Abstract

A full theoretical and experimental analysis of the chain of phase singularities generated when a Gaussian beam passes a double-phase-ramp converter is presented. The overall output beam structure includes a system of interrelated optical vortices (OVs) whose trajectories form a three-dimensional singular skeleton that can be applied for the trapping and guiding of microparticles. The internal structure of each individual phase singularity is characterized by the OV topological charge and by the morphology parameters of equal intensity ellipses in the OV-core area: ellipticity (minor-to-major axes ratio) and the inclination angle. The morphology parameters’ evolution is shown to be valuable for the metrology applications.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

A. N. Khoroshun, A. V. Chernykh, H. O. Tatarchenko, A. Ya. Bekshaev, and A. A. Akhmerov, “Laguerre-Gaussian beam transformations by the double-phase-ramp converter: Singular skeleton formation and its sensitivity to small misalignments,” Proc. SPIE,  10612, 1–9 (2018).
[Crossref]

2017 (3)

A. Bekshaev, A. Chernykh, A. Khoroshun, and L. Mikhaylovskaya, “Singular skeleton evolution and topological reactions in edge-diffracted circular optical-vortex beams,” Opt. Commun. 397, 72–83 (2017).
[Crossref]

A. Khoroshun, A. Chernykh, J. Kirichenko, O. Ryazantsev, and A. Bekshaev, “Singular skeleton of a Laguerre–Gaussian beam transformed by the double-phase-ramp converter,” Appl. Opt. 56(12), 3428–3434 (2017).
[Crossref]

A. Popiolek-Masajada, J. Masajada, and P. Kurzynowski, “Analytical Model of the Optical Vortex Scanning Microscope with a simple phase object,” Photonics 4(4), 38 (2017).
[Crossref]

2016 (2)

A. P. Porfirev and A. S. Shipilov, “Laser trapping based on photophoretic forces using a spatial light modulator,” CEUR Workshop Proc. 1638, 111–116 (2016).
[Crossref]

A. N. Khoroshun, A. V. Chernykh, A. N. Tsimbaluk, J. A. Kirichenko, P. V. Yezhov, A. V. Kuzmenko, and J. T. Kim, “Properties of an Axial Optical Vortex Generated with the use of a Gaussian Beam and Two Ramp,” J. Nanosci. Nanotechnol. 16(2), 2105–2107 (2016).
[Crossref]

2015 (2)

Y. X. Ren, R. De Lu, and L. Gong, “Tailoring light with digital micromirror device,” Ann. Phys. 527(7-8), 447–470 (2015).
[Crossref]

J. Zhao, I. D. Chremmos, D. Song, D. N. Christodoulides, N. K. Efremidis, and Z. Chen, “Curved singular beams for three dimensional particle manipulation,” Sci. Rep. 5(1), 12086 (2015).
[Crossref]

2014 (1)

2013 (1)

A. Ferrando and M. A. Garcıa-March, “Theory for the control of dark rays by means of discrete symmetry diffractive elements,” J. Opt. 15(4), 044014 (2013).
[Crossref]

2012 (3)

M. R. Dennis and J. B. Gotte, “Topological Aberration of Optical Vortex Beams: Determining Dielectric Interfaces by Optical Singularity Shifts,” Phys. Rev. Lett. 109(18), 183903 (2012).
[Crossref]

P. Senthilkumaran, S. Sato, and J. Masajada, “Singular Optics,” Int. J. Opt. 2012, 1–2 (2012).
[Crossref]

F. Ricci, W. Löffler, and M. P. van Exter, “Instability of higher-order optical vortices analyzed with a multi-pinhole interferometer,” Opt. Express 20(20), 22961–22975 (2012).
[Crossref]

2010 (3)

A. N. Khoroshun, “Optimal linear phase mask for the singular beam synthesis from a Gaussian beam and the scheme of its experimental realisation,” J. Mod. Opt. 57(16), 1542–1549 (2010).
[Crossref]

S. Vyas and P. Senthilkumaran, “Vortices from wavefront tilts,” Opt. Lasers Eng. 48(9), 834–840 (2010).
[Crossref]

A. Bekshaev, O. Orlinska, and M. Vasnetsov, “Optical vortex generation with a “fork” hologram under conditions of high-angle diffraction,” Opt. Commun. 283(10), 2006–2016 (2010).
[Crossref]

2009 (3)

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

M. R. Dennis, Y. S. Kivshar, M. S. Soskin, and G. A. Swartzlander, “Singular optics: More ado about nothing,” J. Opt. A: Pure Appl. Opt. 11(9), 090201 (2009).
[Crossref]

V. G. Shvedov, A. S. Desyatnikov, A. V. Rode, W. Krolikowski, and Y. S. Kivshar, “Optical guiding of absorbing nanoclusters in air,” Opt. Express 17(7), 5743–5757 (2009).
[Crossref]

