Abstract

We study the frequency shifts taking place when a random, stationary optical field rotates with respect to an observer. The field is expanded in terms of fully coherent Laguerre–Gaussian basis modes, for which the rotational frequency shifts have been studied previously. We demonstrate the formalism by considering the spectrum of a Gaussian Schell-model field, and show that for a spatially highly incoherent field, significant spectral changes can be expected.

© 2006 Optical Society of America

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  1. L.Allen, S.M.Barnett, and M.J.Padgett, eds., Optical Angular Momentum (IOP Publishing, 2003).
  2. M. J. Padgett and L. Allen, "The angular momentum of light: optical spanners and the rotational frequency shift," Opt. Quantum Electron. 31, 1-12 (1999).
  3. B. A. Garetz and S. Arnold, "Variable frequency shifting of circularly polarized laser radiation via a rotating half-wave retardation plate," Opt. Commun. 31, 1-3 (1979).
  4. J. Courtial, K. Dholakia, D. A. Robertson, 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).
  5. I. V. Basistiy, V. V. Slyusar, M. S. Soskin, M. V. Vasnetsov, and A. Ya. Bekshaev, "Manifestation of the rotational Doppler effect by use of an off-axis optical vortex beam," Opt. Lett. 28, 1185-1187 (2003).
  6. M. J. Padgett, "The mechanism for energy transfer in the rotational frequency shift of a light beam," J. Opt. A, Pure Appl. Opt. 6, S263-S265 (2004).
  7. O. Steuernagel, "Comment on 'The mechanism for energy transfer in the rotational frequency shift of a light beam,' regarding longitudinal momentum transfer," J. Opt. A, Pure Appl. Opt. 6, 1058-1059 (2004).
  8. M. V. Vasnetsov, J. P. Torres, D. V. Petrov, and L. Torner, "Observation of the orbital angular momentum spectrum of a light beam," Opt. Lett. 28, 2285-2287 (2003).
  9. R. Dasgupta and P. K. Gupta, "Measurement of orbital angular momentum of a single photon: a non-interferrometric approach," in Proceedings of the 7th International Conference on Optoelectronics, Fiber Optics, and Photonics, December 9-11, 2004, Cochin, Kerala, India.
  10. J. Arlt, M. P. MacDonald, L. Paterson, W. Sibbett, K. Dholakia, and K. Volke-Sepulveda, "Moving interference patterns created using the angular Doppler effect," Opt. Express 10, 844-852 (2002).
  11. B. Mashhoon, R. Neutze, M. Hannam, and G. E. Stedman, "Observable frequency shifts via spin-rotation coupling," Phys. Lett. A 249, 161-166 (1998).
  12. I. Bialynicki-Birula and Z. Bialynicka-Birula, "Rotational frequency shift," Phys. Rev. Lett. 78, 2539-2542 (1997).
  13. L. Torner, J. P. Torres, and S. Carrasco, "Digital spiral imaging," Opt. Express 13, 873-881 (2005).
  14. G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 4th ed. (Academic, 1995).
  15. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
  16. B. Zhang and B. Lü, "Transformation of Gaussian Schell-model beams and their coherent-mode representation," J. Opt. (Paris) 27, 99-103 (1996).
  17. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed., CD-ROM version 1.0, A.Jeffrey ed. (Academic, 1995).

2005

2004

M. J. Padgett, "The mechanism for energy transfer in the rotational frequency shift of a light beam," J. Opt. A, Pure Appl. Opt. 6, S263-S265 (2004).

O. Steuernagel, "Comment on 'The mechanism for energy transfer in the rotational frequency shift of a light beam,' regarding longitudinal momentum transfer," J. Opt. A, Pure Appl. Opt. 6, 1058-1059 (2004).

2003

2002

1999

M. J. Padgett and L. Allen, "The angular momentum of light: optical spanners and the rotational frequency shift," Opt. Quantum Electron. 31, 1-12 (1999).

1998

B. Mashhoon, R. Neutze, M. Hannam, and G. E. Stedman, "Observable frequency shifts via spin-rotation coupling," Phys. Lett. A 249, 161-166 (1998).

J. Courtial, K. Dholakia, D. A. Robertson, 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).

1997

I. Bialynicki-Birula and Z. Bialynicka-Birula, "Rotational frequency shift," Phys. Rev. Lett. 78, 2539-2542 (1997).

1996

B. Zhang and B. Lü, "Transformation of Gaussian Schell-model beams and their coherent-mode representation," J. Opt. (Paris) 27, 99-103 (1996).

1995

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed., CD-ROM version 1.0, A.Jeffrey ed. (Academic, 1995).

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 4th ed. (Academic, 1995).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

1979

B. A. Garetz and S. Arnold, "Variable frequency shifting of circularly polarized laser radiation via a rotating half-wave retardation plate," Opt. Commun. 31, 1-3 (1979).

Allen, L.

M. J. Padgett and L. Allen, "The angular momentum of light: optical spanners and the rotational frequency shift," Opt. Quantum Electron. 31, 1-12 (1999).

J. Courtial, K. Dholakia, D. A. Robertson, 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).

Arfken, G. B.

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 4th ed. (Academic, 1995).

Arlt, J.

Arnold, S.

B. A. Garetz and S. Arnold, "Variable frequency shifting of circularly polarized laser radiation via a rotating half-wave retardation plate," Opt. Commun. 31, 1-3 (1979).

Basistiy, I. V.

Bekshaev, A. Ya.

Bialynicka-Birula, Z.

I. Bialynicki-Birula and Z. Bialynicka-Birula, "Rotational frequency shift," Phys. Rev. Lett. 78, 2539-2542 (1997).

Bialynicki-Birula, I.

