Abstract

A study of the changes in the spectrum and of the time intensity of the diffraction pattern of nonstationary light sources, started earlier [ J. Opt. Soc. Am. B 12, 1519 ( 1995)] is completed. The evolution of the spectrum for the off-axis points of the diffraction pattern from a source with a Gaussian spectrum is discussed, and the reason for the red and blue shifts of the spectral maximum is found analytically. The maximum values of the shifts are estimated. It is shown that the normalized spatial distribution of energy of the diffraction pattern from a time Gaussian-shaped pulsed source coincides exactly with the normalized spatial distribution of intensity from a stationary source with Gaussian spectral density and the same bandwidth. The influence of the spectral changes on the time intensity of the diffraction pattern for the Gaussian-shaped pulsed source is also discussed. The values of the diffraction angle are calculated when a slit splits the Gaussian-shaped pulse into two separate pulses. Moreover, it is shown that from these values of the diffraction angle two separate pulses can recombine.

© 1996 Optical Society of America

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References

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  1. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).
  2. L. Mandel, J. Opt. Soc. Am. 51, 1342 (1961).
    [CrossRef]
  3. L. Mandel and E. Wolf, J. Soc. Am. 66, 529 (1976).
  4. E. Wolf, Phys. Rev. Lett. 56, 1370 (1986).
    [CrossRef] [PubMed]
  5. E. Wolf, Opt. Commun. 62, 12 (1987).
    [CrossRef]
  6. E. Wolf, Nature (London) 326, 363 (1987).
    [CrossRef]
  7. E. Wolf, Phys. Rev. Lett. 58, 2646 (1987).
    [CrossRef] [PubMed]
  8. M. F. Bocko, D. H. Douglas, and R. S. Knox, Phys. Rev. Lett. 58, 2649 (1987).
    [CrossRef] [PubMed]
  9. G. M. Morris and D. Faklis, Opt. Commun. 62, 5 (1987).
    [CrossRef]
  10. Z. Dacic and E. Wolf, J. Opt. Soc. Am. A 5, 1118 (1988).
    [CrossRef]
  11. D. Faklis and G. M. Morris, Opt. Lett. 13, 4 (1988).
    [CrossRef] [PubMed]
  12. F. Gori, G. Guattari, C. Palma, and C. Padovani, Opt. Commun. 67, 1 (1988).
    [CrossRef]
  13. A. Gamliel and E. Wolf, Opt. Commun. 65, 91 (1988).
    [CrossRef]
  14. E. Wolf, F. T. Foley, and F. Gori, J. Opt. Soc. Am. A 6, 1142 (1989).
    [CrossRef]
  15. G. Indebetouw, J. Mod. Opt. 36, 251 (1989).
    [CrossRef]
  16. H. C. Kandpal, J. C. Vaishya, and K. C. Joshi, Opt. Commun. 73, 169 (1989).
    [CrossRef]
  17. A. Lagendijk, Phys. Lett. A 147, 389 (1990).
    [CrossRef]
  18. T. Foley, Opt. Commun. 75, 347 (1990).
    [CrossRef]
  19. A. Gamliel, J. Opt. Soc. Am. A 7, 1591 (1990).
    [CrossRef]
  20. T. S. McKechnie, J. Opt. Soc. Am. A 8, 339 (1991).
    [CrossRef]
  21. T. Foley, J. Opt. Soc. Am. A 8, 1099 (1991).
    [CrossRef]
  22. B. Cairns and E. Wolf, J. Opt. Soc. Am. A 8, 1922 (1991).
    [CrossRef]
  23. D. F. V. James and E. Wolf, Opt. Commun. 81, 150 (1991).
    [CrossRef]
  24. D. F. V. James and E. Wolf, Phys. Lett. A 157, 6 (1991).
    [CrossRef]
  25. M. Santarsiero and F. Gori, Phys. Lett. A 167, 123 (1992).
    [CrossRef]
  26. W. Wang, R. Simon, and E. Wolf, J. Opt. Soc. Am. A 9, 287 (1992).
    [CrossRef]
  27. H. C. Kandpal, K. Saxena, D. S. Mehta, J. C. Vaishya, and K. C. Joshi, Opt. Commun. 99, 157 (1993).
    [CrossRef]
  28. G. S. Agarwal and D. F. V. James, J. Mod. Opt. 40, 1431 (1993).
    [CrossRef]
  29. G. Hazak and R. Zamir, J. Mod. Opt. 40, 1653 (1993).
    [CrossRef]
  30. W. H. Carter, J. Mod. Opt. 40, 2433 (1993).
    [CrossRef]
  31. D. N. Rao and V. N. Kumar, J. Mod. Opt. 41, 1757 (1994).
    [CrossRef]
  32. H. C. Kandpal, J. C. Vaishya, K. Saxena, D. S. Mehta, and K. C. Joshi, J. Mod. Opt. 42, 455 (1995).
    [CrossRef]
  33. M. Bertolotti, A. Ferrari, and L. Sereda, J. Opt. Soc. Am. B 12, 1519 (1995).
    [CrossRef]
  34. M. Bertolotti, A. Ferrari, and L. Sereda, J. Opt. Soc. Am. B 12, 341 (1995).
    [CrossRef]
  35. E. B. Treacy, J. Quantum Electron. QE-5, 454 (1969).
    [CrossRef]
  36. N. H. Schiller and R. R. Alfano, Opt. Commun. 35, 451 (1980).
    [CrossRef]
  37. C. V. Shank, R. L. Fork, R. H. Stolen, and W. J. Tomlinson, Appl. Phys. Lett. 40, 761 (1982).
    [CrossRef]
  38. R. Gase and M. Shubert, Opt. Acta 29, 1331 (1982).
    [CrossRef]
  39. O. E. Martinez, Opt. Commun. 59, 229 (1986).
    [CrossRef]
  40. R. W. Ziolkowski and J. B. Judkins, J. Opt. Soc. Am. A 9, 2021 (1992).
    [CrossRef]
  41. C. Hirlimann and J.-F. Morhange, Appl. Opt. 31, 3263 (1992).
    [CrossRef] [PubMed]
  42. M. Kàlal, Proc. SPIE1983, 686 (1993).
  43. Zs. Bor and A. P. Kovàcs, Proc. SPIE 1983, 524 (1993).
  44. M. R. Perrone, J. Mod. Opt. 40, 2135 (1993).
    [CrossRef]
  45. E. Fiordilino and V. Miceli, J. Mod. Opt. 41, 1415 (1994).
    [CrossRef]
  46. A relation among the quantities dIQ(r, ω), IQ′(r, ω) (stationary wave field), and IQ″(r, ω) (nonstationary wave field) is considered in Appendix A of Ref. 33.
  47. G. Korn and T. Korn, Mathematical Handbook (McGraw-Hill, New York, 1968).

