Abstract

The modal theory for spectrally partially coherent nonstationary plane waves is introduced. The theory is first developed in the space–frequency domain and then extended to the space–time domain. Propagation properties of the coherent modes are analyzed. The concept of the overall degree of coherence is extended to the domain of nonstationary fields, and it is shown that the overall degree of coherence of partially coherent plane-wave pulses is the same in the space–frequency and space–time domains. The theory is applied to the recently introduced concept of spectrally Gaussian Schell-model plane-wave pulses.

© 2004 Optical Society of America

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995).
  2. B. Cairns, E. Wolf, “The instantenous cross-spectral density of nonstationary wave fields,” Opt. Commun. 62, 215–218 (1986).
    [CrossRef]
  3. M. Bertolotti, A. Ferrari, L. Sereda, “Coherence properties of nonstationary polychromatic light sources,” J. Opt. Soc. Am. B 12, 341–347 (1995).
    [CrossRef]
  4. L. Sereda, M. Bertolotti, A. Ferrari, “Coherence properties of nonstationary light wave fields,” J. Opt. Soc. Am. A 15, 695–705 (1998).
    [CrossRef]
  5. M. Bertolotti, L. Sereda, A. Ferrari, “Application of the spectral representation of stochastic process to the study of nonstationary light radiation: a tutorial,” Pure Appl. Opt. 6, 153–171 (1997).
    [CrossRef]
  6. P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, F. Wyrowski, “Partially coherent Gaussian pulses,” Opt. Commun. 204, 53–58 (2002).
    [CrossRef]
  7. H. Lajunen, J. Tervo, J. Turunen, P. Vahimaa, F. Wyrowski, “Spectral coherence properties of temporally modulated stationary light sources,” Opt. Express 11, 1894–1899 (2003).
    [CrossRef] [PubMed]
  8. E. Wolf, “New spectral representation of random sources and of the partially coherent fields that they generate,” Opt. Commun. 38, 3–6 (1981).
    [CrossRef]
  9. E. Wolf, “New theory of partial coherence in the space–frequency domain. Part I: Spectra and cross spectra of steady-state sources,” J. Opt. Soc. Am. 72, 343–351 (1982).
    [CrossRef]
  10. E. Wolf, “New theory of partial coherence in the space–frequency domain. Part II: Steady-state fields and higher-order correlations,” J. Opt. Soc. Am. A 3, 76–85 (1986).
    [CrossRef]
  11. P. Vahimaa, J. Tervo, “Unified measures for optical fields: degree of polarization and effective degree of coherence,” J. Opt. A Pure Appl. Opt. 6, S41–S44 (2004).
    [CrossRef]
  12. M. J. Bastiaans, “New class of uncertainty relations for partially coherent light,” J. Opt. Soc. Am. A 1, 711–715 (1984).
    [CrossRef]
  13. F. Riesz, B. Sz.- Nagy, Functional Analysis (Ungar, New York, 1978), p. 245.
  14. G. B. Arfken, H. J. Weber, Mathematical Methods for Physicists (Acadamic, San Diego, Calif., 2001).
  15. L. Mandel, E. Wolf, “Complete coherence in the space–frequency domain,” Opt. Commun. 36, 247–249 (1981).
    [CrossRef]
  16. T. Setälä, J. Tervo, A. T. Friberg, “Complete electromagnetic coherence in the space–frequency domain,” Opt. Lett. 29, 328–330 (2004).
    [CrossRef]
  17. A. Starikov, E. Wolf, “Coherent-mode representation of Gaussian Schell-model sources and of their radiation fields,” J. Opt. Soc. Am. 72, 923–928 (1982).
    [CrossRef]
  18. F. Gori, “Collett-Wolf sources and multimode lasers,” Opt. Commun. 34, 301–305 (1980).
    [CrossRef]
  19. I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980), p. 838, formula (7.376.1).

