Abstract

The rotational Doppler shift of a photon with orbital angular momentum ± is shown to be an even multiple of the angular frequency Ω of the reference frame rotation when the photon is reflected from the phase-conjugating mirror. The one-arm phase-conjugating interferometer is considered. It contains N Dove prisms or other angular-momentum-altering elements rotating in opposite directions. When such interferometer is placed in the rotating vehicle, the δω=4(N+1/2)·Ω rotational Doppler shift appears. As a result, the helical interference pattern will rotate with angular frequency δω/2. The accumulation of angular Doppler shift via successive passages through the N image-inverting prisms is due to the phase conjugation; for a conventional parabolic retroreflector, the accumulation is absent. The features of such a vortex phase-conjugating interferometry at the single-photon level are discussed.

© 2012 Optical Society of America

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  1. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997), Chap. 4.
  2. 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]
  3. A. Bekshaev, M. Soskin, and M. Vasnetsov, Paraxial Light Beams with Angular Momentum (Nova Science, 2008).
  4. R. W. Boyd, Nonlinear Optics (Academic, 2003).
  5. B. Y. Zeldovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, 1985).
  6. N. G. Basov, I. G. Zubarev, A. B. Mironov, S. I. Mikhailov, and A. Y. Okulov, “Laser interferometer with wavefront reversing mirrors,” J. Exp. Theor. Phys. 52, 847–851 (1980).
  7. M. Woerdemann, C. Alpmann, and C. Denz, “Self-pumped phase conjugation of light beams carrying orbital angular momentum,” Opt. Express 17, 22791 (2009).
    [CrossRef]
  8. A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Time dependent evolution of an optical vortex in photorefractive media,” Phys. Rev. A 56, R1713 (1997).
    [CrossRef]
  9. A. Yu Okulov, “Angular momentum of photons and phase conjugation,” J. Phys. B 41, 101001 (2008).
    [CrossRef]
  10. B. A. Garetz, “Angular Doppler effect,” J. Opt. Soc. Am. 71, 609–611 (1981).
    [CrossRef]
  11. G. Nienhuis, “Doppler effect induced by rotating lenses,” Opt. Commun. 132, 8–14 (1996).
    [CrossRef]
  12. I. Bialynicki-Birula and Z. Bialynicka-Birula, “Rotational frequency shift,” Phys. Rev. Lett. 78, 2539–2542 (1997).
    [CrossRef]
  13. J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Measurement of the rotational frequency shift imparted to a rotating light beam possessing orbital angular momentum,” Phys. Rev. Lett. 80, 3217–3219 (1998).
    [CrossRef]
  14. J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81, 4828–4830 (1998).
    [CrossRef]
  15. 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]
  16. R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115–125 (1936).
    [CrossRef]
  17. J. E. Sipe, “Photon wave functions,” Phys. Rev. A 52, 1875–1883 (1995).
    [CrossRef]
  18. M. Baier, S. Watanabe, E. Pelucchi, E. Kapon, S. Varoutsis, M. Gallart, I. Robert-Philip, and I. Abram, “Single-photon emission from site-controlled pyramidal quantum dots,” Appl. Phys. Lett. 84, 648–650 (2004).
    [CrossRef]
  19. K. Volke-Sepulveda and R. Jauregui, “All-optical 3D atomic loops generated with Bessel light fields,” J. Phys. B 42, 085303 (2009).
    [CrossRef]
  20. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499 (1987).
    [CrossRef]
  21. 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]
  22. 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).
  23. E. Abramochkin and V. Volostnikov, “Spiral light beams,” Phys. Usp. 47, 1177–1203 (2004).
    [CrossRef]
  24. Ch. V. Felde and P. V. Polyanski, “Static holographic phase conjugation of vortex beams,” Opt. Spectrosc. 98, 913–918 (2005).
    [CrossRef]
  25. A. Yu. Okulov, “Twisted speckle entities inside wavefront reversal mirrors,” Phys. Rev. A 80, 163907 (2009).
    [CrossRef]
  26. M. Bhattacharya, “Lattice with a twist: helical waveguides for ultracold matter,” Opt. Commun. 279, 219–222 (2007).
    [CrossRef]
  27. A. Yu. Okulov, “Phase-conjugation of the isolated optical vortex using a flat surfaces,” J. Opt. Soc. Am. B 27, 2424–2427 (2010).
    [CrossRef]
  28. H. Q. Wei, X. Xue, J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, “Simplified measurement of the orbital angular momentum of single photons,” Opt. Commun. 223, 117–122 (2003).
    [CrossRef]
  29. M. P. J. Lavery, A. Dudley, A. Forbes, J. Courtial1, and M. J. Padgett, “Robust interferometer for the routing of light beams carrying orbital angular momentum,” New J. Phys. 13, 093014 (2011).
    [CrossRef]
  30. D. M. Pepper, “Phase conjugate optics,” Ph.D. dissertation (California Institute of Technology, 1980), p. 37. http://resolver.caltech.edu/CaltechETD-10122006-081036 .
  31. A. V. Nowak, T. R. Moore, and R. A. Fisher, “Observations of internal beam production in barium titanate phase conjugators,” J. Opt. Soc. Am. B 5, 1864–1878 (1988).
    [CrossRef]
  32. S. Sternklar, S. Weiss, and B. Fischer, “Tunable frequency shift of photorefractive oscillators,” Opt. Lett. 11, 165–167 (1986).
    [CrossRef]
  33. E. M. Lifshitz, L. P. Pitaevskii, and V. B. Berestetskii, Quantum Electrodynamics (Butterworth, 1982), Sections 6 and 8.
  34. P. N. Lebedev, “Experimental examination of the light pressure,” Ann. Phys. 6, 433–459 (1901).
    [CrossRef]
  35. 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]
  36. S. Franke-Arnold, G. Gibson, R. W. Boyd, and M. J. Padgett, “Rotary photon drag enhanced by a slow-light medium,” Science 333, 65–67 (2011).
    [CrossRef]
  37. L. Foucault, “Démonstration physique du mouvent de rotation de la Terre, au moyen d’un pendule,” C. R. Hebd. Seances Acad. Sci., 35, 135–138 (1851).
  38. M. Shirasaki, H. A. Haus, and D. L. Wong, “Quantum theory of the nonlinear interferometer,” J. Opt. Soc. Am. B 6, 82–88 (1989).
    [CrossRef]