I. Bialynicki-Birula and Z. Bialynicka-Birula, "Rotational frequency shift," Phys. Rev. Lett. 78, 2539-2542 (1997).

Carrasco, S.

Courtial, J.

J. Courtial, K. Dholakia, D. A. Robertson, 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).

Dasgupta, R.

R. Dasgupta and P. K. Gupta, "Measurement of orbital angular momentum of a single photon: a non-interferrometric approach," in Proceedings of the 7th International Conference on Optoelectronics, Fiber Optics, and Photonics, December 9-11, 2004, Cochin, Kerala, India.

Dholakia, K.

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

J. Courtial, K. Dholakia, D. A. Robertson, 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).

Garetz, B. A.

B. A. Garetz and S. Arnold, "Variable frequency shifting of circularly polarized laser radiation via a rotating half-wave retardation plate," Opt. Commun. 31, 1-3 (1979).

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed., CD-ROM version 1.0, A.Jeffrey ed. (Academic, 1995).

Gupta, P. K.

R. Dasgupta and P. K. Gupta, "Measurement of orbital angular momentum of a single photon: a non-interferrometric approach," in Proceedings of the 7th International Conference on Optoelectronics, Fiber Optics, and Photonics, December 9-11, 2004, Cochin, Kerala, India.

Hannam, M.

B. Mashhoon, R. Neutze, M. Hannam, and G. E. Stedman, "Observable frequency shifts via spin-rotation coupling," Phys. Lett. A 249, 161-166 (1998).

Lü, B.

B. Zhang and B. Lü, "Transformation of Gaussian Schell-model beams and their coherent-mode representation," J. Opt. (Paris) 27, 99-103 (1996).

MacDonald, M. P.

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

Mashhoon, B.

B. Mashhoon, R. Neutze, M. Hannam, and G. E. Stedman, "Observable frequency shifts via spin-rotation coupling," Phys. Lett. A 249, 161-166 (1998).

Neutze, R.

B. Mashhoon, R. Neutze, M. Hannam, and G. E. Stedman, "Observable frequency shifts via spin-rotation coupling," Phys. Lett. A 249, 161-166 (1998).

Padgett, M. J.

M. J. Padgett, "The mechanism for energy transfer in the rotational frequency shift of a light beam," J. Opt. A, Pure Appl. Opt. 6, S263-S265 (2004).

M. J. Padgett and L. Allen, "The angular momentum of light: optical spanners and the rotational frequency shift," Opt. Quantum Electron. 31, 1-12 (1999).

J. Courtial, K. Dholakia, D. A. Robertson, 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).

Paterson, L.

Petrov, D. V.

Robertson, D. A.

J. Courtial, K. Dholakia, D. A. Robertson, 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).

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed., CD-ROM version 1.0, A.Jeffrey ed. (Academic, 1995).

Sibbett, W.

Slyusar, V. V.

Soskin, M. S.

Stedman, G. E.

B. Mashhoon, R. Neutze, M. Hannam, and G. E. Stedman, "Observable frequency shifts via spin-rotation coupling," Phys. Lett. A 249, 161-166 (1998).

Steuernagel, O.

O. Steuernagel, "Comment on 'The mechanism for energy transfer in the rotational frequency shift of a light beam,' regarding longitudinal momentum transfer," J. Opt. A, Pure Appl. Opt. 6, 1058-1059 (2004).

Torner, L.

Torres, J. P.

Vasnetsov, M. V.

Volke-Sepulveda, K.

Weber, H. J.

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 4th ed. (Academic, 1995).

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

Zhang, B.

B. Zhang and B. Lü, "Transformation of Gaussian Schell-model beams and their coherent-mode representation," J. Opt. (Paris) 27, 99-103 (1996).

J. Opt. (Paris)

B. Zhang and B. Lü, "Transformation of Gaussian Schell-model beams and their coherent-mode representation," J. Opt. (Paris) 27, 99-103 (1996).

J. Opt. A, Pure Appl. Opt.

M. J. Padgett, "The mechanism for energy transfer in the rotational frequency shift of a light beam," J. Opt. A, Pure Appl. Opt. 6, S263-S265 (2004).

O. Steuernagel, "Comment on 'The mechanism for energy transfer in the rotational frequency shift of a light beam,' regarding longitudinal momentum transfer," J. Opt. A, Pure Appl. Opt. 6, 1058-1059 (2004).

Opt. Commun.

B. A. Garetz and S. Arnold, "Variable frequency shifting of circularly polarized laser radiation via a rotating half-wave retardation plate," Opt. Commun. 31, 1-3 (1979).

Opt. Express

Opt. Lett.

Opt. Quantum Electron.

M. J. Padgett and L. Allen, "The angular momentum of light: optical spanners and the rotational frequency shift," Opt. Quantum Electron. 31, 1-12 (1999).

Phys. Lett. A

B. Mashhoon, R. Neutze, M. Hannam, and G. E. Stedman, "Observable frequency shifts via spin-rotation coupling," Phys. Lett. A 249, 161-166 (1998).

Phys. Rev. Lett.

I. Bialynicki-Birula and Z. Bialynicka-Birula, "Rotational frequency shift," Phys. Rev. Lett. 78, 2539-2542 (1997).

J. Courtial, K. Dholakia, D. A. Robertson, 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).

Other

L.Allen, S.M.Barnett, and M.J.Padgett, eds., Optical Angular Momentum (IOP Publishing, 2003).

R. Dasgupta and P. K. Gupta, "Measurement of orbital angular momentum of a single photon: a non-interferrometric approach," in Proceedings of the 7th International Conference on Optoelectronics, Fiber Optics, and Photonics, December 9-11, 2004, Cochin, Kerala, India.

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 4th ed. (Academic, 1995).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed., CD-ROM version 1.0, A.Jeffrey ed. (Academic, 1995).

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