Abstract

Matrix optics is applied to a class of random, in time and space, electromagnetic pulsed beam-like (REMPB) radiation interacting with linear optical elements. A 6×6 order matrix describing transformation of a six-dimensional state vector including four spatial and two temporal positions within the field is used to derive conditions for spatio-temporal coupling. An example is included which deals with a spatio-temporal coupling in a typical REMPB on reflection from a reflecting grating. Electromagnetic nature of such interaction is explored via considering dependence of the degree of polarization of the reflected REMPB on its source and on the structure of the grating.

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  1. S. M. Wang and D. M. Zhao, Matrix Optics, (Springer, 2000).
  2. For the collection of original papers by R. C. Jones see W. Swindel, Polarized light, (Dowden, Hutchinson & Ross, (Stroudsburg, Pennsylvania, 1975).
  3. H. Mueller, “The foundations of optics,” J. Opt. Soc. Am. 38, 661–661 (1948); for account of the Mueller’s theory see also E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, Inc., New York, 1993). Chap. 5.
  4. O. Korotkova and E. Wolf, “Effects of linear non-image forming devices on coherence and polarization properties of random electromagnetic beams. Part I. General theory,” J. Mod. Opt. 52, 2659–2671 (2005).
    [CrossRef]
  5. O. Korotkova and E. Wolf, “Effects of linear non-image forming devices on spectra and on coherence and polarization properties ofstochastic electromagnetic beams. Part II. Examples,” J. Mod. Opt. 52, 2673–2685 (2005).
    [CrossRef]
  6. Q. Lin and Y. Cai, “Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schell model beams,” Opt. Lett. 27(4), 216–218 (2002).
    [CrossRef]
  7. M. Yao, Y. Cai, H. T. Eyyuboğlu, Y. Baykal, and O. Korotkova, “Evolution of the degree of polarization of an electromagnetic Gaussian Schell-model beam in a Gaussian cavity,” Opt. Lett. 33(19), 2266–2268 (2008).
    [CrossRef] [PubMed]
  8. O. Korotkova, Y. Cai, and E. Watson, “Stochastic electromagnetic beams for LIDAR systems operating through turbulent atmosphere,” Appl. Phys. B 94(4), 681–690 (2009).
    [CrossRef]
  9. O. E. Martinez, “Matrix formalism for pulse compressors,” IEEE J. Quantum Electron. 24(12), 2530–2536 (1988).
    [CrossRef]
  10. O. E. Martinez, “Matrix formalism for dispersive laser cavities,” IEEE J. Quantum Electron. 25(3), 296–300 (1989).
    [CrossRef]
  11. A. G. Kostenbauder, “Ray-pulse matrices: a rational treatment for dispersive optical systems,” IEEE J. Quantum Electron. 26(6), 1148–1157 (1990).
    [CrossRef]
  12. S. P. Dijaili, A. Dienes, and J. S. Smith, “ABCD matrices for dispersive pulse propagation,” IEEE J. Quantum Electron. 26(6), 1158–1164 (1990).
    [CrossRef]
  13. Q. Lin, S. Wang, J. Alda, and E. Bernabeu, “Transformation of pulsed nonideal beams in a four-dimension domain,” Opt. Lett. 18(9), 669–671 (1993).
    [CrossRef] [PubMed]
  14. P. A. Bélanger, “Beam propagation and the ABCD ray matrices,” Opt. Lett. 16(4), 196–198 (1991).
    [CrossRef] [PubMed]
  15. P. Paakkonen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, “Partially coherent Gaussian pulses,” Opt. Commun. 204(1-6), 53–58 (2002).
    [CrossRef]
  16. Q. Lin, L. Wang, and S. Zhu, “Partially coherent light pulse and its propagation,” Opt. Commun. 219(1-6), 65–70 (2003).
    [CrossRef]
  17. L. G. Wang, Q. Lin, H. Chen, and S. Y. Zhu, “Propagation of partially coherent pulsed beams in the spatiotemporal domain,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(5), 056613 (2003).
    [CrossRef] [PubMed]
  18. H. Lajunen, J. Tervo, and P. Vahimaa, “Overall coherence and coherent-mode expansion of spectrally partially coherent plane-wave pulses,” J. Opt. Soc. Am. A 21(11), 2117–2123 (2004).
    [CrossRef]
  19. Y. Cai and Q. Lin, “The fractional Fourier transform for a partially coherent pulse,” J. Opt. A, Pure Appl. Opt. 6(4), 307–311 (2004).
    [CrossRef]
  20. J. Lancis, V. Torres-Company, E. Silvestre, and P. Andrés, “Space-time analogy for partially coherent plane-wave-type pulses,” Opt. Lett. 30(22), 2973–2975 (2005).
    [CrossRef] [PubMed]
  21. H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, and F. Wyrowski, “Spectrally partially coherent pulse trains in dispersive media,” Opt. Commun. 255(1-3), 12–22 (2005).
    [CrossRef]
  22. H. Lajunen, P. Vahimaa, and J. Tervo, “Theory of spatially and spectrally partially coherent pulses,” J. Opt. Soc. Am. A 22(8), 1536–1545 (2005).
    [CrossRef]
  23. V. Torres-Company, G. Mínguez-Vega, J. Lancis, and A. T. Friberg, “Controllable generation of partially coherent light pulses with direct space-to-time pulse shaper,” Opt. Lett. 32(12), 1608–1610 (2007).
    [CrossRef] [PubMed]
  24. A. T. Friberg, H. Lajunen, and V. Torres-Company, “Spectral elementary-coherence-function representation for partially coherent light pulses,” Opt. Express 15(8), 5160–5165 (2007).
    [CrossRef] [PubMed]
  25. V. Torres-Company, H. Lajunen, J. Lancis, and A. T. Friberg, “Ghost interference with classical partially coherent light pulses,” Phys. Rev. A 77(4), 043811 (2008).
    [CrossRef]
  26. H. Lajunen, V. Torres-Company, J. Lancis, E. Silvestre, and P. Andrès, “Pulse-by-pulse method to characterize partially coherent pulse propagation in instantaneous nonlinear media,” Opt. Express 18(14), 14979–14991 (2010).
    [CrossRef] [PubMed]
  27. C. Ding, L. Pan, and B. Lu, “Characterization of stochastic spatially and spectrally partially coherent electromagnetic pulsed beams,” N. J. Phys. 11(8), 083001 (2009).
    [CrossRef]
  28. C. Ding and B. Lu, “Spectral shifts and spectral switches of diffracted spatially and spectrally partially coherent pulsed beams in the far field,” J. Opt. A, Pure Appl. Opt. 10(9), 095006 (2008).
    [CrossRef]
  29. M. Kempe, U. Stamm, B. Wilhelmi, and W. Rudolph, “Spatial and temporal transformation of femtosecond laser pulses by lenses and lens systems,” J. Opt. Soc. Am. B 9(7), 1158–1165 (1992).
    [CrossRef]
  30. Q. Lin, S. Wang, J. Alda, and E. Bernabeu, “Spatial-temporal coupling in grating-pair pulse compression system analysed by matrix optics,” Opt. Quantum Electron. 27(7), 679–692 (1995).
    [CrossRef]
  31. G. Piquero, R. Borghi, and M. Santarsiero, “Gaussian Schell-model beams propagating through polarization gratings,” J. Opt. Soc. Am. A 18(6), 1399–1405 (2001).
    [CrossRef]
  32. E. Wolf, “Unified theory of coherence and polarization of random electromagnetic fields,” Phys. Lett. A 312(5-6), 263–267 (2003).
    [CrossRef]
  33. F. Gori, “Matrix treatment for partially polarized, partially coherent beams,” Opt. Lett. 23(4), 241–243 (1998).
    [CrossRef]