2011

M. P. J. Lavery, A. Dudley, A. Forbes, J. Courtial1, and M. J. Padgett, “Robust interferometer for the routing of light beams carrying orbital angular momentum,” New J. Phys. 13, 093014 (2011).
[CrossRef]

S. Franke-Arnold, G. Gibson, R. W. Boyd, and M. J. Padgett, “Rotary photon drag enhanced by a slow-light medium,” Science 333, 65–67 (2011).
[CrossRef]

2010

2009

A. Yu. Okulov, “Twisted speckle entities inside wavefront reversal mirrors,” Phys. Rev. A 80, 163907 (2009).
[CrossRef]

M. Woerdemann, C. Alpmann, and C. Denz, “Self-pumped phase conjugation of light beams carrying orbital angular momentum,” Opt. Express 17, 22791 (2009).
[CrossRef]

K. Volke-Sepulveda and R. Jauregui, “All-optical 3D atomic loops generated with Bessel light fields,” J. Phys. B 42, 085303 (2009).
[CrossRef]

2008

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

2007

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]

2005

Ch. V. Felde and P. V. Polyanski, “Static holographic phase conjugation of vortex beams,” Opt. Spectrosc. 98, 913–918 (2005).
[CrossRef]

2004

E. Abramochkin and V. Volostnikov, “Spiral light beams,” Phys. Usp. 47, 1177–1203 (2004).
[CrossRef]

M. Baier, S. Watanabe, E. Pelucchi, E. Kapon, S. Varoutsis, M. Gallart, I. Robert-Philip, and I. Abram, “Single-photon emission from site-controlled pyramidal quantum dots,” Appl. Phys. Lett. 84, 648–650 (2004).
[CrossRef]

2003

H. Q. Wei, X. Xue, J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, “Simplified measurement of the orbital angular momentum of single photons,” Opt. Commun. 223, 117–122 (2003).
[CrossRef]

2002

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).