2008 (4)

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophoton. 2(1), 021875 (2008).
[Crossref]

A. Bekshaev and A. Karamoch, “Astigmatic telescopic transformation of a high-order optical vortex,” Opt. Commun. 281(23), 5687–5696 (2008).
[Crossref]

Y. Izdebskaya, “Optical necklaces generated by the diffraction on a stack of dielectric wedges,” Phys. Lett. A 372(21), 3909–3913 (2008).
[Crossref]

A. Jesacher, C. Maurer, A. Schwaighofer, S. Bernet, and M. Ritsch-Marte, “Full phase and amplitude control of holographic optical tweezers with high efficiency,” Opt. Express 16(7), 4479–4486 (2008).
[Crossref]

2006 (1)

2004 (2)

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A: Pure Appl. Opt. 6(2), 259–268 (2004).
[Crossref]

F. S. Roux, “Spatial evolution of the morphology of an optical vortex dipole,” Opt. Commun. 236(4–6), 433–440 (2004).
[Crossref]

2002 (3)

V. G. Shvedov, Y. V. Izdebskaya, A. N. Alekseev, and A. V. Volyar, “The formation of optical vortices in the course of light diffraction on a dielectric wedge,” Tech. Phys. Lett. 28(3), 256–259 (2002).
[Crossref]

V. N. Gorshkov, A. N. Khoroshun, and M. S. Soskin, “The theory of synthesis of optical vortices by the technique of a phase wedge,” Proc. SPIE. 4705, 65–74 (2002).

Ya. Izdebskaya, V. Shvedov, D. Kurabtzev, A. Alexeyev, and A. Volyar, “The optical vortex generation by optical wedge,” Proc. SPIE 4607, 78–82 (2002).
[Crossref]

2001 (1)

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

1997 (1)

1990 (1)

V. Yu. Bazhenov, M.V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations of the wavefront,” JETP Lett.,  52, 429–431 (1990).

1987 (1)

J. P. Huignard, “Spatial light modulators and their applications,” J. Opt. 18(4), 181–185 (1987).
[Crossref]

1982 (1)

1974 (1)

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336(1605), 165–190 (1974).
[Crossref]

Abramowitz, M.

M. Abramowitz and I. Stegun, “Error Function and Fresnel Integrals,” in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (NBS Applied Mathematics Series 55, Washington, DC, 1972), pp. 296–297.

Akhmerov, A. A.

A. N. Khoroshun, A. V. Chernykh, H. O. Tatarchenko, A. Ya. Bekshaev, and A. A. Akhmerov, “Laguerre-Gaussian beam transformations by the double-phase-ramp converter: Singular skeleton formation and its sensitivity to small misalignments,” Proc. SPIE,  10612, 1–9 (2018).
[Crossref]

Alekseev, A. N.

V. G. Shvedov, Y. V. Izdebskaya, A. N. Alekseev, and A. V. Volyar, “The formation of optical vortices in the course of light diffraction on a dielectric wedge,” Tech. Phys. Lett. 28(3), 256–259 (2002).
[Crossref]

Alexeyev, A.

Ya. Izdebskaya, V. Shvedov, D. Kurabtzev, A. Alexeyev, and A. Volyar, “The optical vortex generation by optical wedge,” Proc. SPIE 4607, 78–82 (2002).
[Crossref]

Ashkin, A.

A. Ashkin, Optical Trapping and Manipulation of Neutral Particles Using Lasers (World Scientific2006)

Bazhenov, V. Yu.

V. Yu. Bazhenov, M.V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations of the wavefront,” JETP Lett.,  52, 429–431 (1990).

Bekshaev, A.

A. Bekshaev, A. Chernykh, A. Khoroshun, and L. Mikhaylovskaya, “Singular skeleton evolution and topological reactions in edge-diffracted circular optical-vortex beams,” Opt. Commun. 397, 72–83 (2017).
[Crossref]

A. Khoroshun, A. Chernykh, J. Kirichenko, O. Ryazantsev, and A. Bekshaev, “Singular skeleton of a Laguerre–Gaussian beam transformed by the double-phase-ramp converter,” Appl. Opt. 56(12), 3428–3434 (2017).
[Crossref]

A. Bekshaev, O. Orlinska, and M. Vasnetsov, “Optical vortex generation with a “fork” hologram under conditions of high-angle diffraction,” Opt. Commun. 283(10), 2006–2016 (2010).
[Crossref]

A. Bekshaev and A. Karamoch, “Astigmatic telescopic transformation of a high-order optical vortex,” Opt. Commun. 281(23), 5687–5696 (2008).
[Crossref]

Bekshaev, A. Ya.