2010 (1)

2009 (2)

C. Ding, L. Pan, and B. Lu, “Characterization of stochastic spatially and spectrally partially coherent electromagnetic pulsed beams,” N. J. Phys. 11(8), 083001 (2009).
[CrossRef]

O. Korotkova, Y. Cai, and E. Watson, “Stochastic electromagnetic beams for LIDAR systems operating through turbulent atmosphere,” Appl. Phys. B 94(4), 681–690 (2009).
[CrossRef]

2008 (3)

M. Yao, Y. Cai, H. T. Eyyuboğlu, Y. Baykal, and O. Korotkova, “Evolution of the degree of polarization of an electromagnetic Gaussian Schell-model beam in a Gaussian cavity,” Opt. Lett. 33(19), 2266–2268 (2008).
[CrossRef] [PubMed]

C. Ding and B. Lu, “Spectral shifts and spectral switches of diffracted spatially and spectrally partially coherent pulsed beams in the far field,” J. Opt. A, Pure Appl. Opt. 10(9), 095006 (2008).
[CrossRef]

V. Torres-Company, H. Lajunen, J. Lancis, and A. T. Friberg, “Ghost interference with classical partially coherent light pulses,” Phys. Rev. A 77(4), 043811 (2008).
[CrossRef]

2007 (2)

2005 (5)

O. Korotkova and E. Wolf, “Effects of linear non-image forming devices on coherence and polarization properties of random electromagnetic beams. Part I. General theory,” J. Mod. Opt. 52, 2659–2671 (2005).
[CrossRef]

O. Korotkova and E. Wolf, “Effects of linear non-image forming devices on spectra and on coherence and polarization properties ofstochastic electromagnetic beams. Part II. Examples,” J. Mod. Opt. 52, 2673–2685 (2005).
[CrossRef]

J. Lancis, V. Torres-Company, E. Silvestre, and P. Andrés, “Space-time analogy for partially coherent plane-wave-type pulses,” Opt. Lett. 30(22), 2973–2975 (2005).
[CrossRef] [PubMed]

H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, and F. Wyrowski, “Spectrally partially coherent pulse trains in dispersive media,” Opt. Commun. 255(1-3), 12–22 (2005).
[CrossRef]