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]

1998

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Measurement of the rotational frequency shift imparted to a rotating light beam possessing orbital angular momentum,” Phys. Rev. Lett. 80, 3217–3219 (1998).
[CrossRef]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81, 4828–4830 (1998).
[CrossRef]

1997

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Time dependent evolution of an optical vortex in photorefractive media,” Phys. Rev. A 56, R1713 (1997).
[CrossRef]

I. Bialynicki-Birula and Z. Bialynicka-Birula, “Rotational frequency shift,” Phys. Rev. Lett. 78, 2539–2542 (1997).
[CrossRef]

1996

G. Nienhuis, “Doppler effect induced by rotating lenses,” Opt. Commun. 132, 8–14 (1996).
[CrossRef]

1995

J. E. Sipe, “Photon wave functions,” Phys. Rev. A 52, 1875–1883 (1995).
[CrossRef]

1992

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]

1989

1988

1987

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

1986

1981

1980

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

1936

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

1901

P. N. Lebedev, “Experimental examination of the light pressure,” Ann. Phys. 6, 433–459 (1901).
[CrossRef]

1851

L. Foucault, “Démonstration physique du mouvent de rotation de la Terre, au moyen d’un pendule,” C. R. Hebd. Seances Acad. Sci., 35, 135–138 (1851).

Abram, I.

M. Baier, S. Watanabe, E. Pelucchi, E. Kapon, S. Varoutsis, M. Gallart, I. Robert-Philip, and I. Abram, “Single-photon emission from site-controlled pyramidal quantum dots,” Appl. Phys. Lett. 84, 648–650 (2004).
[CrossRef]

Abramochkin, E.

E. Abramochkin and V. Volostnikov, “Spiral light beams,” Phys. Usp. 47, 1177–1203 (2004).
[CrossRef]

Allen, L.

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81, 4828–4830 (1998).
[CrossRef]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Measurement of the rotational frequency shift imparted to a rotating light beam possessing orbital angular momentum,” Phys. Rev. Lett. 80, 3217–3219 (1998).
[CrossRef]

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]

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).

Baier, M.

M. Baier, S. Watanabe, E. Pelucchi, E. Kapon, S. Varoutsis, M. Gallart, I. Robert-Philip, and I. Abram, “Single-photon emission from site-controlled pyramidal quantum dots,” Appl. Phys. Lett. 84, 648–650 (2004).
[CrossRef]

Barnett, S. M.

H. Q. Wei, X. Xue, J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, “Simplified measurement of the orbital angular momentum of single photons,” Opt. Commun. 223, 117–122 (2003).
[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]

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,” J. Exp. Theor. Phys. 52, 847–851 (1980).

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]

Bekshaev, A.

A. Bekshaev, M. Soskin, and M. Vasnetsov, Paraxial Light Beams with Angular Momentum (Nova Science, 2008).

Berestetskii, V. B.

E. M. Lifshitz, L. P. Pitaevskii, and V. B. Berestetskii, Quantum Electrodynamics (Butterworth, 1982), Sections 6 and 8.

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]

Bialynicka-Birula, Z.

I. Bialynicki-Birula and Z. Bialynicka-Birula, “Rotational frequency shift,” Phys. Rev. Lett. 78, 2539–2542 (1997).
[CrossRef]

Bialynicki-Birula, I.

I. Bialynicki-Birula and Z. Bialynicka-Birula, “Rotational frequency shift,” Phys. Rev. Lett. 78, 2539–2542 (1997).
[CrossRef]

Boyd, R. W.

S. Franke-Arnold, G. Gibson, R. W. Boyd, and M. J. Padgett, “Rotary photon drag enhanced by a slow-light medium,” Science 333, 65–67 (2011).
[CrossRef]

R. W. Boyd, Nonlinear Optics (Academic, 2003).

Courtial, J.

H. Q. Wei, X. Xue, J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, “Simplified measurement of the orbital angular momentum of single photons,” Opt. Commun. 223, 117–122 (2003).
[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]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Measurement of the rotational frequency shift imparted to a rotating light beam possessing orbital angular momentum,” Phys. Rev. Lett. 80, 3217–3219 (1998).
[CrossRef]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81, 4828–4830 (1998).
[CrossRef]

Courtial1, J.

M. P. J. Lavery, A. Dudley, A. Forbes, J. Courtial1, and M. J. Padgett, “Robust interferometer for the routing of light beams carrying orbital angular momentum,” New J. Phys. 13, 093014 (2011).
[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).