2004 (2)

P. Vahimaa, J. Tervo, “Unified measures for optical fields: degree of polarization and effective degree of coherence,” J. Opt. A Pure Appl. Opt. 6, S41–S44 (2004).
[CrossRef]

T. Setälä, J. Tervo, A. T. Friberg, “Complete electromagnetic coherence in the space–frequency domain,” Opt. Lett. 29, 328–330 (2004).
[CrossRef]

2003 (1)

2002 (1)

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, F. Wyrowski, “Partially coherent Gaussian pulses,” Opt. Commun. 204, 53–58 (2002).
[CrossRef]

1998 (1)

1997 (1)

M. Bertolotti, L. Sereda, A. Ferrari, “Application of the spectral representation of stochastic process to the study of nonstationary light radiation: a tutorial,” Pure Appl. Opt. 6, 153–171 (1997).
[CrossRef]

1995 (1)

1986 (2)

B. Cairns, E. Wolf, “The instantenous cross-spectral density of nonstationary wave fields,” Opt. Commun. 62, 215–218 (1986).
[CrossRef]

E. Wolf, “New theory of partial coherence in the space–frequency domain. Part II: Steady-state fields and higher-order correlations,” J. Opt. Soc. Am. A 3, 76–85 (1986).
[CrossRef]

1984 (1)

1982 (2)

1981 (2)

L. Mandel, E. Wolf, “Complete coherence in the space–frequency domain,” Opt. Commun. 36, 247–249 (1981).
[CrossRef]

E. Wolf, “New spectral representation of random sources and of the partially coherent fields that they generate,” Opt. Commun. 38, 3–6 (1981).
[CrossRef]

1980 (1)

F. Gori, “Collett-Wolf sources and multimode lasers,” Opt. Commun. 34, 301–305 (1980).
[CrossRef]

Arfken, G. B.

G. B. Arfken, H. J. Weber, Mathematical Methods for Physicists (Acadamic, San Diego, Calif., 2001).

Bastiaans, M. J.

Bertolotti, M.

Cairns, B.

B. Cairns, E. Wolf, “The instantenous cross-spectral density of nonstationary wave fields,” Opt. Commun. 62, 215–218 (1986).
[CrossRef]

Ferrari, A.

Friberg, A. T.

T. Setälä, J. Tervo, A. T. Friberg, “Complete electromagnetic coherence in the space–frequency domain,” Opt. Lett. 29, 328–330 (2004).
[CrossRef]

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, F. Wyrowski, “Partially coherent Gaussian pulses,” Opt. Commun. 204, 53–58 (2002).
[CrossRef]

Gori, F.

F. Gori, “Collett-Wolf sources and multimode lasers,” Opt. Commun. 34, 301–305 (1980).
[CrossRef]

Gradshteyn, I. S.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980), p. 838, formula (7.376.1).

Lajunen, H.

Mandel, L.

L. Mandel, E. Wolf, “Complete coherence in the space–frequency domain,” Opt. Commun. 36, 247–249 (1981).
[CrossRef]

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

Nagy, B. Sz.-

F. Riesz, B. Sz.- Nagy, Functional Analysis (Ungar, New York, 1978), p. 245.

Pääkkönen, P.

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, F. Wyrowski, “Partially coherent Gaussian pulses,” Opt. Commun. 204, 53–58 (2002).
[CrossRef]

Riesz, F.

F. Riesz, B. Sz.- Nagy, Functional Analysis (Ungar, New York, 1978), p. 245.

Ryzhik, I. M.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980), p. 838, formula (7.376.1).

Sereda, L.

Setälä, T.

Starikov, A.

Tervo, J.

Turunen, J.

H. Lajunen, J. Tervo, J. Turunen, P. Vahimaa, F. Wyrowski, “Spectral coherence properties of temporally modulated stationary light sources,” Opt. Express 11, 1894–1899 (2003).
[CrossRef] [PubMed]

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, F. Wyrowski, “Partially coherent Gaussian pulses,” Opt. Commun. 204, 53–58 (2002).
[CrossRef]

Vahimaa, P.

