Abstract

In the optical vortex microscopy the focused Gaussian beam with optical vortex scans a sample. An optical vortex can be introduced into a laser beam with the use of a special optical element—a vortex lens. When moving the vortex lens, the optical vortex changes its position inside the spot formed by a focused laser beam. This effect can be used as a new precise scanning technique. In this paper, we study the optical vortex behavior at the sample plane. We also estimate if the new scanning technique results in observable effects that could be used for a phase object detection.

© 2012 Optical Society of America

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References

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  1. J. F. Nye, Natural Focusing and Fine Structure of Light(Institute of Physics, 1999).
  2. M. Vasnetsov and K. Staliunas, eds., Optical Vortices(Nova Science, 1999).
  3. M. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
    [CrossRef]
  4. A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solutions,” Prog. Opt. 47, 291–391 (2005).
    [CrossRef]
  5. M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
    [CrossRef]
  6. V. P. Tychinsky, I. N. Maslov, V. L. Pankov, and D. V. Ublinsky, “Computerized phase microscope for investigation of submicron structures,” Opt. Commun. 74, 37–40 (1989).
    [CrossRef]
  7. V. P. Tychinsky, “On superresolution of phase objects,” Opt. Commun. 74, 41–45 (1989).
    [CrossRef]
  8. V. P. Tychinsky and C. H. Velzel, “Superresolution in microscopy,” in Current Trends in Optics (Academic, 1994), Chap. 18.
  9. C. H. Velzel and J. Masajada, “Superresolution phase image microscope,” Opt. Appl. 39, 293–300 (1999).
  10. M. Totzeck and H. J. Tiziani, “Phase-singularities in 2D diffraction fields and interference microscopy,” Opt. Commun. 138, 365–382 (1997).
    [CrossRef]
  11. T. A. Klar, E. Engel, and S. W. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes,” Phys. Rev. E 64, 066611 (2001).
    [CrossRef]
  12. L. E. Helseth, “Smallest focal hole,” Opt. Commun. 257, 1–8 (2006).
    [CrossRef]
  13. B. Spector, A. Normatov, and J. Shamir, “Experimental validation of 20 nm sensitivity of singular beam microscopy,” Proc. SPIE 6616, 661622 (2007).
    [CrossRef]
  14. B. Spector, A. Normatov, and J. Shamir, “Singular beam microscopy,” Appl. Opt. 47, A78–87 (2008).
    [CrossRef]
  15. B. Spektor, A. Normatov, and J. Shamir, “Singular beam scanning microscopy: preliminary experimental results,” Opt. Eng. 49, 048001 (2010).
    [CrossRef]
  16. J. Masajada, M. Leniec, E. Jankowska, H. Thienpont, H. Ottevaere, and V. Gomez, “Deep microstructure topography characterization with optical vortex interferometer,” Opt. Express 16, 19179–19191 (2008).
    [CrossRef]
  17. J. Masajada, M. Leniec, S. Drobczyński, H. Thienpont, and B. Kress, “Micro-step localization using double charge optical vortex interferometer,” Opt. Express 17, 16144–16159 (2009).
    [CrossRef]
  18. J. Masajada, M. Leniec, and I. Augustyniak, “Optical vortex scanning inside the Gaussian beam,” J. Opt. 13, 035714 (2011).
    [CrossRef]
  19. S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
    [CrossRef]
  20. G. A. Swartzlander, “Achromatic optical vortex lens,” Opt. Lett. 31, 2042–2044 (2006).
    [CrossRef]
  21. W. D. Furlan, F. Gimenez, A. Calatayud, and J. A. Monsoriu, “Devil’s vortex-lenses,” Opt. Express 17, 21891–21896(2009).
    [CrossRef]
  22. A. N. Khoroshun, “Optimal linear phase mask for the singular beam synthesis from a Gaussian beam and the scheme of its experimental realization,” J. Mod. Opt. 57, 1542–1549 (2010).
    [CrossRef]
  23. V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
    [CrossRef]
  24. N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinstein-Dunlop, and M. J. Wegener, “Laser beams with phase singularities,” Opt. Quant. Electron. 24, 951–962 (1992).
    [CrossRef]
  25. A. Ya. Bekshaev and A. I. Karamoch, “Displacements and deformations of a vortex light beam produced by the diffraction grating with embedded phase singularity,” Opt. Commun. 281, 3597–3610 (2008).
    [CrossRef]
  26. A. Ya. Bekshaev and S. V. Sviridova, “Effects of misalignments in the optical vortex transformation performed by holograms with embedded phase singularity,” Opt. Commun. 283, 4866–4876 (2010).
    [CrossRef]
  27. R. K. Singh, P. Senthilkumaran, and K. Singh, “Tight focusing of vortex beams in presence of primary astigmatism,” J. Opt. Soc. Am. A 26, 576–588 (2009).
    [CrossRef]
  28. R. K. Singh, P. Senthilkumaran, and K. Singh, “Structure of a tightly focused vortex beam in the presence of primary coma,” Opt. Commun. 282, 1501–1510 (2009).
    [CrossRef]

