Abstract

The robust method for obtaining the helical interference pattern due to the phase-conjugation of an isolated optical vortex by means of the non-holographic technique is proposed. It is shown that a perfect wavefront reversal of the vortex in a linear polarization state via an even number of reflections is achievable due to the turn of the photon’s momentum pk with respect to the photon’s orbital angular momentum projection Lz. The possible experimental realization is based on cat’s eye-prism-like reflections inside the confocal optical loop cavity. The alternative scheme contains the Dove prism embedded in the optical loop with an odd number of reflections from mirrors. This confocal interferometric technique is applicable to optical tweezers, atomic traps, Sagnac laser loops, and metamaterials fabrication.

© 2010 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  8. A. Yu. Okulov, “Angular momentum of photons and phase conjugation,” J. Phys. B 41, 101001 (2008).
    [CrossRef]
  9. M. Bhattacharya, “Lattice with a twist: Helical waveguides for ultracold matter,” Opt. Commun. 279, 219–222 (2007).
    [CrossRef]
  10. T. Puppe, I. Schuster, A. Grothe, A. Kubanek, K. Murr, P. W. H. Pinkse, and G. Rempe, “Trapping and observing single atoms in a blue-detuned intracavity dipole trap,” Phys. Rev. Lett. 99, 013002 (2007).
    [CrossRef] [PubMed]
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  12. R. Marchiano, F. Coulouvrat, L. Gnjehi, and J.-L. Thomas, “Numerical investigation of the properties of nonlinear acoustical vortices through weakly heterogeneous media,” Phys. Rev. E 77, 016605 (2008).
    [CrossRef]
  13. J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
    [CrossRef]
  14. M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 118–121 (2010).
    [CrossRef]
  15. M. P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, and K. Dholakia, “Revolving interference patterns for the rotation of optically trapped particles,” Opt. Commun. 201, 21–28 (2002).
    [CrossRef]
  16. A. Yu. Okulov, “The effect of roughness of optical elements on the transverse structure of alight field in a nonlinear Talbot cavity,” J. Mod. Opt. 38, 1887–1890 (1991).
    [CrossRef]
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    [CrossRef]
  18. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
    [CrossRef] [PubMed]
  19. J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (2002).
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  20. R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115–125 (1936).
    [CrossRef]
  21. J. Arlt, M. MacDonald, L. Paterson, W. Sibbett, K. Volke-Sepulveda, and K. Dholakia, “Moving interference patterns created using the angular Doppler-effect,” Opt. Express 10, 844–852 (2002).
    [PubMed]
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    [CrossRef]
  23. A. Yu. Okulov, “Scaling of diode-array-pumped solid-state lasers via self-imaging,” Opt. Commun. 99, 350–354 (1993).
    [CrossRef]
  24. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, 1997), Chaps. 4 and 17.
  25. D. Zerrouki, J. Baudry, D. Pine, P. Chaikin, and J. Bibette, “Chiral colloidal clusters,” Nature 455, 380–382 (2008).
    [CrossRef] [PubMed]
  26. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ϵ and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
    [CrossRef]
  27. M. Thiel, H. Fischer, G. von Freymann, and M. Wegener, “Three-dimensional chiral photonic superlattices,” Opt. Lett. 35, 166–168 (2010).
    [CrossRef] [PubMed]
  28. Z. Menachem and M. Mond, “Infrared wave propagation in a helical waveguide with inhomogeneous cross section and application,” PIER 61, 159–162 (2006).
    [CrossRef]

2010 (2)

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 118–121 (2010).
[CrossRef]

M. Thiel, H. Fischer, G. von Freymann, and M. Wegener, “Three-dimensional chiral photonic superlattices,” Opt. Lett. 35, 166–168 (2010).
[CrossRef] [PubMed]

2009 (2)

2008 (5)

A. Yu. Okulov, “Angular momentum of photons and phase conjugation,” J. Phys. B 41, 101001 (2008).
[CrossRef]

A. Yu. Okulov, “Optical and sound helical structures in a Mandelstamm–Brillouin mirrors,” JETP Lett. 88, 487–491 (2008).
[CrossRef]

R. Marchiano, F. Coulouvrat, L. Gnjehi, and J.-L. Thomas, “Numerical investigation of the properties of nonlinear acoustical vortices through weakly heterogeneous media,” Phys. Rev. E 77, 016605 (2008).
[CrossRef]