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Measurement of the rotational frequency shift imparted to a rotating light beam possessing orbital angular momentum,” Phys. Rev. Lett. 80, 3217–3219 (1998).
[CrossRef]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81, 4828–4830 (1998).
[CrossRef]

Dudley, A.

M. P. J. Lavery, A. Dudley, A. Forbes, J. Courtial1, and M. J. Padgett, “Robust interferometer for the routing of light beams carrying orbital angular momentum,” New J. Phys. 13, 093014 (2011).
[CrossRef]

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Felde, Ch. V.

Ch. V. Felde and P. V. Polyanski, “Static holographic phase conjugation of vortex beams,” Opt. Spectrosc. 98, 913–918 (2005).
[CrossRef]

Fischer, B.

Fisher, R. A.

Forbes, A.

M. P. J. Lavery, A. Dudley, A. Forbes, J. Courtial1, and M. J. Padgett, “Robust interferometer for the routing of light beams carrying orbital angular momentum,” New J. Phys. 13, 093014 (2011).
[CrossRef]

Foucault, L.

L. Foucault, “Démonstration physique du mouvent de rotation de la Terre, au moyen d’un pendule,” C. R. Hebd. Seances Acad. Sci., 35, 135–138 (1851).

Franke-Arnold, S.

S. Franke-Arnold, G. Gibson, R. W. Boyd, and M. J. Padgett, “Rotary photon drag enhanced by a slow-light medium,” Science 333, 65–67 (2011).
[CrossRef]

H. Q. Wei, X. Xue, J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, “Simplified measurement of the orbital angular momentum of single photons,” Opt. Commun. 223, 117–122 (2003).
[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]

Gallart, M.

M. Baier, S. Watanabe, E. Pelucchi, E. Kapon, S. Varoutsis, M. Gallart, I. Robert-Philip, and I. Abram, “Single-photon emission from site-controlled pyramidal quantum dots,” Appl. Phys. Lett. 84, 648–650 (2004).
[CrossRef]

Garetz, B. A.

Gibson, G.

S. Franke-Arnold, G. Gibson, R. W. Boyd, and M. J. Padgett, “Rotary photon drag enhanced by a slow-light medium,” Science 333, 65–67 (2011).
[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]

Haus, H. A.

Jauregui, R.

K. Volke-Sepulveda and R. Jauregui, “All-optical 3D atomic loops generated with Bessel light fields,” J. Phys. B 42, 085303 (2009).
[CrossRef]

Kapon, E.

M. Baier, S. Watanabe, E. Pelucchi, E. Kapon, S. Varoutsis, M. Gallart, I. Robert-Philip, and I. Abram, “Single-photon emission from site-controlled pyramidal quantum dots,” Appl. Phys. Lett. 84, 648–650 (2004).
[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]

Lavery, M. P. J.

M. P. J. Lavery, A. Dudley, A. Forbes, J. Courtial1, and M. J. Padgett, “Robust interferometer for the routing of light beams carrying orbital angular momentum,” New J. Phys. 13, 093014 (2011).
[CrossRef]

Leach, J.

H. Q. Wei, X. Xue, J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, “Simplified measurement of the orbital angular momentum of single photons,” Opt. Commun. 223, 117–122 (2003).
[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]

Lebedev, P. N.

P. N. Lebedev, “Experimental examination of the light pressure,” Ann. Phys. 6, 433–459 (1901).
[CrossRef]

Lifshitz, E. M.

E. M. Lifshitz, L. P. Pitaevskii, and V. B. Berestetskii, Quantum Electrodynamics (Butterworth, 1982), Sections 6 and 8.

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]

Mamaev, A. V.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Time dependent evolution of an optical vortex in photorefractive media,” Phys. Rev. A 56, R1713 (1997).
[CrossRef]

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499 (1987).
[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,” J. Exp. Theor. Phys. 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,” J. Exp. Theor. Phys. 52, 847–851 (1980).

Moore, T. R.

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]

Nienhuis, G.

G. Nienhuis, “Doppler effect induced by rotating lenses,” Opt. Commun. 132, 8–14 (1996).
[CrossRef]

Nowak, A. V.

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,” J. Exp. Theor. Phys. 52, 847–851 (1980).