H. Lajunen, P. Vahimaa, and J. Tervo, “Theory of spatially and spectrally partially coherent pulses,” J. Opt. Soc. Am. A 22(8), 1536–1545 (2005).
[CrossRef]

2004 (2)

H. Lajunen, J. Tervo, and P. Vahimaa, “Overall coherence and coherent-mode expansion of spectrally partially coherent plane-wave pulses,” J. Opt. Soc. Am. A 21(11), 2117–2123 (2004).
[CrossRef]

Y. Cai and Q. Lin, “The fractional Fourier transform for a partially coherent pulse,” J. Opt. A, Pure Appl. Opt. 6(4), 307–311 (2004).
[CrossRef]

2003 (3)

Q. Lin, L. Wang, and S. Zhu, “Partially coherent light pulse and its propagation,” Opt. Commun. 219(1-6), 65–70 (2003).
[CrossRef]

L. G. Wang, Q. Lin, H. Chen, and S. Y. Zhu, “Propagation of partially coherent pulsed beams in the spatiotemporal domain,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(5), 056613 (2003).
[CrossRef] [PubMed]

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic fields,” Phys. Lett. A 312(5-6), 263–267 (2003).
[CrossRef]

2002 (2)

P. Paakkonen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, “Partially coherent Gaussian pulses,” Opt. Commun. 204(1-6), 53–58 (2002).
[CrossRef]

Q. Lin and Y. Cai, “Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schell model beams,” Opt. Lett. 27(4), 216–218 (2002).
[CrossRef]

2001 (1)

1998 (1)

1995 (1)

Q. Lin, S. Wang, J. Alda, and E. Bernabeu, “Spatial-temporal coupling in grating-pair pulse compression system analysed by matrix optics,” Opt. Quantum Electron. 27(7), 679–692 (1995).
[CrossRef]

1993 (1)

1992 (1)

1991 (1)

1990 (2)

A. G. Kostenbauder, “Ray-pulse matrices: a rational treatment for dispersive optical systems,” IEEE J. Quantum Electron. 26(6), 1148–1157 (1990).
[CrossRef]

S. P. Dijaili, A. Dienes, and J. S. Smith, “ABCD matrices for dispersive pulse propagation,” IEEE J. Quantum Electron. 26(6), 1158–1164 (1990).
[CrossRef]

1989 (1)

O. E. Martinez, “Matrix formalism for dispersive laser cavities,” IEEE J. Quantum Electron. 25(3), 296–300 (1989).
[CrossRef]

1988 (1)

O. E. Martinez, “Matrix formalism for pulse compressors,” IEEE J. Quantum Electron. 24(12), 2530–2536 (1988).
[CrossRef]

Alda, J.

Q. Lin, S. Wang, J. Alda, and E. Bernabeu, “Spatial-temporal coupling in grating-pair pulse compression system analysed by matrix optics,” Opt. Quantum Electron. 27(7), 679–692 (1995).
[CrossRef]

Q. Lin, S. Wang, J. Alda, and E. Bernabeu, “Transformation of pulsed nonideal beams in a four-dimension domain,” Opt. Lett. 18(9), 669–671 (1993).
[CrossRef] [PubMed]

Andrés, P.

Andrès, P.

Baykal, Y.

Bélanger, P. A.

Bernabeu, E.

Q. Lin, S. Wang, J. Alda, and E. Bernabeu, “Spatial-temporal coupling in grating-pair pulse compression system analysed by matrix optics,” Opt. Quantum Electron. 27(7), 679–692 (1995).
[CrossRef]

Q. Lin, S. Wang, J. Alda, and E. Bernabeu, “Transformation of pulsed nonideal beams in a four-dimension domain,” Opt. Lett. 18(9), 669–671 (1993).
[CrossRef] [PubMed]

Borghi, R.

Cai, Y.

O. Korotkova, Y. Cai, and E. Watson, “Stochastic electromagnetic beams for LIDAR systems operating through turbulent atmosphere,” Appl. Phys. B 94(4), 681–690 (2009).
[CrossRef]

M. Yao, Y. Cai, H. T. Eyyuboğlu, Y. Baykal, and O. Korotkova, “Evolution of the degree of polarization of an electromagnetic Gaussian Schell-model beam in a Gaussian cavity,” Opt. Lett. 33(19), 2266–2268 (2008).
[CrossRef] [PubMed]

Y. Cai and Q. Lin, “The fractional Fourier transform for a partially coherent pulse,” J. Opt. A, Pure Appl. Opt. 6(4), 307–311 (2004).
[CrossRef]

Q. Lin and Y. Cai, “Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schell model beams,” Opt. Lett. 27(4), 216–218 (2002).
[CrossRef]

Chen, H.

L. G. Wang, Q. Lin, H. Chen, and S. Y. Zhu, “Propagation of partially coherent pulsed beams in the spatiotemporal domain,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(5), 056613 (2003).
[CrossRef] [PubMed]

Dienes, A.