2011 (1)

J. Masajada, M. Leniec, and I. Augustyniak, “Optical vortex scanning inside the Gaussian beam,” J. Opt. 13, 035714 (2011).
[CrossRef]

2010 (3)

B. Spektor, A. Normatov, and J. Shamir, “Singular beam scanning microscopy: preliminary experimental results,” Opt. Eng. 49, 048001 (2010).
[CrossRef]

A. N. Khoroshun, “Optimal linear phase mask for the singular beam synthesis from a Gaussian beam and the scheme of its experimental realization,” J. Mod. Opt. 57, 1542–1549 (2010).
[CrossRef]

A. Ya. Bekshaev and S. V. Sviridova, “Effects of misalignments in the optical vortex transformation performed by holograms with embedded phase singularity,” Opt. Commun. 283, 4866–4876 (2010).
[CrossRef]

2009 (5)

2008 (3)

2007 (1)

B. Spector, A. Normatov, and J. Shamir, “Experimental validation of 20 nm sensitivity of singular beam microscopy,” Proc. SPIE 6616, 661622 (2007).
[CrossRef]

2006 (2)

G. A. Swartzlander, “Achromatic optical vortex lens,” Opt. Lett. 31, 2042–2044 (2006).
[CrossRef]

L. E. Helseth, “Smallest focal hole,” Opt. Commun. 257, 1–8 (2006).
[CrossRef]

2005 (1)

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solutions,” Prog. Opt. 47, 291–391 (2005).
[CrossRef]

2001 (2)

M. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
[CrossRef]

T. A. Klar, E. Engel, and S. W. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes,” Phys. Rev. E 64, 066611 (2001).
[CrossRef]

1999 (1)

C. H. Velzel and J. Masajada, “Superresolution phase image microscope,” Opt. Appl. 39, 293–300 (1999).

1997 (1)

M. Totzeck and H. J. Tiziani, “Phase-singularities in 2D diffraction fields and interference microscopy,” Opt. Commun. 138, 365–382 (1997).
[CrossRef]

1992 (3)

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinstein-Dunlop, and M. J. Wegener, “Laser beams with phase singularities,” Opt. Quant. Electron. 24, 951–962 (1992).
[CrossRef]

1989 (2)

V. P. Tychinsky, I. N. Maslov, V. L. Pankov, and D. V. Ublinsky, “Computerized phase microscope for investigation of submicron structures,” Opt. Commun. 74, 37–40 (1989).
[CrossRef]

V. P. Tychinsky, “On superresolution of phase objects,” Opt. Commun. 74, 41–45 (1989).
[CrossRef]

Augustyniak, I.

J. Masajada, M. Leniec, and I. Augustyniak, “Optical vortex scanning inside the Gaussian beam,” J. Opt. 13, 035714 (2011).
[CrossRef]

Bazhenov, V. Y.

V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

Bekshaev, A. Ya.

A. Ya. Bekshaev and S. V. Sviridova, “Effects of misalignments in the optical vortex transformation performed by holograms with embedded phase singularity,” Opt. Commun. 283, 4866–4876 (2010).
[CrossRef]

A. Ya. Bekshaev and A. I. Karamoch, “Displacements and deformations of a vortex light beam produced by the diffraction grating with embedded phase singularity,” Opt. Commun. 281, 3597–3610 (2008).
[CrossRef]

Calatayud, A.

Dennis, M. R.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
[CrossRef]

Desyatnikov, A. S.