1995 (3)

1994 (2)

D. N. Rao and V. N. Kumar, J. Mod. Opt. 41, 1757 (1994).
[CrossRef]

E. Fiordilino and V. Miceli, J. Mod. Opt. 41, 1415 (1994).
[CrossRef]

1993 (6)

Zs. Bor and A. P. Kovàcs, Proc. SPIE 1983, 524 (1993).

M. R. Perrone, J. Mod. Opt. 40, 2135 (1993).
[CrossRef]

H. C. Kandpal, K. Saxena, D. S. Mehta, J. C. Vaishya, and K. C. Joshi, Opt. Commun. 99, 157 (1993).
[CrossRef]

G. S. Agarwal and D. F. V. James, J. Mod. Opt. 40, 1431 (1993).
[CrossRef]

G. Hazak and R. Zamir, J. Mod. Opt. 40, 1653 (1993).
[CrossRef]

W. H. Carter, J. Mod. Opt. 40, 2433 (1993).
[CrossRef]

1992 (4)

1991 (5)

1990 (3)

A. Lagendijk, Phys. Lett. A 147, 389 (1990).
[CrossRef]

T. Foley, Opt. Commun. 75, 347 (1990).
[CrossRef]

A. Gamliel, J. Opt. Soc. Am. A 7, 1591 (1990).
[CrossRef]

1989 (3)