S. P. Dijaili, A. Dienes, and J. S. Smith, “ABCD matrices for dispersive pulse propagation,” IEEE J. Quantum Electron. 26(6), 1158–1164 (1990).
[CrossRef]

Dijaili, S. P.

S. P. Dijaili, A. Dienes, and J. S. Smith, “ABCD matrices for dispersive pulse propagation,” IEEE J. Quantum Electron. 26(6), 1158–1164 (1990).
[CrossRef]

Ding, C.

C. Ding, L. Pan, and B. Lu, “Characterization of stochastic spatially and spectrally partially coherent electromagnetic pulsed beams,” N. J. Phys. 11(8), 083001 (2009).
[CrossRef]

C. Ding and B. Lu, “Spectral shifts and spectral switches of diffracted spatially and spectrally partially coherent pulsed beams in the far field,” J. Opt. A, Pure Appl. Opt. 10(9), 095006 (2008).
[CrossRef]

Eyyuboglu, H. T.

Friberg, A. T.

V. Torres-Company, H. Lajunen, J. Lancis, and A. T. Friberg, “Ghost interference with classical partially coherent light pulses,” Phys. Rev. A 77(4), 043811 (2008).
[CrossRef]

V. Torres-Company, G. Mínguez-Vega, J. Lancis, and A. T. Friberg, “Controllable generation of partially coherent light pulses with direct space-to-time pulse shaper,” Opt. Lett. 32(12), 1608–1610 (2007).
[CrossRef] [PubMed]

A. T. Friberg, H. Lajunen, and V. Torres-Company, “Spectral elementary-coherence-function representation for partially coherent light pulses,” Opt. Express 15(8), 5160–5165 (2007).
[CrossRef] [PubMed]

P. Paakkonen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, “Partially coherent Gaussian pulses,” Opt. Commun. 204(1-6), 53–58 (2002).
[CrossRef]

Gori, F.

Kempe, M.

Korotkova, O.

O. Korotkova, Y. Cai, and E. Watson, “Stochastic electromagnetic beams for LIDAR systems operating through turbulent atmosphere,” Appl. Phys. B 94(4), 681–690 (2009).
[CrossRef]

M. Yao, Y. Cai, H. T. Eyyuboğlu, Y. Baykal, and O. Korotkova, “Evolution of the degree of polarization of an electromagnetic Gaussian Schell-model beam in a Gaussian cavity,” Opt. Lett. 33(19), 2266–2268 (2008).
[CrossRef] [PubMed]

O. Korotkova and E. Wolf, “Effects of linear non-image forming devices on coherence and polarization properties of random electromagnetic beams. Part I. General theory,” J. Mod. Opt. 52, 2659–2671 (2005).
[CrossRef]

O. Korotkova and E. Wolf, “Effects of linear non-image forming devices on spectra and on coherence and polarization properties ofstochastic electromagnetic beams. Part II. Examples,” J. Mod. Opt. 52, 2673–2685 (2005).
[CrossRef]

Kostenbauder, A. G.

A. G. Kostenbauder, “Ray-pulse matrices: a rational treatment for dispersive optical systems,” IEEE J. Quantum Electron. 26(6), 1148–1157 (1990).
[CrossRef]

Lajunen, H.

Lancis, J.

Lin, Q.

Y. Cai and Q. Lin, “The fractional Fourier transform for a partially coherent pulse,” J. Opt. A, Pure Appl. Opt. 6(4), 307–311 (2004).
[CrossRef]

L. G. Wang, Q. Lin, H. Chen, and S. Y. Zhu, “Propagation of partially coherent pulsed beams in the spatiotemporal domain,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(5), 056613 (2003).
[CrossRef] [PubMed]

Q. Lin, L. Wang, and S. Zhu, “Partially coherent light pulse and its propagation,” Opt. Commun. 219(1-6), 65–70 (2003).
[CrossRef]

Q. Lin and Y. Cai, “Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schell model beams,” Opt. Lett. 27(4), 216–218 (2002).
[CrossRef]

Q. Lin, S. Wang, J. Alda, and E. Bernabeu, “Spatial-temporal coupling in grating-pair pulse compression system analysed by matrix optics,” Opt. Quantum Electron. 27(7), 679–692 (1995).
[CrossRef]

Q. Lin, S. Wang, J. Alda, and E. Bernabeu, “Transformation of pulsed nonideal beams in a four-dimension domain,” Opt. Lett. 18(9), 669–671 (1993).
[CrossRef] [PubMed]

Lu, B.

C. Ding, L. Pan, and B. Lu, “Characterization of stochastic spatially and spectrally partially coherent electromagnetic pulsed beams,” N. J. Phys. 11(8), 083001 (2009).
[CrossRef]

C. Ding and B. Lu, “Spectral shifts and spectral switches of diffracted spatially and spectrally partially coherent pulsed beams in the far field,” J. Opt. A, Pure Appl. Opt. 10(9), 095006 (2008).
[CrossRef]

Martinez, O. E.