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solutions,” Prog. Opt. 47, 291–391 (2005).
[CrossRef]

Drobczynski, S.

Engel, E.

T. A. Klar, E. Engel, and S. W. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes,” Phys. Rev. E 64, 066611 (2001).
[CrossRef]

Furlan, W. D.

Gimenez, F.

Gomez, V.

Heckenberg, N. R.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinstein-Dunlop, and M. J. Wegener, “Laser beams with phase singularities,” Opt. Quant. Electron. 24, 951–962 (1992).
[CrossRef]

Hell, S. W.

T. A. Klar, E. Engel, and S. W. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes,” Phys. Rev. E 64, 066611 (2001).
[CrossRef]

Helseth, L. E.

L. E. Helseth, “Smallest focal hole,” Opt. Commun. 257, 1–8 (2006).
[CrossRef]

Jankowska, E.

Karamoch, A. I.

A. Ya. Bekshaev and A. I. Karamoch, “Displacements and deformations of a vortex light beam produced by the diffraction grating with embedded phase singularity,” Opt. Commun. 281, 3597–3610 (2008).
[CrossRef]

Khonina, S. N.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

Khoroshun, A. N.

A. N. Khoroshun, “Optimal linear phase mask for the singular beam synthesis from a Gaussian beam and the scheme of its experimental realization,” J. Mod. Opt. 57, 1542–1549 (2010).
[CrossRef]

Kivshar, Y. S.

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solutions,” Prog. Opt. 47, 291–391 (2005).
[CrossRef]

Klar, T. A.

T. A. Klar, E. Engel, and S. W. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes,” Phys. Rev. E 64, 066611 (2001).
[CrossRef]

Kotlyar, V. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

Kress, B.

Leniec, M.

Masajada, J.

Maslov, I. N.

V. P. Tychinsky, I. N. Maslov, V. L. Pankov, and D. V. Ublinsky, “Computerized phase microscope for investigation of submicron structures,” Opt. Commun. 74, 37–40 (1989).
[CrossRef]

McDuff, R.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinstein-Dunlop, and M. J. Wegener, “Laser beams with phase singularities,” Opt. Quant. Electron. 24, 951–962 (1992).
[CrossRef]

Monsoriu, J. A.

Normatov, A.

B. Spektor, A. Normatov, and J. Shamir, “Singular beam scanning microscopy: preliminary experimental results,” Opt. Eng. 49, 048001 (2010).
[CrossRef]

B. Spector, A. Normatov, and J. Shamir, “Singular beam microscopy,” Appl. Opt. 47, A78–87 (2008).
[CrossRef]

B. Spector, A. Normatov, and J. Shamir, “Experimental validation of 20 nm sensitivity of singular beam microscopy,” Proc. SPIE 6616, 661622 (2007).
[CrossRef]

Nye, J. F.

J. F. Nye, Natural Focusing and Fine Structure of Light(Institute of Physics, 1999).

O’Holleran, K.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
[CrossRef]

Ottevaere, H.

Padgett, M. J.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
[CrossRef]

Pankov, V. L.

V. P. Tychinsky, I. N. Maslov, V. L. Pankov, and D. V. Ublinsky, “Computerized phase microscope for investigation of submicron structures,” Opt. Commun. 74, 37–40 (1989).
[CrossRef]

Rubinstein-Dunlop, H.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinstein-Dunlop, and M. J. Wegener, “Laser beams with phase singularities,” Opt. Quant. Electron. 24, 951–962 (1992).
[CrossRef]

Senthilkumaran, P.

R. K. Singh, P. Senthilkumaran, and K. Singh, “Tight focusing of vortex beams in presence of primary astigmatism,” J. Opt. Soc. Am. A 26, 576–588 (2009).
[CrossRef]

R. K. Singh, P. Senthilkumaran, and K. Singh, “Structure of a tightly focused vortex beam in the presence of primary coma,” Opt. Commun. 282, 1501–1510 (2009).
[CrossRef]

Shamir, J.

B. Spektor, A. Normatov, and J. Shamir, “Singular beam scanning microscopy: preliminary experimental results,” Opt. Eng. 49, 048001 (2010).
[CrossRef]

B. Spector, A. Normatov, and J. Shamir, “Singular beam microscopy,” Appl. Opt. 47, A78–87 (2008).
[CrossRef]

B. Spector, A. Normatov, and J. Shamir, “Experimental validation of 20 nm sensitivity of singular beam microscopy,” Proc. SPIE 6616, 661622 (2007).
[CrossRef]

Shinkaryev, M. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

Singh, K.