Okulov, A. Yu

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

Okulov, A. Yu.

A. Yu. Okulov, “Phase-conjugation of the isolated optical vortex using a flat surfaces,” J. Opt. Soc. Am. B 27, 2424–2427 (2010).
[CrossRef]

A. Yu. Okulov, “Twisted speckle entities inside wavefront reversal mirrors,” Phys. Rev. A 80, 163907 (2009).
[CrossRef]

Padgett, M. J.

M. P. J. Lavery, A. Dudley, A. Forbes, J. Courtial1, and M. J. Padgett, “Robust interferometer for the routing of light beams carrying orbital angular momentum,” New J. Phys. 13, 093014 (2011).
[CrossRef]

S. Franke-Arnold, G. Gibson, R. W. Boyd, and M. J. Padgett, “Rotary photon drag enhanced by a slow-light medium,” Science 333, 65–67 (2011).
[CrossRef]

H. Q. Wei, X. Xue, J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, “Simplified measurement of the orbital angular momentum of single photons,” Opt. Commun. 223, 117–122 (2003).
[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]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Measurement of the rotational frequency shift imparted to a rotating light beam possessing orbital angular momentum,” Phys. Rev. Lett. 80, 3217–3219 (1998).
[CrossRef]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81, 4828–4830 (1998).
[CrossRef]

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).

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]

Pelucchi, E.

M. Baier, S. Watanabe, E. Pelucchi, E. Kapon, S. Varoutsis, M. Gallart, I. Robert-Philip, and I. Abram, “Single-photon emission from site-controlled pyramidal quantum dots,” Appl. Phys. Lett. 84, 648–650 (2004).
[CrossRef]

Pepper, D. M.

D. M. Pepper, “Phase conjugate optics,” Ph.D. dissertation (California Institute of Technology, 1980), p. 37. http://resolver.caltech.edu/CaltechETD-10122006-081036 .

Pilipetsky, N. F.

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

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]

Pitaevskii, L. P.

E. M. Lifshitz, L. P. Pitaevskii, and V. B. Berestetskii, Quantum Electrodynamics (Butterworth, 1982), Sections 6 and 8.

Polyanski, P. V.

Ch. V. Felde and P. V. Polyanski, “Static holographic phase conjugation of vortex beams,” Opt. Spectrosc. 98, 913–918 (2005).
[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]

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]

Robert-Philip, I.

M. Baier, S. Watanabe, E. Pelucchi, E. Kapon, S. Varoutsis, M. Gallart, I. Robert-Philip, and I. Abram, “Single-photon emission from site-controlled pyramidal quantum dots,” Appl. Phys. Lett. 84, 648–650 (2004).
[CrossRef]

Robertson, D. A.

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81, 4828–4830 (1998).
[CrossRef]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Measurement of the rotational frequency shift imparted to a rotating light beam possessing orbital angular momentum,” Phys. Rev. Lett. 80, 3217–3219 (1998).
[CrossRef]

Saffman, M.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Time dependent evolution of an optical vortex in photorefractive media,” Phys. Rev. A 56, R1713 (1997).
[CrossRef]

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]

Scully, M. O.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997), Chap. 4.

Shirasaki, M.

Shkunov, V. V.

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

Sibbett, W.

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).

Sipe, J. E.

J. E. Sipe, “Photon wave functions,” Phys. Rev. A 52, 1875–1883 (1995).
[CrossRef]

Soskin, M.

A. Bekshaev, M. Soskin, and M. Vasnetsov, Paraxial Light Beams with Angular Momentum (Nova Science, 2008).

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]

Sternklar, S.

Varoutsis, S.

M. Baier, S. Watanabe, E. Pelucchi, E. Kapon, S. Varoutsis, M. Gallart, I. Robert-Philip, and I. Abram, “Single-photon emission from site-controlled pyramidal quantum dots,” Appl. Phys. Lett. 84, 648–650 (2004).
[CrossRef]

Vasnetsov, M.

A. Bekshaev, M. Soskin, and M. Vasnetsov, Paraxial Light Beams with Angular Momentum (Nova Science, 2008).

Volke-Sepulveda, K.

K. Volke-Sepulveda and R. Jauregui, “All-optical 3D atomic loops generated with Bessel light fields,” J. Phys. B 42, 085303 (2009).
[CrossRef]

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).