O. E. Martinez, “Matrix formalism for dispersive laser cavities,” IEEE J. Quantum Electron. 25(3), 296–300 (1989).
[CrossRef]

O. E. Martinez, “Matrix formalism for pulse compressors,” IEEE J. Quantum Electron. 24(12), 2530–2536 (1988).
[CrossRef]

Mínguez-Vega, G.

Paakkonen, P.

P. Paakkonen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, “Partially coherent Gaussian pulses,” Opt. Commun. 204(1-6), 53–58 (2002).
[CrossRef]

Pan, L.

C. Ding, L. Pan, and B. Lu, “Characterization of stochastic spatially and spectrally partially coherent electromagnetic pulsed beams,” N. J. Phys. 11(8), 083001 (2009).
[CrossRef]

Piquero, G.

Rudolph, W.

Santarsiero, M.

Silvestre, E.

Smith, J. S.

S. P. Dijaili, A. Dienes, and J. S. Smith, “ABCD matrices for dispersive pulse propagation,” IEEE J. Quantum Electron. 26(6), 1158–1164 (1990).
[CrossRef]

Stamm, U.

Tervo, J.

Torres-Company, V.

Turunen, J.

H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, and F. Wyrowski, “Spectrally partially coherent pulse trains in dispersive media,” Opt. Commun. 255(1-3), 12–22 (2005).
[CrossRef]

P. Paakkonen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, “Partially coherent Gaussian pulses,” Opt. Commun. 204(1-6), 53–58 (2002).
[CrossRef]

Vahimaa, P.

H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, and F. Wyrowski, “Spectrally partially coherent pulse trains in dispersive media,” Opt. Commun. 255(1-3), 12–22 (2005).
[CrossRef]

H. Lajunen, P. Vahimaa, and J. Tervo, “Theory of spatially and spectrally partially coherent pulses,” J. Opt. Soc. Am. A 22(8), 1536–1545 (2005).
[CrossRef]

H. Lajunen, J. Tervo, and P. Vahimaa, “Overall coherence and coherent-mode expansion of spectrally partially coherent plane-wave pulses,” J. Opt. Soc. Am. A 21(11), 2117–2123 (2004).
[CrossRef]

P. Paakkonen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, “Partially coherent Gaussian pulses,” Opt. Commun. 204(1-6), 53–58 (2002).
[CrossRef]

Wang, L.

Q. Lin, L. Wang, and S. Zhu, “Partially coherent light pulse and its propagation,” Opt. Commun. 219(1-6), 65–70 (2003).
[CrossRef]

Wang, L. G.

L. G. Wang, Q. Lin, H. Chen, and S. Y. Zhu, “Propagation of partially coherent pulsed beams in the spatiotemporal domain,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(5), 056613 (2003).
[CrossRef] [PubMed]

Wang, S.

Q. Lin, S. Wang, J. Alda, and E. Bernabeu, “Spatial-temporal coupling in grating-pair pulse compression system analysed by matrix optics,” Opt. Quantum Electron. 27(7), 679–692 (1995).
[CrossRef]

Q. Lin, S. Wang, J. Alda, and E. Bernabeu, “Transformation of pulsed nonideal beams in a four-dimension domain,” Opt. Lett. 18(9), 669–671 (1993).
[CrossRef] [PubMed]

Watson, E.

O. Korotkova, Y. Cai, and E. Watson, “Stochastic electromagnetic beams for LIDAR systems operating through turbulent atmosphere,” Appl. Phys. B 94(4), 681–690 (2009).
[CrossRef]

Wilhelmi, B.

Wolf, E.

O. Korotkova and E. Wolf, “Effects of linear non-image forming devices on spectra and on coherence and polarization properties ofstochastic electromagnetic beams. Part II. Examples,” J. Mod. Opt. 52, 2673–2685 (2005).
[CrossRef]

O. Korotkova and E. Wolf, “Effects of linear non-image forming devices on coherence and polarization properties of random electromagnetic beams. Part I. General theory,” J. Mod. Opt. 52, 2659–2671 (2005).
[CrossRef]

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic fields,” Phys. Lett. A 312(5-6), 263–267 (2003).
[CrossRef]

Wyrowski, F.

H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, and F. Wyrowski, “Spectrally partially coherent pulse trains in dispersive media,” Opt. Commun. 255(1-3), 12–22 (2005).
[CrossRef]

P. Paakkonen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, “Partially coherent Gaussian pulses,” Opt. Commun. 204(1-6), 53–58 (2002).
[CrossRef]

Yao, M.

Zhu, S.

Q. Lin, L. Wang, and S. Zhu, “Partially coherent light pulse and its propagation,” Opt. Commun. 219(1-6), 65–70 (2003).
[CrossRef]

Zhu, S. Y.

