogle Scholar
  6. 6.
    Sheppard, C.J.R. and Choudhury, A., Annular Pupils, Radial Polarization, and Superresolution, Appl. Opt., 2004, vol. 43, no. 22, pp. 4322–4327.CrossRefGoogle Scholar
  7. 7.
    Pereira, S.F. and van de Nes, A.S., Superresolution by Means of Polarisation, Phase and Amplitude Pupil Masks, Opt. Commun., 2004, vol. 234, pp. 119–124.CrossRefGoogle Scholar
  8. 8.
    Wang, H., Shi, L., Lukyanchuk, B., Sheppard, C., and Chong, C.T., Creation of a Needle of Longitudinally Polarized Light in Vacuum Using Binary Optics, Nat. Photonics, 2008, vol. 2, pp. 501–505.CrossRefGoogle Scholar
  9. 9.
    Kozawa, Y. and Sato, S., Sharper Focal Spot Formed by Higher-Order Radially Polarized Laser Beams, J. Opt. Soc. Am., Ser. A, 2007, vol. 24, pp. 1793–1798.CrossRefGoogle Scholar
  10. 10.
    Lerman, G.M. and Levy, U., Effect of Radial Polarization and Apodization on Spot Size under Tight Focusing Conditions, Opt. Express, 2008, vol. 16, no. 7, pp. 4567–4581.CrossRefGoogle Scholar
  11. 11.
    Kotlyar, V.V. and Stafeev, S.S., Modeling the Sharp Focus of a Radially Polarized Laser Mode Using a Conical and a Binary Microaxicon, J. Opt. Soc. Am., Ser. B, 2010, vol. 27, no. 10, pp. 1991–1997.CrossRefGoogle Scholar
  12. 12.
    Zhan, Q., Cylindrical Vector Beams: from Mathematical Concepts to Applications, Adv. Opt. Photonics, 2009, vol. 1, pp. 1–57.CrossRefGoogle Scholar
  13. 13.
    Kozawa, Y. and Sato, S., Generation of a Radially Polarized Laser Beam by Use of a Conical Brewster Prism, Opt. Lett., 2005, vol. 30, no. 22, pp. 3063–3065.CrossRefGoogle Scholar
  14. 14.
    Niziev, V.G., Yakunin, V.P., and Turkin, N.G., Generating Polarization Heterogeneous Modes in High-Capacity CO2 Laser, Quantum Electronics, 2009, vol. 39, no. 6, pp. 505–514.CrossRefGoogle Scholar
  15. 15.
    Bomzon, Z., Biener, G., Kleiner, V., and Hasman, E., Radially and Azimuthally Polarized Beams Generated by Space-Variant Dielectric Subwavelength Gratings, Opt. Lett., 2002, vol. 27, no. 5, pp. 285–287.CrossRefGoogle Scholar
  16. 16.
    Yonezawa, K., Kozawa, Y., and Sato, S., Compact Laser with Radial Polarization Using Birefringent Laser Medium, Jpn. J. Appl. Phys., 2007, vol. 46, no. 8, pp. 5160–5163.CrossRefGoogle Scholar
  17. 17.
    Tidwell, S.C., Ford, D.H., and Kimura, W.D., Generating Radially Polarized Beams Interferometrically, Appl. Opt., 1990, vol. 29, pp. 2234–2239.CrossRefGoogle Scholar
  18. 18.
    Passilly, N., de Saint Denis, R., and Aït-Ameur, K., Treussart, F., Hierle, R., and Roch, J.-F., Simple Interferometric Technique for Generation of a Radially Polarized Light Beam, J. Opt. Soc. Am., Ser. A, 2005, vol. 22, no. 5, pp. 984–991.CrossRefGoogle Scholar
  19. 19.
    Volpe, G. and Petrov, D., Generation of Cylindrical Vector Beams with Few-Mode Fibers Excited by Laguerre-Gaussian Beams, Opt. Comm., 2004, vol. 237, pp. 89–95.CrossRefGoogle Scholar
  20. 20.
    Davis, J.A., McNamara, D.E., Cottrell, D.M., and Sonehara, T., Two Dimensional Polarization Encoding with a Phase Only Liquid-Crystal Spatial Light Modulator, Appl. Opt., 2000, vol. 39, pp. 1549–15541.CrossRefGoogle Scholar
  21. 21.