A. N. Khoroshun, A. V. Chernykh, H. O. Tatarchenko, A. Ya. Bekshaev, and A. A. Akhmerov, “Laguerre-Gaussian beam transformations by the double-phase-ramp converter: Singular skeleton formation and its sensitivity to small misalignments,” Proc. SPIE,  10612, 1–9 (2018).
[Crossref]

Bernet, S.

Berry, M. V.

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A: Pure Appl. Opt. 6(2), 259–268 (2004).
[Crossref]

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336(1605), 165–190 (1974).
[Crossref]

Chang, J. S.

Chen, Z.

J. Zhao, I. D. Chremmos, D. Song, D. N. Christodoulides, N. K. Efremidis, and Z. Chen, “Curved singular beams for three dimensional particle manipulation,” Sci. Rep. 5(1), 12086 (2015).
[Crossref]

Cheng, T.

Chernykh, A.

A. Khoroshun, A. Chernykh, J. Kirichenko, O. Ryazantsev, and A. Bekshaev, “Singular skeleton of a Laguerre–Gaussian beam transformed by the double-phase-ramp converter,” Appl. Opt. 56(12), 3428–3434 (2017).
[Crossref]

A. Bekshaev, A. Chernykh, A. Khoroshun, and L. Mikhaylovskaya, “Singular skeleton evolution and topological reactions in edge-diffracted circular optical-vortex beams,” Opt. Commun. 397, 72–83 (2017).
[Crossref]

Chernykh, A. V.

A. N. Khoroshun, A. V. Chernykh, H. O. Tatarchenko, A. Ya. Bekshaev, and A. A. Akhmerov, “Laguerre-Gaussian beam transformations by the double-phase-ramp converter: Singular skeleton formation and its sensitivity to small misalignments,” Proc. SPIE,  10612, 1–9 (2018).
[Crossref]

A. N. Khoroshun, A. V. Chernykh, A. N. Tsimbaluk, J. A. Kirichenko, P. V. Yezhov, A. V. Kuzmenko, and J. T. Kim, “Properties of an Axial Optical Vortex Generated with the use of a Gaussian Beam and Two Ramp,” J. Nanosci. Nanotechnol. 16(2), 2105–2107 (2016).
[Crossref]

Chremmos, I. D.

J. Zhao, I. D. Chremmos, D. Song, D. N. Christodoulides, N. K. Efremidis, and Z. Chen, “Curved singular beams for three dimensional particle manipulation,” Sci. Rep. 5(1), 12086 (2015).
[Crossref]

Christodoulides, D. N.

J. Zhao, I. D. Chremmos, D. Song, D. N. Christodoulides, N. K. Efremidis, and Z. Chen, “Curved singular beams for three dimensional particle manipulation,” Sci. Rep. 5(1), 12086 (2015).
[Crossref]

De Lu, R.

Y. X. Ren, R. De Lu, and L. Gong, “Tailoring light with digital micromirror device,” Ann. Phys. 527(7-8), 447–470 (2015).
[Crossref]

Dennis, M. R.

M. R. Dennis and J. B. Gotte, “Topological Aberration of Optical Vortex Beams: Determining Dielectric Interfaces by Optical Singularity Shifts,” Phys. Rev. Lett. 109(18), 183903 (2012).
[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]

M. R. Dennis, Y. S. Kivshar, M. S. Soskin, and G. A. Swartzlander, “Singular optics: More ado about nothing,” J. Opt. A: Pure Appl. Opt. 11(9), 090201 (2009).
[Crossref]

Desyatnikov, A. S.

Dholakia, K.

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophoton. 2(1), 021875 (2008).
[Crossref]

Dienerowitz, M.

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophoton. 2(1), 021875 (2008).
[Crossref]

Efremidis, N. K.

J. Zhao, I. D. Chremmos, D. Song, D. N. Christodoulides, N. K. Efremidis, and Z. Chen, “Curved singular beams for three dimensional particle manipulation,” Sci. Rep. 5(1), 12086 (2015).
[Crossref]

Ferrando, A.

A. Ferrando and M. A. Garcıa-March, “Theory for the control of dark rays by means of discrete symmetry diffractive elements,” J. Opt. 15(4), 044014 (2013).
[Crossref]

Garcia-March, M. A.

A. Ferrando and M. A. Garcıa-March, “Theory for the control of dark rays by means of discrete symmetry diffractive elements,” J. Opt. 15(4), 044014 (2013).
[Crossref]

Gong, L.

Y. X. Ren, R. De Lu, and L. Gong, “Tailoring light with digital micromirror device,” Ann. Phys. 527(7-8), 447–470 (2015).
[Crossref]

Gorshkov, V. N.

V. N. Gorshkov, A. N. Khoroshun, and M. S. Soskin, “The theory of synthesis of optical vortices by the technique of a phase wedge,” Proc. SPIE. 4705, 65–74 (2002).

Gotte, J. B.

