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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  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

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

2010

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]

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

2009

2008

2007

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

2006

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

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

2005

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

2001

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

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

1997

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

1992

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]

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]

1989

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, “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]

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, “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]

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, 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]

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.

J. Mod. Opt.

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.

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

Opt. Appl.

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

Opt. Commun.

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.

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

Opt. Express

Opt. Lett.

Opt. Quant. Electron.

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

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

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.

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

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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