    Neil, M.A.A., Massoumian, F., Juskaitis, R., and Wilson, T., Method for the Generation of Arbitrary Complex Vector Wave Fronts, Opt. Lett., 2002, vol. 27, no. 21, pp. 1929–1931.CrossRefGoogle Scholar
  22. 22.
    Iglesias, I. and Vohnsen, B., Polarization Structuring for Focal Volume Shaping in High-Resolution Microscopy, Opt. Commun., 2007, vol. 271, pp. 40–47.CrossRefGoogle Scholar
  23. 23.
    Khonina, S.N. and Karpeev, S.V., Grating-Based Optical Scheme for the Universal Generation of Inhomogeneously Polarized Laser Beams, App. Opt., 2010, vol. 49, no. 10, pp. 1734–1738.CrossRefGoogle Scholar
  24. 24.
    Simpson, N.B., Allen, L., and Padgett, M.J., Optical Tweezers and Optical Spanners with Laguerre-Gaussian Modes, J. Mod. Opt., 1996, vol. 43, no. 12, pp. 2485–2491.CrossRefGoogle Scholar
  25. 25.
    Heckenberg, N.R., Nieminen, T.A., Friese, M.E.J., and Rubinsztein-Dunlop, H., Trapping Microscopic Particles with Singular Beams, Proc. SPIE, 1998, vol. 3487, pp. 46–53.CrossRefGoogle Scholar
  26. 26.
    Helseth, L.E., Mesoscopic Orbital in Strongly Focused Light, Opt. Commun., 2003, vol. 224, pp. 255–261.CrossRefGoogle Scholar
  27. 27.
    Dholakia, K., Spalding, G., and MacDonald, M., Optical Tweezers: the Next Generation, Physics World, 2002, pp. 31–35.Google Scholar
  28. 28.
    Soifer, V.A., Kotlyar, V.V., and Khonina, S.N., Optical Microparticle Manipulation: Advances and New Possibilities Created by Diffractive Optics, Phys. Part. Nucl., 2004, vol. 35, no. 6, pp. 733–766.Google Scholar
  29. 29.
    Khonina, S.N., Skidanov, R.V., Kotlyar, V.V., Soifer, V.A., and Turunen, J., DOE-Generated Laser Beams with Given Orbital Angular Moment: Application for Micromanipulation, Proc. SPIE Int. Soc. Opt. Eng., 2005, vol. 5962, p. 59622W.Google Scholar
  30. 30.
    Levenson, M.D., Ebihara, T., Dai, G., Morikawa, Y., Hayashi, N., and Tan, S.M., Optical Vortex Masks for via Levels, J. Microlith. Microfab. Microsys., 2004, vol. 3, no. 2, pp. 293–304.CrossRefGoogle Scholar
  31. 31.
    Unno, Y., Ebihara, T., and Levenson, M.D., Impact of Mask Errors and Lens Aberrations on the Image Formation by a Vortex Mask, J. Microlith. Microfab. Microsys., 2005, vol. 4, no. 2, p. 023006.CrossRefGoogle Scholar
  32. 32.
    Willig, K.I., Keller, J., Bossi, M., and Hell, S.W., STED Microscopy Resolves Nanoparticle Assemblies, New J. Phys., 2006, vol. 8, p. 106.CrossRefGoogle Scholar
  33. 33.
    Torok, P. and Munro, P.R.T., The Use of Gauss-Laguerre Vector Beams in STED Microscopy, Opt. Express, 2004, vol. 12, no. 15, pp. 3605–3617.CrossRefGoogle Scholar
  34. 34.
    Desyatnikov, A.S., Torner, L., and Kivshar, Y.S., Optical Vortices and Vortex Solitons, in Progress Optics, Wolf, E., ed., North-Holland, Amsterdam, 2005, vol. 47, pp. 219–319.Google Scholar
  35. 35.
    Molina-Terriza, G., Torres, J.P., and Torner, L., Twisted Photons, Nat. Phys., 2007, vol. 3, pp. 305–310.CrossRefGoogle Scholar
  36. 36.
    Franke-Arnold, S., Allen, L., and Padgett, M., Advances in Optical Angular Momentum, Laser Photonics Rev., 2008, vol. 2, pp. 299–313.CrossRefGoogle Scholar
  37. 37.
    Helseth, L.E., Optical Vortices in Focal Regions, Opt. Commun., 2004, vol. 229, pp. 85–91.CrossRefGoogle Scholar
  38. 38.