E. Wolf, F. T. Foley, and F. Gori, J. Opt. Soc. Am. A 6, 1142 (1989).
[CrossRef]

G. Indebetouw, J. Mod. Opt. 36, 251 (1989).
[CrossRef]

H. C. Kandpal, J. C. Vaishya, and K. C. Joshi, Opt. Commun. 73, 169 (1989).
[CrossRef]

1988 (4)

Z. Dacic and E. Wolf, J. Opt. Soc. Am. A 5, 1118 (1988).
[CrossRef]

D. Faklis and G. M. Morris, Opt. Lett. 13, 4 (1988).
[CrossRef] [PubMed]

F. Gori, G. Guattari, C. Palma, and C. Padovani, Opt. Commun. 67, 1 (1988).
[CrossRef]

A. Gamliel and E. Wolf, Opt. Commun. 65, 91 (1988).
[CrossRef]

1987 (5)

E. Wolf, Opt. Commun. 62, 12 (1987).
[CrossRef]

E. Wolf, Nature (London) 326, 363 (1987).
[CrossRef]

E. Wolf, Phys. Rev. Lett. 58, 2646 (1987).
[CrossRef] [PubMed]

M. F. Bocko, D. H. Douglas, and R. S. Knox, Phys. Rev. Lett. 58, 2649 (1987).
[CrossRef] [PubMed]

G. M. Morris and D. Faklis, Opt. Commun. 62, 5 (1987).
[CrossRef]

1986 (2)

E. Wolf, Phys. Rev. Lett. 56, 1370 (1986).
[CrossRef] [PubMed]

O. E. Martinez, Opt. Commun. 59, 229 (1986).
[CrossRef]

1982 (2)

C. V. Shank, R. L. Fork, R. H. Stolen, and W. J. Tomlinson, Appl. Phys. Lett. 40, 761 (1982).
[CrossRef]

R. Gase and M. Shubert, Opt. Acta 29, 1331 (1982).
[CrossRef]

1980 (1)

N. H. Schiller and R. R. Alfano, Opt. Commun. 35, 451 (1980).
[CrossRef]

1976 (1)

L. Mandel and E. Wolf, J. Soc. Am. 66, 529 (1976).

1969 (1)

E. B. Treacy, J. Quantum Electron. QE-5, 454 (1969).
[CrossRef]

1961 (1)

Agarwal, G. S.

G. S. Agarwal and D. F. V. James, J. Mod. Opt. 40, 1431 (1993).
[CrossRef]

Alfano, R. R.

N. H. Schiller and R. R. Alfano, Opt. Commun. 35, 451 (1980).
[CrossRef]

Bertolotti, M.

Bocko, M. F.

M. F. Bocko, D. H. Douglas, and R. S. Knox, Phys. Rev. Lett. 58, 2649 (1987).
[CrossRef] [PubMed]

Bor, Zs.

Zs. Bor and A. P. Kovàcs, Proc. SPIE 1983, 524 (1993).

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

Cairns, B.

Carter, W. H.

W. H. Carter, J. Mod. Opt. 40, 2433 (1993).
[CrossRef]

Dacic, Z.

Douglas, D. H.

M. F. Bocko, D. H. Douglas, and R. S. Knox, Phys. Rev. Lett. 58, 2649 (1987).
[CrossRef] [PubMed]

Faklis, D.

D. Faklis and G. M. Morris, Opt. Lett. 13, 4 (1988).
[CrossRef] [PubMed]

G. M. Morris and D. Faklis, Opt. Commun. 62, 5 (1987).
[CrossRef]

Ferrari, A.

Fiordilino, E.

E. Fiordilino and V. Miceli, J. Mod. Opt. 41, 1415 (1994).
[CrossRef]

Foley, F. T.

Foley, T.

Fork, R. L.

C. V. Shank, R. L. Fork, R. H. Stolen, and W. J. Tomlinson, Appl. Phys. Lett. 40, 761 (1982).
[CrossRef]

Gamliel, A.