P. Vahimaa, J. Tervo, “Unified measures for optical fields: degree of polarization and effective degree of coherence,” J. Opt. A Pure Appl. Opt. 6, S41–S44 (2004).
[CrossRef]

H. Lajunen, J. Tervo, J. Turunen, P. Vahimaa, F. Wyrowski, “Spectral coherence properties of temporally modulated stationary light sources,” Opt. Express 11, 1894–1899 (2003).
[CrossRef] [PubMed]

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, F. Wyrowski, “Partially coherent Gaussian pulses,” Opt. Commun. 204, 53–58 (2002).
[CrossRef]

Weber, H. J.

G. B. Arfken, H. J. Weber, Mathematical Methods for Physicists (Acadamic, San Diego, Calif., 2001).

Wolf, E.

E. Wolf, “New theory of partial coherence in the space–frequency domain. Part II: Steady-state fields and higher-order correlations,” J. Opt. Soc. Am. A 3, 76–85 (1986).
[CrossRef]

B. Cairns, E. Wolf, “The instantenous cross-spectral density of nonstationary wave fields,” Opt. Commun. 62, 215–218 (1986).
[CrossRef]

E. Wolf, “New theory of partial coherence in the space–frequency domain. Part I: Spectra and cross spectra of steady-state sources,” J. Opt. Soc. Am. 72, 343–351 (1982).
[CrossRef]

A. Starikov, E. Wolf, “Coherent-mode representation of Gaussian Schell-model sources and of their radiation fields,” J. Opt. Soc. Am. 72, 923–928 (1982).
[CrossRef]

E. Wolf, “New spectral representation of random sources and of the partially coherent fields that they generate,” Opt. Commun. 38, 3–6 (1981).
[CrossRef]

L. Mandel, E. Wolf, “Complete coherence in the space–frequency domain,” Opt. Commun. 36, 247–249 (1981).
[CrossRef]

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

Wyrowski, F.

H. Lajunen, J. Tervo, J. Turunen, P. Vahimaa, F. Wyrowski, “Spectral coherence properties of temporally modulated stationary light sources,” Opt. Express 11, 1894–1899 (2003).
[CrossRef] [PubMed]

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, F. Wyrowski, “Partially coherent Gaussian pulses,” Opt. Commun. 204, 53–58 (2002).
[CrossRef]

J. Opt. A Pure Appl. Opt. (1)

P. Vahimaa, J. Tervo, “Unified measures for optical fields: degree of polarization and effective degree of coherence,” J. Opt. A Pure Appl. Opt. 6, S41–S44 (2004).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (3)

J. Opt. Soc. Am. B (1)

Opt. Commun. (5)

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, F. Wyrowski, “Partially coherent Gaussian pulses,” Opt. Commun. 204, 53–58 (2002).
[CrossRef]

E. Wolf, “New spectral representation of random sources and of the partially coherent fields that they generate,” Opt. Commun. 38, 3–6 (1981).
[CrossRef]

B. Cairns, E. Wolf, “The instantenous cross-spectral density of nonstationary wave fields,” Opt. Commun. 62, 215–218 (1986).
[CrossRef]

L. Mandel, E. Wolf, “Complete coherence in the space–frequency domain,” Opt. Commun. 36, 247–249 (1981).
[CrossRef]

F. Gori, “Collett-Wolf sources and multimode lasers,” Opt. Commun. 34, 301–305 (1980).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Pure Appl. Opt. (1)

M. Bertolotti, L. Sereda, A. Ferrari, “Application of the spectral representation of stochastic process to the study of nonstationary light radiation: a tutorial,” Pure Appl. Opt. 6, 153–171 (1997).
[CrossRef]

Other (4)

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

F. Riesz, B. Sz.- Nagy, Functional Analysis (Ungar, New York, 1978), p. 245.

G. B. Arfken, H. J. Weber, Mathematical Methods for Physicists (Acadamic, San Diego, Calif., 2001).

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980), p. 838, formula (7.376.1).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Metrics