M. R. Dennis and J. B. Gotte, “Topological Aberration of Optical Vortex Beams: Determining Dielectric Interfaces by Optical Singularity Shifts,” Phys. Rev. Lett. 109(18), 183903 (2012).
[Crossref]

Hanson, S.

Huignard, J. P.

J. P. Huignard, “Spatial light modulators and their applications,” J. Opt. 18(4), 181–185 (1987).
[Crossref]

Ina, H.

Ishijima, R.

Izdebskaya, Y.

Y. Izdebskaya, “Optical necklaces generated by the diffraction on a stack of dielectric wedges,” Phys. Lett. A 372(21), 3909–3913 (2008).
[Crossref]

Izdebskaya, Y. V.

V. G. Shvedov, Y. V. Izdebskaya, A. N. Alekseev, and A. V. Volyar, “The formation of optical vortices in the course of light diffraction on a dielectric wedge,” Tech. Phys. Lett. 28(3), 256–259 (2002).
[Crossref]

Izdebskaya, Ya.

Ya. Izdebskaya, V. Shvedov, D. Kurabtzev, A. Alexeyev, and A. Volyar, “The optical vortex generation by optical wedge,” Proc. SPIE 4607, 78–82 (2002).
[Crossref]

Jeon, J. H.

Jesacher, A.

Karamoch, A.

A. Bekshaev and A. Karamoch, “Astigmatic telescopic transformation of a high-order optical vortex,” Opt. Commun. 281(23), 5687–5696 (2008).
[Crossref]

Khoroshun, A.

A. Bekshaev, A. Chernykh, A. Khoroshun, and L. Mikhaylovskaya, “Singular skeleton evolution and topological reactions in edge-diffracted circular optical-vortex beams,” Opt. Commun. 397, 72–83 (2017).
[Crossref]

A. Khoroshun, A. Chernykh, J. Kirichenko, O. Ryazantsev, and A. Bekshaev, “Singular skeleton of a Laguerre–Gaussian beam transformed by the double-phase-ramp converter,” Appl. Opt. 56(12), 3428–3434 (2017).
[Crossref]

Khoroshun, A. N.

A. N. Khoroshun, A. V. Chernykh, H. O. Tatarchenko, A. Ya. Bekshaev, and A. A. Akhmerov, “Laguerre-Gaussian beam transformations by the double-phase-ramp converter: Singular skeleton formation and its sensitivity to small misalignments,” Proc. SPIE,  10612, 1–9 (2018).
[Crossref]

A. N. Khoroshun, A. V. Chernykh, A. N. Tsimbaluk, J. A. Kirichenko, P. V. Yezhov, A. V. Kuzmenko, and J. T. Kim, “Properties of an Axial Optical Vortex Generated with the use of a Gaussian Beam and Two Ramp,” J. Nanosci. Nanotechnol. 16(2), 2105–2107 (2016).
[Crossref]

A. N. Khoroshun, “Optimal linear phase mask for the singular beam synthesis from a Gaussian beam and the scheme of its experimental realisation,” J. Mod. Opt. 57(16), 1542–1549 (2010).
[Crossref]

V. N. Gorshkov, A. N. Khoroshun, and M. S. Soskin, “The theory of synthesis of optical vortices by the technique of a phase wedge,” Proc. SPIE. 4705, 65–74 (2002).

Kim, G. H.

Kim, J. T.

A. N. Khoroshun, A. V. Chernykh, A. N. Tsimbaluk, J. A. Kirichenko, P. V. Yezhov, A. V. Kuzmenko, and J. T. Kim, “Properties of an Axial Optical Vortex Generated with the use of a Gaussian Beam and Two Ramp,” J. Nanosci. Nanotechnol. 16(2), 2105–2107 (2016).
[Crossref]

Kirichenko, J.

Kirichenko, J. A.

A. N. Khoroshun, A. V. Chernykh, A. N. Tsimbaluk, J. A. Kirichenko, P. V. Yezhov, A. V. Kuzmenko, and J. T. Kim, “Properties of an Axial Optical Vortex Generated with the use of a Gaussian Beam and Two Ramp,” J. Nanosci. Nanotechnol. 16(2), 2105–2107 (2016).
[Crossref]

Kivshar, Y. S.

M. R. Dennis, Y. S. Kivshar, M. S. Soskin, and G. A. Swartzlander, “Singular optics: More ado about nothing,” J. Opt. A: Pure Appl. Opt. 11(9), 090201 (2009).
[Crossref]

V. G. Shvedov, A. S. Desyatnikov, A. V. Rode, W. Krolikowski, and Y. S. Kivshar, “Optical guiding of absorbing nanoclusters in air,” Opt. Express 17(7), 5743–5757 (2009).
[Crossref]

Ko, K. H.

Kobayashi, S.

Krolikowski, W.

Kurabtzev, D.