R. K. Singh, P. Senthilkumaran, and K. Singh, “Structure of a tightly focused vortex beam in the presence of primary coma,” Opt. Commun. 282, 1501–1510 (2009).
[CrossRef]

R. K. Singh, P. Senthilkumaran, and K. Singh, “Tight focusing of vortex beams in presence of primary astigmatism,” J. Opt. Soc. Am. A 26, 576–588 (2009).
[CrossRef]

Singh, R. K.

R. K. Singh, P. Senthilkumaran, and K. Singh, “Structure of a tightly focused vortex beam in the presence of primary coma,” Opt. Commun. 282, 1501–1510 (2009).
[CrossRef]

R. K. Singh, P. Senthilkumaran, and K. Singh, “Tight focusing of vortex beams in presence of primary astigmatism,” J. Opt. Soc. Am. A 26, 576–588 (2009).
[CrossRef]

Smith, C. P.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinstein-Dunlop, and M. J. Wegener, “Laser beams with phase singularities,” Opt. Quant. Electron. 24, 951–962 (1992).
[CrossRef]

Soifer, V. A.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

Soskin, M.

M. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
[CrossRef]

Soskin, M. S.

V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

Spector, B.

B. Spector, A. Normatov, and J. Shamir, “Singular beam microscopy,” Appl. Opt. 47, A78–87 (2008).
[CrossRef]

B. Spector, A. Normatov, and J. Shamir, “Experimental validation of 20 nm sensitivity of singular beam microscopy,” Proc. SPIE 6616, 661622 (2007).
[CrossRef]

Spektor, B.

B. Spektor, A. Normatov, and J. Shamir, “Singular beam scanning microscopy: preliminary experimental results,” Opt. Eng. 49, 048001 (2010).
[CrossRef]

Sviridova, S. V.

A. Ya. Bekshaev and S. V. Sviridova, “Effects of misalignments in the optical vortex transformation performed by holograms with embedded phase singularity,” Opt. Commun. 283, 4866–4876 (2010).
[CrossRef]

Swartzlander, G. A.

Thienpont, H.

Tiziani, H. J.

M. Totzeck and H. J. Tiziani, “Phase-singularities in 2D diffraction fields and interference microscopy,” Opt. Commun. 138, 365–382 (1997).
[CrossRef]

Torner, L.

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solutions,” Prog. Opt. 47, 291–391 (2005).
[CrossRef]

Totzeck, M.

M. Totzeck and H. J. Tiziani, “Phase-singularities in 2D diffraction fields and interference microscopy,” Opt. Commun. 138, 365–382 (1997).
[CrossRef]

Tychinsky, V. P.

V. P. Tychinsky, “On superresolution of phase objects,” Opt. Commun. 74, 41–45 (1989).
[CrossRef]

V. P. Tychinsky, I. N. Maslov, V. L. Pankov, and D. V. Ublinsky, “Computerized phase microscope for investigation of submicron structures,” Opt. Commun. 74, 37–40 (1989).
[CrossRef]

V. P. Tychinsky and C. H. Velzel, “Superresolution in microscopy,” in Current Trends in Optics (Academic, 1994), Chap. 18.

Ublinsky, D. V.

V. P. Tychinsky, I. N. Maslov, V. L. Pankov, and D. V. Ublinsky, “Computerized phase microscope for investigation of submicron structures,” Opt. Commun. 74, 37–40 (1989).
[CrossRef]

Uspleniev, G. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

Vasnetsov, M. V.

M. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
[CrossRef]

V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

Velzel, C. H.

C. H. Velzel and J. Masajada, “Superresolution phase image microscope,” Opt. Appl. 39, 293–300 (1999).

V. P. Tychinsky and C. H. Velzel, “Superresolution in microscopy,” in Current Trends in Optics (Academic, 1994), Chap. 18.