Volostnikov, V.

E. Abramochkin and V. Volostnikov, “Spiral light beams,” Phys. Usp. 47, 1177–1203 (2004).
[CrossRef]

Watanabe, S.

M. Baier, S. Watanabe, E. Pelucchi, E. Kapon, S. Varoutsis, M. Gallart, I. Robert-Philip, and I. Abram, “Single-photon emission from site-controlled pyramidal quantum dots,” Appl. Phys. Lett. 84, 648–650 (2004).
[CrossRef]

Wei, H. Q.

H. Q. Wei, X. Xue, J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, “Simplified measurement of the orbital angular momentum of single photons,” Opt. Commun. 223, 117–122 (2003).
[CrossRef]

Weiss, S.

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).
[CrossRef]

Wong, D. L.

Xue, X.

H. Q. Wei, X. Xue, J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, “Simplified measurement of the orbital angular momentum of single photons,” Opt. Commun. 223, 117–122 (2003).
[CrossRef]

Yao, E.

H. Q. Wei, X. Xue, J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, “Simplified measurement of the orbital angular momentum of single photons,” Opt. Commun. 223, 117–122 (2003).
[CrossRef]

Zeldovich, B. Y.

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

Zozulya, A. A.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Time dependent evolution of an optical vortex in photorefractive media,” Phys. Rev. A 56, R1713 (1997).
[CrossRef]

Zubairy, M. S.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997), Chap. 4.

Zubarev, I. G.

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

Ann. Phys.

P. N. Lebedev, “Experimental examination of the light pressure,” Ann. Phys. 6, 433–459 (1901).
[CrossRef]

Appl. Phys. Lett.

M. Baier, S. Watanabe, E. Pelucchi, E. Kapon, S. Varoutsis, M. Gallart, I. Robert-Philip, and I. Abram, “Single-photon emission from site-controlled pyramidal quantum dots,” Appl. Phys. Lett. 84, 648–650 (2004).
[CrossRef]

C. R. Hebd. Seances Acad. Sci.

L. Foucault, “Démonstration physique du mouvent de rotation de la Terre, au moyen d’un pendule,” C. R. Hebd. Seances Acad. Sci., 35, 135–138 (1851).

J. Exp. Theor. Phys.

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

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

J. Phys. B

K. Volke-Sepulveda and R. Jauregui, “All-optical 3D atomic loops generated with Bessel light fields,” J. Phys. B 42, 085303 (2009).
[CrossRef]

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

New J. Phys.

M. P. J. Lavery, A. Dudley, A. Forbes, J. Courtial1, and M. J. Padgett, “Robust interferometer for the routing of light beams carrying orbital angular momentum,” New J. Phys. 13, 093014 (2011).
[CrossRef]

Opt. Commun.

H. Q. Wei, X. Xue, J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, “Simplified measurement of the orbital angular momentum of single photons,” Opt. Commun. 223, 117–122 (2003).
[CrossRef]

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

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]

G. Nienhuis, “Doppler effect induced by rotating lenses,” Opt. Commun. 132, 8–14 (1996).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Spectrosc.

Ch. V. Felde and P. V. Polyanski, “Static holographic phase conjugation of vortex beams,” Opt. Spectrosc. 98, 913–918 (2005).
[CrossRef]

Phys. Rev.

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

Phys. Rev. A

J. E. Sipe, “Photon wave functions,” Phys. Rev. A 52, 1875–1883 (1995).
[CrossRef]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Time dependent evolution of an optical vortex in photorefractive media,” Phys. Rev. A 56, R1713 (1997).
[CrossRef]

A. Yu. Okulov, “Twisted speckle entities inside wavefront reversal mirrors,” Phys. Rev. A 80, 163907 (2009).
[CrossRef]

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]

Phys. Rev. Lett.

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]

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]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

I. Bialynicki-Birula and Z. Bialynicka-Birula, “Rotational frequency shift,” Phys. Rev. Lett. 78, 2539–2542 (1997).
[CrossRef]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Measurement of the rotational frequency shift imparted to a rotating light beam possessing orbital angular momentum,” Phys. Rev. Lett. 80, 3217–3219 (1998).
[CrossRef]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81, 4828–4830 (1998).
[CrossRef]

Phys. Usp.