    Singh, R.K., Senthilkumaran, P., and Singh, K., Tight Focusing of Vortex Beams in Presence of Primary Astigmatism, J. Opt. Soc. Am., Ser. A, 2009, vol. 26, no. 3, pp. 576–588.CrossRefGoogle Scholar
  39. 39.
    Chen, B. and Pu, J., Tight Focusing of Elliptically Polarized Vortex Beams, Appl. Opt., 2009, vol. 48, no. 7, pp. 1288–1294.CrossRefGoogle Scholar
  40. 40.
    Rao, L., Pu, J., Chen, Z., and Yei, P., Focus Shaping of Cylindrically Polarized Vortex Beams by a High Numerical-Aperture Lens, Opt. Las. Techn., 2009, vol. 41, pp. 241–246.Google Scholar
  41. 41.
    Beth, R.A., Mechanical Detection and Measurement of the Angular Momentum of Light, Phys. Rev., 1936, vol. 50, pp. 115–125.CrossRefGoogle Scholar
  42. 42.
    Holbourn, A.H.S., Angular Momentum of Circularly Polarized Light, Nature (London), 1936, vol. 137, p. 31.CrossRefGoogle Scholar
  43. 43.
    Allen, L., Beijersbergen, M.W., Spreeuw, R.J.C., and Woerdman, J.P., Orbital Angular Momentum of Light and the Transformation of Laguerre-Gaussian Laser Modes, Phys. Rev., Ser. A, 1992, vol. 45, pp. 8185–8189.CrossRefGoogle Scholar
  44. 44.
    Barnett, S.M. and Allen, L., Orbital Angular-Momentum and Nonparaxial Light-Beams, Opt. Commun., 1994, vol. 110, pp. 670–678.CrossRefGoogle Scholar
  45. 45.
    Soskin, M.S., Gorshkov, V.N., Vasnetsov, M.V., Malos, J.T., and Heckenberg, N.R., Topological Charge and Angular Momentum of Light Beams Carrying Optical Vortices, Phys. Rev., Ser. A, 1997, vol. 56, pp. 4064–4075.CrossRefGoogle Scholar
  46. 46.
    Richards, B. and Wolf, E., Electromagnetic Diffraction in Optical Systems II. Structure of the Image Field in an Aplanatic System, Proc. Royal Soc., Ser. A, 1959, vol. 253, pp. 358–379.CrossRefMATHGoogle Scholar
  47. 47.
    Prudnikov, A.P., Brychkov, Y.A., and Marichev, O.I., Integrals and Series. Special Functions, M.: Nauka, 1983.MATHGoogle Scholar
  48. 48.
    Gori, F., Polarization Basis for Vortex Beams, J. Opt. Soc. Am., Ser. A, 2001, vol. 18, no. 7, pp. 1612–1617.CrossRefMathSciNetGoogle Scholar
  49. 49.
    Schwartz, C. and Dogariu, A., Backscattered Polarization Patterns, Optical Vortices, and the Angular Momentum of Light, Opt. Lett., 2006, vol. 31, no. 8, pp. 1121–1123.CrossRefGoogle Scholar
  50. 50.
    Bokor, N. and Davidson, N., A Three Dimensional Dark Focal Spot Uniformly Surrounded by Light, Opt. Commun., 2007, vol. 279, pp. 229–234.CrossRefGoogle Scholar
  51. 51.
    Grosjean, T. and Courjon, D., Photopolymers As Vectorial Sensors of the Electric Field, Opt. Express, 2006, vol. 14, no. 6, pp. 2203–2210.CrossRefGoogle Scholar
  52. 52.
    Xie, X.S. and Dunn, R.C., Probing Single Molecule Dynamics, Science, 1994, vol. 265, pp. 361–364.CrossRefGoogle Scholar
  53. 53.
    Beversluis, M.R., Novotny, L., and Stranick, S.J., Programmable Vector Point-Spread Function Engineering, Opt. Express, 2006, vol. 14, pp. 2650–2656.CrossRefGoogle Scholar

Copyright information

© Allerton Press, Inc. 2011

Authors and Affiliations

  • S. N. Khonina
    • 1
    • 2
  • N. L. Kazanskiy
    • 1
    • 2
  • S. G. Volotovsky
    • 1
  1. 1.Image Processing Systems Institute of Russian Academy of SciencesSamaraRussia
  2. 2.Samara State Aerospace UniversitySamaraRussia

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