Ch. V. Felde, P. V. Polyanski, and H. V. Bogatyryova, “Comparative analysis of techniques for diagnostics of phase singularities,” Ukr. J. Phys. Opt. 9, 82–90 (2008).
[CrossRef]

D. Zerrouki, J. Baudry, D. Pine, P. Chaikin, and J. Bibette, “Chiral colloidal clusters,” Nature 455, 380–382 (2008).
[CrossRef] [PubMed]

2007 (2)

M. Bhattacharya, “Lattice with a twist: Helical waveguides for ultracold matter,” Opt. Commun. 279, 219–222 (2007).
[CrossRef]

T. Puppe, I. Schuster, A. Grothe, A. Kubanek, K. Murr, P. W. H. Pinkse, and G. Rempe, “Trapping and observing single atoms in a blue-detuned intracavity dipole trap,” Phys. Rev. Lett. 99, 013002 (2007).
[CrossRef] [PubMed]

2006 (1)

Z. Menachem and M. Mond, “Infrared wave propagation in a helical waveguide with inhomogeneous cross section and application,” PIER 61, 159–162 (2006).
[CrossRef]

2005 (1)

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[CrossRef]

2002 (3)

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef] [PubMed]

M. P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, and K. Dholakia, “Revolving interference patterns for the rotation of optically trapped particles,” Opt. Commun. 201, 21–28 (2002).
[CrossRef]

J. Arlt, M. MacDonald, L. Paterson, W. Sibbett, K. Volke-Sepulveda, and K. Dholakia, “Moving interference patterns created using the angular Doppler-effect,” Opt. Express 10, 844–852 (2002).
[PubMed]

1995 (1)

I. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wave-front dislocations and their properties,” Opt. Commun. 119, 604–612 (1995).
[CrossRef]

1993 (1)

A. Yu. Okulov, “Scaling of diode-array-pumped solid-state lasers via self-imaging,” Opt. Commun. 99, 350–354 (1993).
[CrossRef]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

1991 (1)

A. Yu. Okulov, “The effect of roughness of optical elements on the transverse structure of alight field in a nonlinear Talbot cavity,” J. Mod. Opt. 38, 1887–1890 (1991).
[CrossRef]

1990 (1)

1980 (1)

N. G. Basov, I. G. Zubarev, A. B. Mironov, S. I. Mikhailov, and A. Y. Okulov, “Laser interferometer with wavefront reversing mirrors,” Sov. Phys. JETP 52, 847–851 (1980).

1977 (1)

1974 (1)

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

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ϵ and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
[CrossRef]

1936 (1)

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115–125 (1936).
[CrossRef]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Alpmann, C.

Arlt, J.

M. P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, and K. Dholakia, “Revolving interference patterns for the rotation of optically trapped particles,” Opt. Commun. 201, 21–28 (2002).
[CrossRef]

J. Arlt, M. MacDonald, L. Paterson, W. Sibbett, K. Volke-Sepulveda, and K. Dholakia, “Moving interference patterns created using the angular Doppler-effect,” Opt. Express 10, 844–852 (2002).
[PubMed]

Barnett, S. M.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef] [PubMed]

Basistiy, I.

I. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wave-front dislocations and their properties,” Opt. Commun. 119, 604–612 (1995).
[CrossRef]

Basov, N. G.

N. G. Basov, I. G. Zubarev, A. B. Mironov, S. I. Mikhailov, and A. Y. Okulov, “Laser interferometer with wavefront reversing mirrors,” Sov. Phys. JETP 52, 847–851 (1980).

Baudry, J.

D. Zerrouki, J. Baudry, D. Pine, P. Chaikin, and J. Bibette, “Chiral colloidal clusters,” Nature 455, 380–382 (2008).
[CrossRef] [PubMed]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Berry, M. V.

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

Beth, R. A.

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115–125 (1936).
[CrossRef]

Bhattacharya, M.

M. Bhattacharya, “Lattice with a twist: Helical waveguides for ultracold matter,” Opt. Commun. 279, 219–222 (2007).
[CrossRef]

Bibette, J.

D. Zerrouki, J. Baudry, D. Pine, P. Chaikin, and J. Bibette, “Chiral colloidal clusters,” Nature 455, 380–382 (2008).
[CrossRef] [PubMed]

Bogatyryova, H. V.