L. G. Wang, Q. Lin, H. Chen, and S. Y. Zhu, “Propagation of partially coherent pulsed beams in the spatiotemporal domain,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(5), 056613 (2003).
[CrossRef] [PubMed]

Appl. Phys. B (1)

O. Korotkova, Y. Cai, and E. Watson, “Stochastic electromagnetic beams for LIDAR systems operating through turbulent atmosphere,” Appl. Phys. B 94(4), 681–690 (2009).
[CrossRef]

IEEE J. Quantum Electron. (4)

O. E. Martinez, “Matrix formalism for pulse compressors,” IEEE J. Quantum Electron. 24(12), 2530–2536 (1988).
[CrossRef]

O. E. Martinez, “Matrix formalism for dispersive laser cavities,” IEEE J. Quantum Electron. 25(3), 296–300 (1989).
[CrossRef]

A. G. Kostenbauder, “Ray-pulse matrices: a rational treatment for dispersive optical systems,” IEEE J. Quantum Electron. 26(6), 1148–1157 (1990).
[CrossRef]

S. P. Dijaili, A. Dienes, and J. S. Smith, “ABCD matrices for dispersive pulse propagation,” IEEE J. Quantum Electron. 26(6), 1158–1164 (1990).
[CrossRef]

J. Mod. Opt. (2)

O. Korotkova and E. Wolf, “Effects of linear non-image forming devices on coherence and polarization properties of random electromagnetic beams. Part I. General theory,” J. Mod. Opt. 52, 2659–2671 (2005).
[CrossRef]

O. Korotkova and E. Wolf, “Effects of linear non-image forming devices on spectra and on coherence and polarization properties ofstochastic electromagnetic beams. Part II. Examples,” J. Mod. Opt. 52, 2673–2685 (2005).
[CrossRef]

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

Y. Cai and Q. Lin, “The fractional Fourier transform for a partially coherent pulse,” J. Opt. A, Pure Appl. Opt. 6(4), 307–311 (2004).
[CrossRef]

C. Ding and B. Lu, “Spectral shifts and spectral switches of diffracted spatially and spectrally partially coherent pulsed beams in the far field,” J. Opt. A, Pure Appl. Opt. 10(9), 095006 (2008).
[CrossRef]

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

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

N. J. Phys. (1)

C. Ding, L. Pan, and B. Lu, “Characterization of stochastic spatially and spectrally partially coherent electromagnetic pulsed beams,” N. J. Phys. 11(8), 083001 (2009).
[CrossRef]

Opt. Commun. (3)

H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, and F. Wyrowski, “Spectrally partially coherent pulse trains in dispersive media,” Opt. Commun. 255(1-3), 12–22 (2005).
[CrossRef]

P. Paakkonen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, “Partially coherent Gaussian pulses,” Opt. Commun. 204(1-6), 53–58 (2002).
[CrossRef]

Q. Lin, L. Wang, and S. Zhu, “Partially coherent light pulse and its propagation,” Opt. Commun. 219(1-6), 65–70 (2003).
[CrossRef]

Opt. Express (2)

Opt. Lett. (7)

Opt. Quantum Electron. (1)

Q. Lin, S. Wang, J. Alda, and E. Bernabeu, “Spatial-temporal coupling in grating-pair pulse compression system analysed by matrix optics,” Opt. Quantum Electron. 27(7), 679–692 (1995).
[CrossRef]

Phys. Lett. A (1)

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic fields,” Phys. Lett. A 312(5-6), 263–267 (2003).
[CrossRef]

Phys. Rev. A (1)

V. Torres-Company, H. Lajunen, J. Lancis, and A. T. Friberg, “Ghost interference with classical partially coherent light pulses,” Phys. Rev. A 77(4), 043811 (2008).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

L. G. Wang, Q. Lin, H. Chen, and S. Y. Zhu, “Propagation of partially coherent pulsed beams in the spatiotemporal domain,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(5), 056613 (2003).
[CrossRef] [PubMed]

Other (3)

S. M. Wang and D. M. Zhao, Matrix Optics, (Springer, 2000).

For the collection of original papers by R. C. Jones see W. Swindel, Polarized light, (Dowden, Hutchinson & Ross, (Stroudsburg, Pennsylvania, 1975).

H. Mueller, “The foundations of optics,” J. Opt. Soc. Am. 38, 661–661 (1948); for account of the Mueller’s theory see also E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, Inc., New York, 1993). Chap. 5.

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Figures (11)

Fig. 1
Fig. 1

Propagation scheme for a pulse beam through dispersive optical system and free space.

Fig. 2
Fig. 2

Illustrating notation for reflection of a pulse from a reflecting grating.

Fig. 3
Fig. 3

Dependence of the degree of polarization of a REMPB on the propagation distance z and the pulse duration σ t 0 for different diffraction orders m with σ I 0 = 1 m m , δ I 0 x x = 1 m m , δ t 0 = 2 p s .

Fig. 6
Fig. 6

Dependence of the degree of polarization P on the propagation distance z and the r.m.s. width of spatial degree of coherence δ I 0 x x for different diffraction orders m with σ I 0 = 1 m m , σ t 0 = 2 p s , δ t 0 = 2 p s .

Fig. 4
Fig. 4

Dependence of the degree of polarization P of a REMPB on the propagation distance z and the r.m.s. width σ I 0 of the intensity for different diffraction orders m with δ I 0 x x = 1 m m , σ t 0 = 2 p s , δ t 0 = 2 p s .