Wegener, M. J.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinstein-Dunlop, and M. J. Wegener, “Laser beams with phase singularities,” Opt. Quant. Electron. 24, 951–962 (1992).
[CrossRef]

Appl. Opt. (1)

J. Mod. Opt. (3)

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

A. N. Khoroshun, “Optimal linear phase mask for the singular beam synthesis from a Gaussian beam and the scheme of its experimental realization,” J. Mod. Opt. 57, 1542–1549 (2010).
[CrossRef]

V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

J. Opt. (1)

J. Masajada, M. Leniec, and I. Augustyniak, “Optical vortex scanning inside the Gaussian beam,” J. Opt. 13, 035714 (2011).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Appl. (1)

C. H. Velzel and J. Masajada, “Superresolution phase image microscope,” Opt. Appl. 39, 293–300 (1999).

Opt. Commun. (7)

M. Totzeck and H. J. Tiziani, “Phase-singularities in 2D diffraction fields and interference microscopy,” Opt. Commun. 138, 365–382 (1997).
[CrossRef]

V. P. Tychinsky, I. N. Maslov, V. L. Pankov, and D. V. Ublinsky, “Computerized phase microscope for investigation of submicron structures,” Opt. Commun. 74, 37–40 (1989).
[CrossRef]

V. P. Tychinsky, “On superresolution of phase objects,” Opt. Commun. 74, 41–45 (1989).
[CrossRef]

L. E. Helseth, “Smallest focal hole,” Opt. Commun. 257, 1–8 (2006).
[CrossRef]

R. K. Singh, P. Senthilkumaran, and K. Singh, “Structure of a tightly focused vortex beam in the presence of primary coma,” Opt. Commun. 282, 1501–1510 (2009).
[CrossRef]

A. Ya. Bekshaev and A. I. Karamoch, “Displacements and deformations of a vortex light beam produced by the diffraction grating with embedded phase singularity,” Opt. Commun. 281, 3597–3610 (2008).
[CrossRef]

A. Ya. Bekshaev and S. V. Sviridova, “Effects of misalignments in the optical vortex transformation performed by holograms with embedded phase singularity,” Opt. Commun. 283, 4866–4876 (2010).
[CrossRef]

Opt. Eng. (1)

B. Spektor, A. Normatov, and J. Shamir, “Singular beam scanning microscopy: preliminary experimental results,” Opt. Eng. 49, 048001 (2010).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Opt. Quant. Electron. (1)

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinstein-Dunlop, and M. J. Wegener, “Laser beams with phase singularities,” Opt. Quant. Electron. 24, 951–962 (1992).
[CrossRef]

Phys. Rev. E (1)

T. A. Klar, E. Engel, and S. W. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes,” Phys. Rev. E 64, 066611 (2001).
[CrossRef]

Proc. SPIE (1)

B. Spector, A. Normatov, and J. Shamir, “Experimental validation of 20 nm sensitivity of singular beam microscopy,” Proc. SPIE 6616, 661622 (2007).
[CrossRef]

Prog. Opt. (3)

M. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
[CrossRef]

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solutions,” Prog. Opt. 47, 291–391 (2005).
[CrossRef]

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
[CrossRef]

Other (3)

J. F. Nye, Natural Focusing and Fine Structure of Light(Institute of Physics, 1999).

M. Vasnetsov and K. Staliunas, eds., Optical Vortices(Nova Science, 1999).

V. P. Tychinsky and C. H. Velzel, “Superresolution in microscopy,” in Current Trends in Optics (Academic, 1994), Chap. 18.

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Figures (11)

Fig. 1.
Fig. 1.

In the new scanning technique the vortex lens is moved at the micrometer range. After passing the microscopic objective the vortex point shifts at nanometer range. The observation is made at the plane close to the waist plane of the focused beam.

Fig. 2.
Fig. 2.

Vortex point’s trajectory versus the zo position of the observation plane. The Gaussian beam waist is w0=0.3mm in (a) and w0=3mm in (b). We find from the condition (3) that the special zo value of is zo=24.341mm in (a) and zo=24.998mm in (b). For both the cases the distance between the beam waist and the vortex lens is 600 and λ=633nm; f=25mm.

Fig. 3.
Fig. 3.

Scheme of the experimental setup.

Fig. 4.
Fig. 4.