A. Gamliel, J. Opt. Soc. Am. A 7, 1591 (1990).
[CrossRef]

A. Gamliel and E. Wolf, Opt. Commun. 65, 91 (1988).
[CrossRef]

Gase, R.

R. Gase and M. Shubert, Opt. Acta 29, 1331 (1982).
[CrossRef]

Gori, F.

M. Santarsiero and F. Gori, Phys. Lett. A 167, 123 (1992).
[CrossRef]

E. Wolf, F. T. Foley, and F. Gori, J. Opt. Soc. Am. A 6, 1142 (1989).
[CrossRef]

F. Gori, G. Guattari, C. Palma, and C. Padovani, Opt. Commun. 67, 1 (1988).
[CrossRef]

Guattari, G.

F. Gori, G. Guattari, C. Palma, and C. Padovani, Opt. Commun. 67, 1 (1988).
[CrossRef]

Hazak, G.

G. Hazak and R. Zamir, J. Mod. Opt. 40, 1653 (1993).
[CrossRef]

Hirlimann, C.

Indebetouw, G.

G. Indebetouw, J. Mod. Opt. 36, 251 (1989).
[CrossRef]

James, D. F. V.

G. S. Agarwal and D. F. V. James, J. Mod. Opt. 40, 1431 (1993).
[CrossRef]

D. F. V. James and E. Wolf, Opt. Commun. 81, 150 (1991).
[CrossRef]

D. F. V. James and E. Wolf, Phys. Lett. A 157, 6 (1991).
[CrossRef]

Joshi, K. C.

H. C. Kandpal, J. C. Vaishya, K. Saxena, D. S. Mehta, and K. C. Joshi, J. Mod. Opt. 42, 455 (1995).
[CrossRef]

H. C. Kandpal, K. Saxena, D. S. Mehta, J. C. Vaishya, and K. C. Joshi, Opt. Commun. 99, 157 (1993).
[CrossRef]

H. C. Kandpal, J. C. Vaishya, and K. C. Joshi, Opt. Commun. 73, 169 (1989).
[CrossRef]

Judkins, J. B.

Kàlal, M.

M. Kàlal, Proc. SPIE1983, 686 (1993).

Kandpal, H. C.

H. C. Kandpal, J. C. Vaishya, K. Saxena, D. S. Mehta, and K. C. Joshi, J. Mod. Opt. 42, 455 (1995).
[CrossRef]

H. C. Kandpal, K. Saxena, D. S. Mehta, J. C. Vaishya, and K. C. Joshi, Opt. Commun. 99, 157 (1993).
[CrossRef]

H. C. Kandpal, J. C. Vaishya, and K. C. Joshi, Opt. Commun. 73, 169 (1989).
[CrossRef]

Knox, R. S.

M. F. Bocko, D. H. Douglas, and R. S. Knox, Phys. Rev. Lett. 58, 2649 (1987).
[CrossRef] [PubMed]

Korn, G.

G. Korn and T. Korn, Mathematical Handbook (McGraw-Hill, New York, 1968).

Korn, T.

G. Korn and T. Korn, Mathematical Handbook (McGraw-Hill, New York, 1968).

Kovàcs, A. P.

Zs. Bor and A. P. Kovàcs, Proc. SPIE 1983, 524 (1993).

Kumar, V. N.

D. N. Rao and V. N. Kumar, J. Mod. Opt. 41, 1757 (1994).
[CrossRef]

Lagendijk, A.

A. Lagendijk, Phys. Lett. A 147, 389 (1990).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, J. Soc. Am. 66, 529 (1976).

L. Mandel, J. Opt. Soc. Am. 51, 1342 (1961).
[CrossRef]

Martinez, O. E.

O. E. Martinez, Opt. Commun. 59, 229 (1986).
[CrossRef]

McKechnie, T. S.

Mehta, D. S.