Ya. Izdebskaya, V. Shvedov, D. Kurabtzev, A. Alexeyev, and A. Volyar, “The optical vortex generation by optical wedge,” Proc. SPIE 4607, 78–82 (2002).
[Crossref]

Kurzynowski, P.

A. Popiolek-Masajada, J. Masajada, and P. Kurzynowski, “Analytical Model of the Optical Vortex Scanning Microscope with a simple phase object,” Photonics 4(4), 38 (2017).
[Crossref]

Kuzmenko, A. V.

A. N. Khoroshun, A. V. Chernykh, A. N. Tsimbaluk, J. A. Kirichenko, P. V. Yezhov, A. V. Kuzmenko, and J. T. Kim, “Properties of an Axial Optical Vortex Generated with the use of a Gaussian Beam and Two Ramp,” J. Nanosci. Nanotechnol. 16(2), 2105–2107 (2016).
[Crossref]

Lee, J. H.

Liu, F.

Löffler, W.

Masajada, J.

A. Popiolek-Masajada, J. Masajada, and P. Kurzynowski, “Analytical Model of the Optical Vortex Scanning Microscope with a simple phase object,” Photonics 4(4), 38 (2017).
[Crossref]

P. Senthilkumaran, S. Sato, and J. Masajada, “Singular Optics,” Int. J. Opt. 2012, 1–2 (2012).
[Crossref]

Maurer, C.

Mazilu, M.

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophoton. 2(1), 021875 (2008).
[Crossref]

Mikhaylovskaya, L.

A. Bekshaev, A. Chernykh, A. Khoroshun, and L. Mikhaylovskaya, “Singular skeleton evolution and topological reactions in edge-diffracted circular optical-vortex beams,” Opt. Commun. 397, 72–83 (2017).
[Crossref]

Miyamoto, Y.

Moon, H. J.

Nye, J. F.

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336(1605), 165–190 (1974).
[Crossref]

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]

Orlinska, O.

A. Bekshaev, O. Orlinska, and M. Vasnetsov, “Optical vortex generation with a “fork” hologram under conditions of high-angle diffraction,” Opt. Commun. 283(10), 2006–2016 (2010).
[Crossref]

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]

Popiolek-Masajada, A.

A. Popiolek-Masajada, J. Masajada, and P. Kurzynowski, “Analytical Model of the Optical Vortex Scanning Microscope with a simple phase object,” Photonics 4(4), 38 (2017).
[Crossref]

Porfirev, A. P.

A. P. Porfirev and A. S. Shipilov, “Laser trapping based on photophoretic forces using a spatial light modulator,” CEUR Workshop Proc. 1638, 111–116 (2016).
[Crossref]

Ren, Y. X.

Y. X. Ren, R. De Lu, and L. Gong, “Tailoring light with digital micromirror device,” Ann. Phys. 527(7-8), 447–470 (2015).
[Crossref]

Ricci, F.

Ritsch-Marte, M.

Rode, A. V.

Roux, F. S.

F. S. Roux, “Spatial evolution of the morphology of an optical vortex dipole,” Opt. Commun. 236(4–6), 433–440 (2004).
[Crossref]

Ryazantsev, O.

Sato, S.

P. Senthilkumaran, S. Sato, and J. Masajada, “Singular Optics,” Int. J. Opt. 2012, 1–2 (2012).
[Crossref]

Schwaighofer, A.

Senthilkumaran, P.

P. Senthilkumaran, S. Sato, and J. Masajada, “Singular Optics,” Int. J. Opt. 2012, 1–2 (2012).
[Crossref]

S. Vyas and P. Senthilkumaran, “Vortices from wavefront tilts,” Opt. Lasers Eng. 48(9), 834–840 (2010).
[Crossref]

Shipilov, A. S.

A. P. Porfirev and A. S. Shipilov, “Laser trapping based on photophoretic forces using a spatial light modulator,” CEUR Workshop Proc. 1638, 111–116 (2016).
[Crossref]

Shvedov, V.

Ya. Izdebskaya, V. Shvedov, D. Kurabtzev, A. Alexeyev, and A. Volyar, “The optical vortex generation by optical wedge,” Proc. SPIE 4607, 78–82 (2002).
[Crossref]

Shvedov, V. G.

V. G. Shvedov, A. S. Desyatnikov, A. V. Rode, W. Krolikowski, and Y. S. Kivshar, “Optical guiding of absorbing nanoclusters in air,” Opt. Express 17(7), 5743–5757 (2009).
[Crossref]

V. G. Shvedov, Y. V. Izdebskaya, A. N. Alekseev, and A. V. Volyar, “The formation of optical vortices in the course of light diffraction on a dielectric wedge,” Tech. Phys. Lett. 28(3), 256–259 (2002).
[Crossref]

Song, D.