Fig. 5
Fig. 5

Dependence of the degree of polarization P on the propagation distance z and the r.m.s. width of temporal degree of coherence δ t 0 for different diffraction orders m with σ I 0 = 1 m m , δ I 0 x x = 1 m m , σ t 0 = 2 p s .

Fig. 7
Fig. 7

Dependence of the degree of polarization P on the propagation distance z for different diffraction orders m with σ I 0 = 1 m m , δ I 0 x x = 1 m m , σ t 0 = 2 p s , δ t 0 = 2 p s .

Fig. 11
Fig. 11

Dependence of the degree of polarization P on the r.m.s. width of spatial degree of coherence δ I 0 x x for different diffraction orders m at z = 200 m with σ I 0 = 1 m m , σ t 0 = 2 p s , δ t 0 = 2 p s .

Fig. 9
Fig. 9

Dependence of the degree of polarization P on the r.m.s. width σ I 0 of the intensity for different diffraction orders m at z = 200m with δ I 0 x x = 1 m m , σ t 0 = 2 p s , δ t 0 = 2 p s .

Fig. 8
Fig. 8

Dependence of the degree of polarization P on the pulse duration σ t 0 for different diffraction orders m at z = 200m with σ I 0 = 1 m m , δ I 0 x x = 1 m m , δ t 0 = 2 p s .

Fig. 10
Fig. 10

Dependence of the degree of polarization P on the r.m.s. width of temporal degree of coherence δ t 0 for different diffraction orders m at z = 200m with σ I 0 = 1 m m , δ I 0 x x = 1 m m , δ t 0 = 2 p s .

Equations (22)