H. C. Kandpal, J. C. Vaishya, K. Saxena, D. S. Mehta, and K. C. Joshi, J. Mod. Opt. 42, 455 (1995).
[CrossRef]

H. C. Kandpal, K. Saxena, D. S. Mehta, J. C. Vaishya, and K. C. Joshi, Opt. Commun. 99, 157 (1993).
[CrossRef]

Miceli, V.

E. Fiordilino and V. Miceli, J. Mod. Opt. 41, 1415 (1994).
[CrossRef]

Morhange, J.-F.

Morris, G. M.

D. Faklis and G. M. Morris, Opt. Lett. 13, 4 (1988).
[CrossRef] [PubMed]

G. M. Morris and D. Faklis, Opt. Commun. 62, 5 (1987).
[CrossRef]

Padovani, C.

F. Gori, G. Guattari, C. Palma, and C. Padovani, Opt. Commun. 67, 1 (1988).
[CrossRef]

Palma, C.

F. Gori, G. Guattari, C. Palma, and C. Padovani, Opt. Commun. 67, 1 (1988).
[CrossRef]

Perrone, M. R.

M. R. Perrone, J. Mod. Opt. 40, 2135 (1993).
[CrossRef]

Rao, D. N.

D. N. Rao and V. N. Kumar, J. Mod. Opt. 41, 1757 (1994).
[CrossRef]

Santarsiero, M.

M. Santarsiero and F. Gori, Phys. Lett. A 167, 123 (1992).
[CrossRef]

Saxena, K.

H. C. Kandpal, J. C. Vaishya, K. Saxena, D. S. Mehta, and K. C. Joshi, J. Mod. Opt. 42, 455 (1995).
[CrossRef]

H. C. Kandpal, K. Saxena, D. S. Mehta, J. C. Vaishya, and K. C. Joshi, Opt. Commun. 99, 157 (1993).
[CrossRef]

Schiller, N. H.

N. H. Schiller and R. R. Alfano, Opt. Commun. 35, 451 (1980).
[CrossRef]

Sereda, L.

Shank, C. V.

C. V. Shank, R. L. Fork, R. H. Stolen, and W. J. Tomlinson, Appl. Phys. Lett. 40, 761 (1982).
[CrossRef]

Shubert, M.

R. Gase and M. Shubert, Opt. Acta 29, 1331 (1982).
[CrossRef]

Simon, R.

Stolen, R. H.

C. V. Shank, R. L. Fork, R. H. Stolen, and W. J. Tomlinson, Appl. Phys. Lett. 40, 761 (1982).
[CrossRef]

Tomlinson, W. J.

C. V. Shank, R. L. Fork, R. H. Stolen, and W. J. Tomlinson, Appl. Phys. Lett. 40, 761 (1982).
[CrossRef]

Treacy, E. B.

E. B. Treacy, J. Quantum Electron. QE-5, 454 (1969).
[CrossRef]

Vaishya, J. C.

H. C. Kandpal, J. C. Vaishya, K. Saxena, D. S. Mehta, and K. C. Joshi, J. Mod. Opt. 42, 455 (1995).
[CrossRef]

H. C. Kandpal, K. Saxena, D. S. Mehta, J. C. Vaishya, and K. C. Joshi, Opt. Commun. 99, 157 (1993).
[CrossRef]

H. C. Kandpal, J. C. Vaishya, and K. C. Joshi, Opt. Commun. 73, 169 (1989).
[CrossRef]

Wang, W.

Wolf, E.

W. Wang, R. Simon, and E. Wolf, J. Opt. Soc. Am. A 9, 287 (1992).
[CrossRef]

B. Cairns and E. Wolf, J. Opt. Soc. Am. A 8, 1922 (1991).
[CrossRef]

D. F. V. James and E. Wolf, Phys. Lett. A 157, 6 (1991).
[CrossRef]

D. F. V. James and E. Wolf, Opt. Commun. 81, 150 (1991).
[CrossRef]

E. Wolf, F. T. Foley, and F. Gori, J. Opt. Soc. Am. A 6, 1142 (1989).
[CrossRef]

A. Gamliel and E. Wolf, Opt. Commun. 65, 91 (1988).
[CrossRef]

Z. Dacic and E. Wolf, J. Opt. Soc. Am. A 5, 1118 (1988).
[CrossRef]

E. Wolf, Opt. Commun. 62, 12 (1987).
[CrossRef]

E. Wolf, Nature (London) 326, 363 (1987).
[CrossRef]

E. Wolf, Phys. Rev. Lett. 58, 2646 (1987).
[CrossRef] [PubMed]

E. Wolf, Phys. Rev. Lett. 56, 1370 (1986).
[CrossRef] [PubMed]

L. Mandel and E. Wolf, J. Soc. Am. 66, 529 (1976).

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

Zamir, R.