J. Zhao, I. D. Chremmos, D. Song, D. N. Christodoulides, N. K. Efremidis, and Z. Chen, “Curved singular beams for three dimensional particle manipulation,” Sci. Rep. 5(1), 12086 (2015).
[Crossref]

Soskin, M. S.

M. R. Dennis, Y. S. Kivshar, M. S. Soskin, and G. A. Swartzlander, “Singular optics: More ado about nothing,” J. Opt. A: Pure Appl. Opt. 11(9), 090201 (2009).
[Crossref]

V. N. Gorshkov, A. N. Khoroshun, and M. S. Soskin, “The theory of synthesis of optical vortices by the technique of a phase wedge,” Proc. SPIE. 4705, 65–74 (2002).

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

V. Yu. Bazhenov, M.V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations of the wavefront,” JETP Lett.,  52, 429–431 (1990).

Stegun, I.

M. Abramowitz and I. Stegun, “Error Function and Fresnel Integrals,” in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (NBS Applied Mathematics Series 55, Washington, DC, 1972), pp. 296–297.

Swartzlander, G. A.

M. R. Dennis, Y. S. Kivshar, M. S. Soskin, and G. A. Swartzlander, “Singular optics: More ado about nothing,” J. Opt. A: Pure Appl. Opt. 11(9), 090201 (2009).
[Crossref]

Takeda, H. M.

Takeda, M.

Tatarchenko, H. O.

A. N. Khoroshun, A. V. Chernykh, H. O. Tatarchenko, A. Ya. Bekshaev, and A. A. Akhmerov, “Laguerre-Gaussian beam transformations by the double-phase-ramp converter: Singular skeleton formation and its sensitivity to small misalignments,” Proc. SPIE,  10612, 1–9 (2018).
[Crossref]

Tsimbaluk, A. N.

A. N. Khoroshun, A. V. Chernykh, A. N. Tsimbaluk, J. A. Kirichenko, P. V. Yezhov, A. V. Kuzmenko, and J. T. Kim, “Properties of an Axial Optical Vortex Generated with the use of a Gaussian Beam and Two Ramp,” J. Nanosci. Nanotechnol. 16(2), 2105–2107 (2016).
[Crossref]

van Exter, M. P.

Vasnetsov, M.

A. Bekshaev, O. Orlinska, and M. Vasnetsov, “Optical vortex generation with a “fork” hologram under conditions of high-angle diffraction,” Opt. Commun. 283(10), 2006–2016 (2010).
[Crossref]

Vasnetsov, M. V.

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

Vasnetsov, M.V.

V. Yu. Bazhenov, M.V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations of the wavefront,” JETP Lett.,  52, 429–431 (1990).

Volyar, A.

Ya. Izdebskaya, V. Shvedov, D. Kurabtzev, A. Alexeyev, and A. Volyar, “The optical vortex generation by optical wedge,” Proc. SPIE 4607, 78–82 (2002).
[Crossref]

Volyar, A. V.

V. G. Shvedov, Y. V. Izdebskaya, A. N. Alekseev, and A. V. Volyar, “The formation of optical vortices in the course of light diffraction on a dielectric wedge,” Tech. Phys. Lett. 28(3), 256–259 (2002).
[Crossref]

Vyas, S.

S. Vyas and P. Senthilkumaran, “Vortices from wavefront tilts,” Opt. Lasers Eng. 48(9), 834–840 (2010).
[Crossref]

Wada, A.

Wang, W.

Wei, Y.

Wu, X.

Yezhov, P. V.

A. N. Khoroshun, A. V. Chernykh, A. N. Tsimbaluk, J. A. Kirichenko, P. V. Yezhov, A. V. Kuzmenko, and J. T. Kim, “Properties of an Axial Optical Vortex Generated with the use of a Gaussian Beam and Two Ramp,” J. Nanosci. Nanotechnol. 16(2), 2105–2107 (2016).
[Crossref]

Yokozeki, T.

Zhang, Q.

Zhang, Z.

Zhao, J.

J. Zhao, I. D. Chremmos, D. Song, D. N. Christodoulides, N. K. Efremidis, and Z. Chen, “Curved singular beams for three dimensional particle manipulation,” Sci. Rep. 5(1), 12086 (2015).
[Crossref]

Ann. Phys. (1)

Y. X. Ren, R. De Lu, and L. Gong, “Tailoring light with digital micromirror device,” Ann. Phys. 527(7-8), 447–470 (2015).
[Crossref]

Appl. Opt. (2)

CEUR Workshop Proc. (1)

A. P. Porfirev and A. S. Shipilov, “Laser trapping based on photophoretic forces using a spatial light modulator,” CEUR Workshop Proc. 1638, 111–116 (2016).
[Crossref]

Int. J. Opt. (1)