Ch. V. Felde, P. V. Polyanski, and H. V. Bogatyryova, “Comparative analysis of techniques for diagnostics of phase singularities,” Ukr. J. Phys. Opt. 9, 82–90 (2008).
[CrossRef]

Chaikin, P.

D. Zerrouki, J. Baudry, D. Pine, P. Chaikin, and J. Bibette, “Chiral colloidal clusters,” Nature 455, 380–382 (2008).
[CrossRef] [PubMed]

Coulouvrat, F.

R. Marchiano, F. Coulouvrat, L. Gnjehi, and J.-L. Thomas, “Numerical investigation of the properties of nonlinear acoustical vortices through weakly heterogeneous media,” Phys. Rev. E 77, 016605 (2008).
[CrossRef]

Courtial, J.

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[CrossRef]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef] [PubMed]

Dennis, M. R.

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 118–121 (2010).
[CrossRef]

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[CrossRef]

Denz, C.

Dholakia, K.

M. P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, and K. Dholakia, “Revolving interference patterns for the rotation of optically trapped particles,” Opt. Commun. 201, 21–28 (2002).
[CrossRef]

J. Arlt, M. MacDonald, L. Paterson, W. Sibbett, K. Volke-Sepulveda, and K. Dholakia, “Moving interference patterns created using the angular Doppler-effect,” Opt. Express 10, 844–852 (2002).
[PubMed]

Felde, Ch. V.

Ch. V. Felde, P. V. Polyanski, and H. V. Bogatyryova, “Comparative analysis of techniques for diagnostics of phase singularities,” Ukr. J. Phys. Opt. 9, 82–90 (2008).
[CrossRef]

Fischer, H.

Franke-Arnold, S.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef] [PubMed]

Gnjehi, L.

R. Marchiano, F. Coulouvrat, L. Gnjehi, and J.-L. Thomas, “Numerical investigation of the properties of nonlinear acoustical vortices through weakly heterogeneous media,” Phys. Rev. E 77, 016605 (2008).
[CrossRef]

Grothe, A.

T. Puppe, I. Schuster, A. Grothe, A. Kubanek, K. Murr, P. W. H. Pinkse, and G. Rempe, “Trapping and observing single atoms in a blue-detuned intracavity dipole trap,” Phys. Rev. Lett. 99, 013002 (2007).
[CrossRef] [PubMed]

Hellwarth, R.

Jack, B.

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 118–121 (2010).
[CrossRef]

King, R. P.

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 118–121 (2010).
[CrossRef]

Kubanek, A.

T. Puppe, I. Schuster, A. Grothe, A. Kubanek, K. Murr, P. W. H. Pinkse, and G. Rempe, “Trapping and observing single atoms in a blue-detuned intracavity dipole trap,” Phys. Rev. Lett. 99, 013002 (2007).
[CrossRef] [PubMed]

Leach, J.

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[CrossRef]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef] [PubMed]

MacDonald, M.

MacDonald, M. P.

M. P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, and K. Dholakia, “Revolving interference patterns for the rotation of optically trapped particles,” Opt. Commun. 201, 21–28 (2002).
[CrossRef]

Marchiano, R.

R. Marchiano, F. Coulouvrat, L. Gnjehi, and J.-L. Thomas, “Numerical investigation of the properties of nonlinear acoustical vortices through weakly heterogeneous media,” Phys. Rev. E 77, 016605 (2008).
[CrossRef]

Menachem, Z.

Z. Menachem and M. Mond, “Infrared wave propagation in a helical waveguide with inhomogeneous cross section and application,” PIER 61, 159–162 (2006).
[CrossRef]

Mikhailov, S. I.

N. G. Basov, I. G. Zubarev, A. B. Mironov, S. I. Mikhailov, and A. Y. Okulov, “Laser interferometer with wavefront reversing mirrors,” Sov. Phys. JETP 52, 847–851 (1980).

Mironov, A. B.

N. G. Basov, I. G. Zubarev, A. B. Mironov, S. I. Mikhailov, and A. Y. Okulov, “Laser interferometer with wavefront reversing mirrors,” Sov. Phys. JETP 52, 847–851 (1980).

Mond, M.