G. Hazak and R. Zamir, J. Mod. Opt. 40, 1653 (1993).
[CrossRef]

Ziolkowski, R. W.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

C. V. Shank, R. L. Fork, R. H. Stolen, and W. J. Tomlinson, Appl. Phys. Lett. 40, 761 (1982).
[CrossRef]

J. Mod. Opt. (8)

G. Indebetouw, J. Mod. Opt. 36, 251 (1989).
[CrossRef]

G. S. Agarwal and D. F. V. James, J. Mod. Opt. 40, 1431 (1993).
[CrossRef]

G. Hazak and R. Zamir, J. Mod. Opt. 40, 1653 (1993).
[CrossRef]

W. H. Carter, J. Mod. Opt. 40, 2433 (1993).
[CrossRef]

D. N. Rao and V. N. Kumar, J. Mod. Opt. 41, 1757 (1994).
[CrossRef]

H. C. Kandpal, J. C. Vaishya, K. Saxena, D. S. Mehta, and K. C. Joshi, J. Mod. Opt. 42, 455 (1995).
[CrossRef]

M. R. Perrone, J. Mod. Opt. 40, 2135 (1993).
[CrossRef]

E. Fiordilino and V. Miceli, J. Mod. Opt. 41, 1415 (1994).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (8)

J. Opt. Soc. Am. B (2)

J. Quantum Electron. (1)

E. B. Treacy, J. Quantum Electron. QE-5, 454 (1969).
[CrossRef]

J. Soc. Am. (1)

L. Mandel and E. Wolf, J. Soc. Am. 66, 529 (1976).

Nature (London) (1)

E. Wolf, Nature (London) 326, 363 (1987).
[CrossRef]

Opt. Acta (1)

R. Gase and M. Shubert, Opt. Acta 29, 1331 (1982).
[CrossRef]

Opt. Commun. (10)

O. E. Martinez, Opt. Commun. 59, 229 (1986).
[CrossRef]

T. Foley, Opt. Commun. 75, 347 (1990).
[CrossRef]

H. C. Kandpal, K. Saxena, D. S. Mehta, J. C. Vaishya, and K. C. Joshi, Opt. Commun. 99, 157 (1993).
[CrossRef]

H. C. Kandpal, J. C. Vaishya, and K. C. Joshi, Opt. Commun. 73, 169 (1989).
[CrossRef]

N. H. Schiller and R. R. Alfano, Opt. Commun. 35, 451 (1980).
[CrossRef]

E. Wolf, Opt. Commun. 62, 12 (1987).
[CrossRef]

D. F. V. James and E. Wolf, Opt. Commun. 81, 150 (1991).
[CrossRef]

G. M. Morris and D. Faklis, Opt. Commun. 62, 5 (1987).
[CrossRef]

F. Gori, G. Guattari, C. Palma, and C. Padovani, Opt. Commun. 67, 1 (1988).
[CrossRef]

A. Gamliel and E. Wolf, Opt. Commun. 65, 91 (1988).
[CrossRef]

Opt. Lett. (1)

Phys. Lett. A (3)

D. F. V. James and E. Wolf, Phys. Lett. A 157, 6 (1991).
[CrossRef]

M. Santarsiero and F. Gori, Phys. Lett. A 167, 123 (1992).
[CrossRef]

A. Lagendijk, Phys. Lett. A 147, 389 (1990).
[CrossRef]

Phys. Rev. Lett. (3)

E. Wolf, Phys. Rev. Lett. 58, 2646 (1987).
[CrossRef] [PubMed]

M. F. Bocko, D. H. Douglas, and R. S. Knox, Phys. Rev. Lett. 58, 2649 (1987).
[CrossRef] [PubMed]

E. Wolf, Phys. Rev. Lett. 56, 1370 (1986).
[CrossRef] [PubMed]

Proc. SPIE (1)

Zs. Bor and A. P. Kovàcs, Proc. SPIE 1983, 524 (1993).