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Γ 0 α β ( r 01 , τ 01 ; r 02 , τ 02 ) = A α A β B α β exp [ r 01 2 + r 02 2 4 σ I 0 α β 2 ( r 01 r 02 ) 2 2 δ I 0 α β 2 ]                                     × exp [ τ 01 2 + τ 02 2 2 σ τ 0 α β 2 ( τ 01 τ 02 ) 2 2 δ τ 0 α β 2 ] exp [ i ω 0 ( τ 01 τ 02 ) ] ,
Γ 0 α β ( r ¯ 0 ) = A α A β B α β exp [ i k 0 2 r ¯ 0 T Q ¯ 0 α β 1 r ¯ 0 ] exp [ i ω 0 ( τ 01 τ 02 ) ] ,    ( α = x , y ; β = x , y )
Q ¯ 0 α β 1 = ( i k 0 ( 1 2 σ I 0 α β 2 + δ I 0 α β 2 ) I 0 21 i k 0 δ I 0 α β 2 I 0 21 0 12 i k 0 ( σ τ 0 α β 2 + δ τ 0 α β 2 ) 0 12 i k 0 δ τ 0 α β 2 i k 0 δ I 0 α β 2 I 0 21 i k 0 ( 1 2 σ I 0 α β 2 + δ I 0 α β 2 ) I 0 21 0 12 i k 0 δ τ 0 α β 2 0 12 i k 0 ( σ τ 0 α β 2 + δ τ 0 α β 2 ) )
Γ 1 α β ( r ¯ 1 ) = A α A β B α β [ det ( A ¯ 1 + B ¯ 1 Q ¯ 0 α β 1 ) ] 1 / 2 exp [ i k 0 2 r ¯ 1 T Q ¯ 1 α β 1 r ¯ 1 ] ,
Q ¯ 1 α β 1 = ( C ¯ 1 + D ¯ 1 Q ¯ 0 α β 1 ) ( A ¯ 1 + B ¯ 1 Q ¯ 0 α β 1 ) 1 .
Q ¯ 1 α β 1 = ( q 11 q 12 q 13 q 14 q 15 q 16 q 21 q 22 q 23 q 24 q 25 q 26 q 31 q 32 q 33 q 34 q 35 q 36 q 41 q 42 q 43 q 44 q 45 q 46 q 51 q 52 q 53 q 54 q 55 q 56 q 61 q 62 q 63 q 64 q 65 q 66 ) .
A ¯ 1 = ( A ˜ 11 0 33 0 33 A ˜ 12 ) ,   B ¯ 1 = ( B ˜ 11 0 33 0 33 B ˜ 12 * ) ,   C ¯ 1 = ( C ˜ 11 0 33 0 33 C ˜ 12 * ) ,   D 1 = ( D ˜ 11 0 33 0 33 D ˜ 12 )
Γ 2 α β ( r ¯ 2 ) = A α A β B α β [ det ( A ¯ 1 + B ¯ 1 Q ¯ 0 α β 1 ) ] 1 / 2 [ det ( A ¯ 2 + B ¯ 2 Q ¯ 1 α β 1 ) ] 1 / 2 exp [ i k 0 2 r ¯ 2 T Q ¯ 2 α β 1 r ¯ 2 ] ,
A ˜ 21 = D ˜ 21 = ( 1 0 0 0 1 0 0 0 1 ) ,   B ˜ 21 = ( z 0 0 0 z 0 0 0 1 ) ,   C ˜ 21 = ( 0 0 0 0 0 0 0 0 0 ) .
W j α β ( r j 1 , ω 1 ; r j 2 , ω 2 ) = 1 2 π + + Γ j α β ( r j 1 , τ j 1 ; r j 2 , τ j 2 ) exp [ ( ω 1 τ j 1 ω 2 τ j 2 ) ] d τ j 1 d τ j 2 ,
P j ω ( r j , ω ) = 1 4 D e t [ W j ( r j , ω , r j , ω ) ] { T r [ W j ( r j , ω , r j , ω ) ] } 2 ,
A ˜ 11 = ( sin ϕ sin ψ 0 0 0 1 0 cos ψ cos ϕ sin ψ 0 1 ) ,    B ˜ 11 = C ˜ 11 = 0 ,    D ˜ 11 = ( sin ψ sin ϕ 0 cos ψ cos ϕ sin ϕ 0 1 0 0 0 1 ) ,
d G ( cos ϕ cos ψ ) = m λ 0 ,
Γ 1 α β ( r ¯ 1 ) = A α A β B α β sin ψ sin ϕ exp [ i k 0 2 r ¯ 1 T Q ¯ 1 α β 1 r ¯ 1 ] ,
Q ¯ 1 α β 1 = ( q 11 0 q 13 q 14 0 q 16 0 q 22 0 0 q 25 0 q 31 0 q 33 q 34 0 q 36 q 41 0 q 43 q 44 0 q 46 0 q 52 0 0 q 55 0 q 61 0 q 63 q 64 0 q 66 ) .
q 11 = q 44 = i g 1 2 2 k 0 ( σ I 0 α β 2 + 2 δ I 0 α β 2 ) i g 2 2 k 0 ( σ τ 0 α β 2 + δ τ 0 α β 2 ) , q 13 = q 31 = q 46 = q 64 = i g 2 k 0 ( σ τ 0 α β 2 + δ τ 0 α β 2 ) , q 14 = q 41 = i k 0 ( g 1 2 δ I 0 α β 2 + g 2 2 δ τ 0 α β 2 ) , q 16 = q 34 = q 43 = q 61 = i g 2 k 0 δ τ 0 α β 2 , q 22 = q 55 = i 2 k 0 ( σ I 0 α β 2 + 2 δ I 0 α β 2 ) , q 25 = q 52 = i k 0 δ I 0 α β 2 , q 33 = q 66 = i k 0 ( σ τ 0 α β 2 + δ τ 0 α β 2 ) , q 36 = q 63 = i k 0 δ τ 0 α β 2 .
Γ 2 α β = A α A β B α β g 1 [ 1 + z 2 4 k 0 2 σ I 0 α β 2 ( 4 δ I 0 α β 2 + σ I 0 α β 2 ) ] 1 / 2            × { 1 + z 2 4 k 0 2 ( g 1 2 σ I 0 α β 2 + 2 g 2 2 σ τ 0 α β 2 ) [ g 1 2 ( 4 δ I 0 α β 2 + σ I 0 α β 2 ) + 2 g 2 2 ( 2 δ τ 0 α β 2 + σ τ 0 α β 2 ) ] } 1 / 2 ,
P τ ( z ) = 1 4 D e t ( Γ 2 ) T r ( Γ 2 ) = | Γ 2 x x Γ 2 y y Γ 2 x x + Γ 2 y y | = | A x 2 Δ x x A y 2 Δ y y A x 2 Δ x x + A y 2 Δ y y |
Δ α β = [ 1 + z 2 4 k 0 2 σ I 0 α β 2 ( 4 δ I 0 α β 2 + σ I 0 α β 2 ) ] 1 / 2        × { 1 + z 2 4 k 0 2 ( g 1 2 σ I 0 α β 2 + 2 g 2 2 σ τ 0 α β 2 ) [ g 1 2 ( 4 δ I 0 α β 2 + σ I 0 α β 2 ) + 2 g 2 2 ( 2 δ τ 0 α β 2 + σ τ 0 α β 2 ) ] } 1 / 2 .
Δ α β = [ 1 + z 2 4 k 0 2 σ I 0 α β 2 ( 4 δ I 0 α β 2 + σ I 0 α β 2 ) ] 1 .
lim z P τ ( z ) = | A x 2 Ω x x A y 2 Ω y y A x 2 Ω x x + A y 2 Ω y y | ,
Ω α β = { σ I 0 α β 2 ( 4 δ I 0 α β 2 + σ I 0 α β 2 ) ( g 1 2 σ I 0 α β 2 + 2 g 2 2 σ τ 0 α β 2 ) } 1 / 2           × { [ g 1 2 ( 4 δ I 0 α β 2 + σ I 0 α β 2 ) + 2 g 2 2 ( 2 δ τ 0 α β 2 + σ τ 0 α β 2 ) ] } 1 / 2

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