Z. Menachem and M. Mond, “Infrared wave propagation in a helical waveguide with inhomogeneous cross section and application,” PIER 61, 159–162 (2006).
[CrossRef]

Murr, K.

T. Puppe, I. Schuster, A. Grothe, A. Kubanek, K. Murr, P. W. H. Pinkse, and G. Rempe, “Trapping and observing single atoms in a blue-detuned intracavity dipole trap,” Phys. Rev. Lett. 99, 013002 (2007).
[CrossRef] [PubMed]

Nye, J. F.

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

O’Holleran, K.

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 118–121 (2010).
[CrossRef]

Okulov, A. Y.

N. G. Basov, I. G. Zubarev, A. B. Mironov, S. I. Mikhailov, and A. Y. Okulov, “Laser interferometer with wavefront reversing mirrors,” Sov. Phys. JETP 52, 847–851 (1980).

Okulov, A. Yu.

A. Yu. Okulov, “Twisted speckle entities inside wavefront reversal mirrors,” Phys. Rev. A 80, 013837 (2009).
[CrossRef]

A. Yu. Okulov, “Angular momentum of photons and phase conjugation,” J. Phys. B 41, 101001 (2008).
[CrossRef]

A. Yu. Okulov, “Optical and sound helical structures in a Mandelstamm–Brillouin mirrors,” JETP Lett. 88, 487–491 (2008).
[CrossRef]

A. Yu. Okulov, “Scaling of diode-array-pumped solid-state lasers via self-imaging,” Opt. Commun. 99, 350–354 (1993).
[CrossRef]

A. Yu. Okulov, “The effect of roughness of optical elements on the transverse structure of alight field in a nonlinear Talbot cavity,” J. Mod. Opt. 38, 1887–1890 (1991).
[CrossRef]

A. Yu. Okulov, “Two-dimensional periodic structures in nonlinear resonator,” J. Opt. Soc. Am. B 7, 1045–1050 (1990).
[CrossRef]

Padgett, M. J.

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 118–121 (2010).
[CrossRef]

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[CrossRef]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef] [PubMed]

Paterson, L.

J. Arlt, M. MacDonald, L. Paterson, W. Sibbett, K. Volke-Sepulveda, and K. Dholakia, “Moving interference patterns created using the angular Doppler-effect,” Opt. Express 10, 844–852 (2002).
[PubMed]

M. P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, and K. Dholakia, “Revolving interference patterns for the rotation of optically trapped particles,” Opt. Commun. 201, 21–28 (2002).
[CrossRef]

Pilipetsky, N. F.

B. Y. Zeldovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, 1985).

Pine, D.

D. Zerrouki, J. Baudry, D. Pine, P. Chaikin, and J. Bibette, “Chiral colloidal clusters,” Nature 455, 380–382 (2008).
[CrossRef] [PubMed]

Pinkse, P. W. H.

T. Puppe, I. Schuster, A. Grothe, A. Kubanek, K. Murr, P. W. H. Pinkse, and G. Rempe, “Trapping and observing single atoms in a blue-detuned intracavity dipole trap,” Phys. Rev. Lett. 99, 013002 (2007).
[CrossRef] [PubMed]

Polyanski, P. V.

Ch. V. Felde, P. V. Polyanski, and H. V. Bogatyryova, “Comparative analysis of techniques for diagnostics of phase singularities,” Ukr. J. Phys. Opt. 9, 82–90 (2008).
[CrossRef]

Puppe, T.

T. Puppe, I. Schuster, A. Grothe, A. Kubanek, K. Murr, P. W. H. Pinkse, and G. Rempe, “Trapping and observing single atoms in a blue-detuned intracavity dipole trap,” Phys. Rev. Lett. 99, 013002 (2007).
[CrossRef] [PubMed]

Rempe, G.

T. Puppe, I. Schuster, A. Grothe, A. Kubanek, K. Murr, P. W. H. Pinkse, and G. Rempe, “Trapping and observing single atoms in a blue-detuned intracavity dipole trap,” Phys. Rev. Lett. 99, 013002 (2007).
[CrossRef] [PubMed]

Schuster, I.

T. Puppe, I. Schuster, A. Grothe, A. Kubanek, K. Murr, P. W. H. Pinkse, and G. Rempe, “Trapping and observing single atoms in a blue-detuned intracavity dipole trap,” Phys. Rev. Lett. 99, 013002 (2007).
[CrossRef] [PubMed]

Scully, M. O.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, 1997), Chaps. 4 and 17.