E. Abramochkin and V. Volostnikov, “Spiral light beams,” Phys. Usp. 47, 1177–1203 (2004).
[CrossRef]

Science

S. Franke-Arnold, G. Gibson, R. W. Boyd, and M. J. Padgett, “Rotary photon drag enhanced by a slow-light medium,” Science 333, 65–67 (2011).
[CrossRef]

Other

E. M. Lifshitz, L. P. Pitaevskii, and V. B. Berestetskii, Quantum Electrodynamics (Butterworth, 1982), Sections 6 and 8.

D. M. Pepper, “Phase conjugate optics,” Ph.D. dissertation (California Institute of Technology, 1980), p. 37. http://resolver.caltech.edu/CaltechETD-10122006-081036 .

A. Bekshaev, M. Soskin, and M. Vasnetsov, Paraxial Light Beams with Angular Momentum (Nova Science, 2008).

R. W. Boyd, Nonlinear Optics (Academic, 2003).

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

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997), Chap. 4.

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Figures (3)

Fig. 1.
Fig. 1.

Additivity of RDS for the PCM-reflected photon in the rest frame. Rotation of the Dove prism (positive Ω) decreases frequency to 2·Ω of the corotating incident photon with Lz=+. Reflection from the helical grating inside the PCM [7,8] alters Lz projection to the opposite one, and counterclockwise rotation of the Dove prism (as seen to backward photon) again decreases the frequency of the corotating photon to 2·Ω. The helical interference pattern is static between the prism and the PCM (where δω=0) and rotates before the prism with angular velocity θ.=2Ω having opposite handedness.

Fig. 2.
Fig. 2.

Mutual cancellation of RDS for a retroreflected photon. Rotation of the Dove prism again decreases frequency of the corotating forward photon with Lz=+ by 2·Ω. In backward propagation, the Dove prism is counterrotating with respect to the photon. Backward RDS is positive; thus, the resulting δω is zero and the toroidal interference pattern is static for all Z.

Fig. 3.
Fig. 3.

Additivity of RDS in PCVI inside the rotating vehicle. The sign of δω is positive when optical torque T produced by a bunch of the rotating photons upon the mirror has the opposite direction compared to the rotation frequency of the PCM Ω. When the Dove prism rotates in the opposite direction versus the PCM, the net RDS reaches the sixfold value δω=±6·Ω due to the additional OAM alternation. The sequence of N counterrotating OAM-altering elements (including helical wave plates and cylindrical lenses) will produce net RDS of δω=4·Ω(N+1/2) value. |Ψ1,2,3,4 designates the antibunching of photons, which belongs to the two (for =1) helical wave functions, separated by a λ/2 interval, deflected by the entrance beam splitter [7].

Equations (10)

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

Ψ(f,b)(z,r,θ,t)E(f,b)02ϵ0·exp[iω(f,b)t±ik(f,b)z±iθ](1+iz/zR)(r/D0)||exp[r2D02(1+iz/zR)],zR=k(f,b)D02,
z=zzpc,|Ψ|2=|Ψf+Ψb|2Itw(z,r,θ,t)=2ϵ0c|E(f,b)|22(||+1)(r/D0)2||π!D02(1+z2/zR2)·exp[2r2D02(1+z2/zR2)][1+R2+2R·cos[δω·t(kf+kb)z+2θ]],
Izz·Ω+Lz=Izz·Ω+Lzωf+IzzΩ22=ω+IzzΩ22,
ΩΩ=2·Izz.
δω=ωωf=Izz2(ΩΩ)(Ω+Ω)=2·Ω2·Izz.
|Ψ|2=|Ψf+Ψb|2Itor(z,r,θ,t)=2ϵ0c|E(f,b)|22(||+1)(r/D0)2||π!D02(1+z2/zR2)·exp[2r2D02(1+z2/zR2)][1+R2+2R·cos[δω·t(kf+kb)z]].
δω=ωbωf=±2·Ω+2·(Izz)PCM.
|ΨH=12(|Ψ±f+|Ψb)=12jh|Ψjh.
|ΨH=12(|ΨBlue+|ΨYellow).
|Ψtor=12(|Ψ±f+|Ψ±b)=1NtorjtorΨjtor.

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