P. Senthilkumaran, S. Sato, and J. Masajada, “Singular Optics,” Int. J. Opt. 2012, 1–2 (2012).
[Crossref]

J. Mod. Opt. (1)

A. N. Khoroshun, “Optimal linear phase mask for the singular beam synthesis from a Gaussian beam and the scheme of its experimental realisation,” J. Mod. Opt. 57(16), 1542–1549 (2010).
[Crossref]

J. Nanophoton. (1)

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophoton. 2(1), 021875 (2008).
[Crossref]

J. Nanosci. Nanotechnol. (1)

A. N. Khoroshun, A. V. Chernykh, A. N. Tsimbaluk, J. A. Kirichenko, P. V. Yezhov, A. V. Kuzmenko, and J. T. Kim, “Properties of an Axial Optical Vortex Generated with the use of a Gaussian Beam and Two Ramp,” J. Nanosci. Nanotechnol. 16(2), 2105–2107 (2016).
[Crossref]

J. Opt. (2)

A. Ferrando and M. A. Garcıa-March, “Theory for the control of dark rays by means of discrete symmetry diffractive elements,” J. Opt. 15(4), 044014 (2013).
[Crossref]

J. P. Huignard, “Spatial light modulators and their applications,” J. Opt. 18(4), 181–185 (1987).
[Crossref]

J. Opt. A: Pure Appl. Opt. (2)

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A: Pure Appl. Opt. 6(2), 259–268 (2004).
[Crossref]

M. R. Dennis, Y. S. Kivshar, M. S. Soskin, and G. A. Swartzlander, “Singular optics: More ado about nothing,” J. Opt. A: Pure Appl. Opt. 11(9), 090201 (2009).
[Crossref]

J. Opt. Soc. Am. (1)

JETP Lett. (1)

V. Yu. Bazhenov, M.V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations of the wavefront,” JETP Lett.,  52, 429–431 (1990).

Opt. Commun. (4)

A. Bekshaev and A. Karamoch, “Astigmatic telescopic transformation of a high-order optical vortex,” Opt. Commun. 281(23), 5687–5696 (2008).
[Crossref]

A. Bekshaev, O. Orlinska, and M. Vasnetsov, “Optical vortex generation with a “fork” hologram under conditions of high-angle diffraction,” Opt. Commun. 283(10), 2006–2016 (2010).
[Crossref]

F. S. Roux, “Spatial evolution of the morphology of an optical vortex dipole,” Opt. Commun. 236(4–6), 433–440 (2004).
[Crossref]

A. Bekshaev, A. Chernykh, A. Khoroshun, and L. Mikhaylovskaya, “Singular skeleton evolution and topological reactions in edge-diffracted circular optical-vortex beams,” Opt. Commun. 397, 72–83 (2017).
[Crossref]

Opt. Express (5)

Opt. Lasers Eng. (1)

S. Vyas and P. Senthilkumaran, “Vortices from wavefront tilts,” Opt. Lasers Eng. 48(9), 834–840 (2010).
[Crossref]

Photonics (1)

A. Popiolek-Masajada, J. Masajada, and P. Kurzynowski, “Analytical Model of the Optical Vortex Scanning Microscope with a simple phase object,” Photonics 4(4), 38 (2017).
[Crossref]

Phys. Lett. A (1)

Y. Izdebskaya, “Optical necklaces generated by the diffraction on a stack of dielectric wedges,” Phys. Lett. A 372(21), 3909–3913 (2008).
[Crossref]

Phys. Rev. Lett. (1)

M. R. Dennis and J. B. Gotte, “Topological Aberration of Optical Vortex Beams: Determining Dielectric Interfaces by Optical Singularity Shifts,” Phys. Rev. Lett. 109(18), 183903 (2012).
[Crossref]

Proc. R. Soc. London, Ser. A (1)

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336(1605), 165–190 (1974).
[Crossref]

Proc. SPIE (2)

A. N. Khoroshun, A. V. Chernykh, H. O. Tatarchenko, A. Ya. Bekshaev, and A. A. Akhmerov, “Laguerre-Gaussian beam transformations by the double-phase-ramp converter: Singular skeleton formation and its sensitivity to small misalignments,” Proc. SPIE,  10612, 1–9 (2018).
[Crossref]

Ya. Izdebskaya, V. Shvedov, D. Kurabtzev, A. Alexeyev, and A. Volyar, “The optical vortex generation by optical wedge,” Proc. SPIE 4607, 78–82 (2002).
[Crossref]

Proc. SPIE. (1)

V. N. Gorshkov, A. N. Khoroshun, and M. S. Soskin, “The theory of synthesis of optical vortices by the technique of a phase wedge,” Proc. SPIE. 4705, 65–74 (2002).