Shkunov, V. V.

B. Y. Zeldovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, 1985).

Sibbett, W.

J. Arlt, M. MacDonald, L. Paterson, W. Sibbett, K. Volke-Sepulveda, and K. Dholakia, “Moving interference patterns created using the angular Doppler-effect,” Opt. Express 10, 844–852 (2002).
[PubMed]

M. P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, and K. Dholakia, “Revolving interference patterns for the rotation of optically trapped particles,” Opt. Commun. 201, 21–28 (2002).
[CrossRef]

Soskin, M. S.

I. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wave-front dislocations and their properties,” Opt. Commun. 119, 604–612 (1995).
[CrossRef]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Thiel, M.

Thomas, J. -L.

R. Marchiano, F. Coulouvrat, L. Gnjehi, and J.-L. Thomas, “Numerical investigation of the properties of nonlinear acoustical vortices through weakly heterogeneous media,” Phys. Rev. E 77, 016605 (2008).
[CrossRef]

Vasnetsov, M. V.

I. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wave-front dislocations and their properties,” Opt. Commun. 119, 604–612 (1995).
[CrossRef]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ϵ and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
[CrossRef]

Volke-Sepulveda, K.

M. P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, and K. Dholakia, “Revolving interference patterns for the rotation of optically trapped particles,” Opt. Commun. 201, 21–28 (2002).
[CrossRef]

J. Arlt, M. MacDonald, L. Paterson, W. Sibbett, K. Volke-Sepulveda, and K. Dholakia, “Moving interference patterns created using the angular Doppler-effect,” Opt. Express 10, 844–852 (2002).
[PubMed]

von Freymann, G.

Wegener, M.

Woerdemann, M.

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
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Figures (3)

Fig. 1
Fig. 1

(a) Intertwining of the helical interference patterns in the optical speckle [7]. The size of pattern is 32 μ m in X-direction and 64 μ m in Z-direction. The period of longitudinal ( Z ) modulation is λ / 2 . (b) In contrast to optical vortices in a speckle the isolated LG optical vortices propagate rectilinearly. Interference pattern (4) is sliced at Y = 0 , 5 , 10 μ m distances from the vortex axis Z.

Fig. 2
Fig. 2

Two consecutive reflections of LG beam emitted by continuous-wave laser with mode converter MC. Each total internal reflection inside the cat’s eye prism from plane prism surface changes the topological charge of LG to the opposite one. After two reflections at 45° angle the optical vortex has the opposite direction of propagation and opposite direction of the angular momentum. The counterpropagating LG has the same topological charge ; hence composite wavetrain produces the helical interference pattern. Confocal telescope consisting of the thin lenses L compensates the free-space propagation parabolic wavefront.

Fig. 3
Fig. 3

Single reflection inside Dove prism changes the topological charge. After the two refractions the LG propagates with conserved momentum and overturned angular momentum. This leads to helical interference pattern due to overlapping with counterpropagating LG, having opposite OAMs.

Equations (5)

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E ( f , b ) ( z , r , t ) z + n ( z , r ) c E ( f , b ) t ± i 2 k ( f , b ) Δ E ( f , b ) = 0 ,
E ( f ) ( r , 0 ) E ( f ) 0 j x , j y N g A j x , j y   exp [ i k j x , j y r + i θ j x , j y ] .
E ( f , b ) ( z , r , θ , t ) E ( f , b ) 0   exp [ i ( ω ( f , b ) t ± k ( f , b ) z ) ± i θ ] ( 1 + i z / ( k ( f , b ) D 0 2 ) ) 2 ( r / D 0 ) exp [ r 2 D 0 2 ( 1 + i z / ( k ( f , b ) D 0 2 ) ) ] ,
| E f ( z , r , θ , t ) + E b ( z , r , θ , t ) | 2 | E ( f , b ) 0 | 2 ( r / D 0 ) 2 exp [ 2 r 2 D 0 2 ( 1 + i z / ( k ( f , b ) D 0 2 ) ) ] [ 1 + cos [ ( ω f ω b ) t ( k f + k b ) z + 2 θ ] ] .
Ω = ( ω f ω b ) = 16 π 2 A Ω r P λ ,

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