Vortex point’s trajectory computed with numerical integration of formula (3) for three positions of the observation plane. Dashed lines were plotted from the Eq. (1). The numbers printed by each point indicate the vortex lens shift in micrometers. The triangle marks represent the case when condition (3) is met. The positions marked by crosses were calculated with independent numerical procedures.

Fig. 5.
Fig. 5.

(a) The phase step splits the object plane into two parts. These parts introduce different phase shifts into incoming laser beam. Nevertheless, there is still symmetry against dashed line, L. So one or two vortices appearing on this dashed line can be expected at the diffraction pattern. These vortices are marked as black and white point. The difference in amplitude (b) and phase (c) distribution, calculated at the observation plane for the centrally position vortex lens and the vortex lens shifted by 10 μm. The maximal amplitude difference is less than 3% of the focused beam maximal amplitude. In the case of (b) and (c) the beam waist was 0.3 mm, the distance between the beam waist and vortex lens was z=600mm, f=25mm and zo=24.341mm. For this zo value the condition (3) holds.

Fig. 6.
Fig. 6.

The calculated intensity distribution of the diffraction pattern—examples. The calculations were made for f=25mm, λ=633nm and w0=0.5mm. The distance between the phase step and the observation plane was 40 mm and between the beam waist and the vortex lens 600 mm. The step introduced a π/2 phase difference and was located at the plane where condition (3) holds (zo=24.8mm). The thick dashed lines (column III) indicate the phase step orientation. White numbers in rows A-C show the vortex lens shift in micrometers. Row A: the phase step is perpendicular to the vortex lens shift; Row B: the phase step is parallel to the vortex lens shift and positioned centrally; Row C: the orientation of the phase step is the same, but now it is moved by 1 micrometer to the left side; Row D: the whole beam is moved through the step and the vortex point is in the scanning beam center. Now the white numbers show the beam shift in micrometers.

Fig. 7.
Fig. 7.

The incident Gaussian beam illuminates the phase step in such a way that its waist coincides with the upper surface of the step. Then the beam travelling in the air and in glass acquire different radius at the plane of lower step surface. Figure 2 shows that this difference can change vortex point’s behavior in a strong way.

Fig. 8.
Fig. 8.

The vortex trajectories plotted for the three different cases with m2π phase difference introduced by the phase step. All observed phenomenon are caused by variations in beam curvature on the right and left side of the phase step. In a small window the phase difference introduced by the phase step is λ/4+m2π. The system parameters are: w0=0.5mm, distance between beam waist and sample plane is 600 mm, λ=633nm.

Fig. 9.
Fig. 9.

(a) The plot of vortex trajectory recorded for 5× microscopic objective (f=26mm). These three trajectories were registered for different positions of the observation plane. Due to large sensitivity it was difficult to find the position of critical plane where a vortex point would go perpendicularly to the vortex lens shift. For this reason, the horizontal trajectory is still a bit inclined. The skew trajectories were recorded when the observation plane was moved by 250 μm back or forward. (b) shows the same example but for 10× microscopic objective. Now the skew trajectories are even more inclined (for the same shift of the observation plane). (c) shows exemplary photos of the images taken by our camera. To show the vortex point’s position the camera were oversaturated. The photos are recorded for 5× microscopic objective.

Fig. 10.
Fig. 10.

The triangles show the vortex point trajectory when the step is moved away (but the substrate plate is still there). The circles show the vortex point trajectory when the step is positioned about 1 micrometer away from the center on the right side. The diamonds show the same but for the edge moved 1 μm further. A few questionable points were not marked in this figure. Here we used 5× microscopic objective.

Fig. 11.
Fig. 11.

The vortex point’s trajectory for three different positions of the sample plane: (a) critical plane; (b) 50 μm below the critical plane; (c) 100 μm below the critical plane. Here we used 5× microscopic objective.

Equations (9)

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xo=zoxcg(z)+xc,
yo=2zokw2(z)xc,
g(z)=1R(z)+1f.
tan(α)=yoxo=2kw2(z)(g(z)1zo)2kw2(z)g(z).
1zo=g(z),
u(ρ1,φ1,xc)=ic3π2c132exp{c2xc2}02πexp{iφ}exp{c32c1}dφ,
c1=ik2f+ik2zo1ωz2+ik2R,
c2=ik2f1ωz2+ik2R,
c3=c2xccos(φ)+iπρ1cos(φφ1).

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