Prog. Opt. (2)

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

Sci. Rep. (1)

J. Zhao, I. D. Chremmos, D. Song, D. N. Christodoulides, N. K. Efremidis, and Z. Chen, “Curved singular beams for three dimensional particle manipulation,” Sci. Rep. 5(1), 12086 (2015).
[Crossref]

Tech. Phys. Lett. (1)

V. G. Shvedov, Y. V. Izdebskaya, A. N. Alekseev, and A. V. Volyar, “The formation of optical vortices in the course of light diffraction on a dielectric wedge,” Tech. Phys. Lett. 28(3), 256–259 (2002).
[Crossref]

Other (3)

M. Abramowitz and I. Stegun, “Error Function and Fresnel Integrals,” in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (NBS Applied Mathematics Series 55, Washington, DC, 1972), pp. 296–297.

A. Ashkin, Optical Trapping and Manipulation of Neutral Particles Using Lasers (World Scientific2006)

F. M. Dickey ed., Laser Beam Shaping: Theory and Techniques, (CRC Press-P2017).

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Figures (6)

Fig. 1.
Fig. 1. View of the DPR-converter mask (the phase correction (3) varies from –π (black) to +π (white)) realized by the SLM for the synthesis of (a) five optical vortices with topological charge m = +1 and (b) seven OVs with topological charge m = –1 in the high-quality visible area of the output beam cross section. The dashed circle illustrates the radius of a Gaussian beam illuminating the SLM. (c, d) The calculated intensity distributions after passing a Gaussian beam through the mask at the observation distance z = zR from the DPR converter. The equal-intensity ellipses in the near-core dark areas are depicted by white contours on (c) and (d).
Fig. 2.
Fig. 2. Parameters of the OV core structure in the beam cross-section (XY plane) with the intensity pattern as a background. The equal-intensity contour is an ellipse with the center at the amplitude zero position. The major ellipse’s semi-axis a, minor semi-axis b and the angle φ between the positive direction of X-axis and the major semi-axis are marked.
Fig. 3.
Fig. 3. (a) The experimental setup shown schematically; (b) view of the phase correction (2) profile realized the SLM. (c) The intensity pattern contains five well-resolved OVs and two OVs in the low-intensity area, with equal the topological charges m=+1; (d) the interferogram of the field obtained by interference with a Gaussian beam contains seven fringe-bifurcation regions.
Fig. 4.
Fig. 4. (a) The view of the Fourier spectrum for the interferogram presented in Fig. 3d. The rectangle marks the first-order spectrum area. (b) The phase map recovered with the help of the inverse Fourier transform enables precise localization of the OVs.
Fig. 5.
Fig. 5. (a) External features of the singular skeleton in the propagating field formed by the input Gaussian beam transformed by the DPR converter of Eq. (2) with the phase gradient K = 10, topological charge of the OVs is + 1. Images (b), (c) and (d) represent the singular skeleton projections onto the longitudinal XZ, YZ planes and the transverse XY plane, correspondingly. Solid lines indicate the theoretical results, markers show the experimental data. Ordinal numbers –2nd, –1st, 0th, 1st, and 2nd denote the individual OVs.
Fig. 6.
Fig. 6. Internal features of the OV represented by the OV morphology parameters. (a), (b), (c) Dependencies of the ellipticity γ and (d), (e), (f) of the inclination angle φ for the OV for 0th, (upper row), 1st (middle row) and 2nd (bottom row) versus the distance z behind the SLM modeling the DPR converter with the phase correction (2). Theoretical curves are shown by solid black lines and the experimental data are represented by the markers with the error-bars.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

E ( ρ , z 0 ) = E G w 0 w ( z 0 ) exp ( ρ 2 w 2 ( z 0 ) ) exp i [ k z + k ρ 2 2 R ( z 0 ) arctan ( z 0 z R ) ]
Φ ( x , y , z 0 ) = { 2 π K x / w ( z 0 ) ,   y > 0 π + K x / w ( z 0 ) ,   y 0
E ( x , y , z ) = exp ( i k z ) a ( z ) z exp ( i k ( x 2 + y 2 ) 2 z k 2 ( x 2 + y 2 ) 4 z 2 a ( z ) K 2 4 a ( z ) ) [ exp ( k K x 2 a ( z ) z ) ( 1 e r f ( i k y 2 z a ( z ) ) ) exp ( k K x 2 a ( z ) z ) ( 1 + e r f ( i k y 2 z a ( z ) ) ) ]
γ ( z ) = ( B C ) / ( B + C )
φ = 1 2 arccot [ 1 2 2 π b 1 K c 1 4 π K b 1 c 1 a 1 c 1 + c 1 2 b 1 b 1 c 1 c 1 2 b 1 ] + π 2 .
Δ x = Δ x c c d + Δ x ( z ) + Δ x ( t ) .
Δ γ = γ ( Δ x x ) 2 + ( Δ y y ) 2
Δ φ = Δ y a cos ( ϕ )

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