Other (4)

M. Kàlal, Proc. SPIE1983, 686 (1993).

A relation among the quantities dIQ(r, ω), IQ′(r, ω) (stationary wave field), and IQ″(r, ω) (nonstationary wave field) is considered in Appendix A of Ref. 33.

G. Korn and T. Korn, Mathematical Handbook (McGraw-Hill, New York, 1968).

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

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Figures (10)

Fig. 1
Fig. 1

Geometry of the diffraction of a plane wave from a slit.

Fig. 2
Fig. 2

Spectra of the Gaussian-shaped pulse in diffraction from a slit at different diffraction angles β = (a/λ0) sin Θ, normalized to the maximum value at the center of the diffraction pattern (β = 0). The horizontal axis for all curves is ω = (ωω0)/ω0.

Fig. 3
Fig. 3

Spatial distribution of the intensity of the central monochromatic component of the Gaussian-shaped pulse, diffracted from a slit. The intensity is normalized to its maximum value at the center of the diffraction pattern (β = 0). Zones of the blue shift of the pulse’s spectral maximum, corresponding to the pulse’s band width γ = 1/(ω0τ) = 0, 32 are hatched, and the other zones correspond to the red shift. A shift of the spectral maximum does not occur only at points 1–4, corresponding to the diffraction maxima of the pulse’s central monochromatic component.

Fig. 4
Fig. 4

Formation of the red shift of the pulse’s spectral maximum. The diffraction angle is β = (a/λ0) sin Θ = 0, 5; the pulse’s bandwidth is γ = 1/(ω0τ) = 0, 32.

Fig. 5
Fig. 5

Formation of the blue shift of the pulse’s spectral maximum. The diffraction angle is β = (a/λ0) sin Θ = 0, 615; the pulse’s bandwidth is γ = 1/(ω0τ) = 0, 32.

Fig. 6
Fig. 6

Change of the shift of the pulse’s spectral maximum from red to blue between the first diffraction minimum and the first diffraction maximum of the pulse’s central monochromatic component. β = (a/λ0) sin Θ is the diffraction angle; the pulse’s bandwidth is γ = 1/(ω0τ) = 0, 32.

Fig. 7
Fig. 7

Decrease of the blue shift of the pulse’s spectral maximum to zero as the diffraction angle β = (a/λ0) sin Θ increases until the first diffraction maximum of the pulse’s central monochromatic component. The pulse’s bandwidth is γ = 1/(ω0τ) = 0, 32.

Fig. 8
Fig. 8

Spatial distribution of energy of the diffraction pattern from the Gaussian-shaped pulsed source for different values of pulse bandwidth γ = 1/(ω0τ). Energies are normalized to their own maximum values at the center of the diffraction pattern (β = 0).

Fig. 9
Fig. 9

Time intensity of the diffraction pattern from the Gaussian-shaped pulsed source at different diffraction angles β = (a/λ0) sin Θ, corresponding to that of Fig. 2. Intensities are normalized to the maximum value at the center of the diffraction pattern (β = 0). The pulse’s bandwidth is γ = 1/(ω0τ) = 0, 16. The horizontal axis for all curves is t = (tR0/ν)/τ.

Fig. 10
Fig. 10

Time intensity of the diffraction pattern from the Gaussian-shaped pulsed source at different diffraction angles β = (a/λ0) sin Θ, corresponding to that of Fig. 2. Intensities are normalized to the maximum value at the center of the diffraction pattern (β = 0). The pulse’s bandwidth is γ = 1/(ω0τ) = 0, 32. The horizontal axis for all curves is t = (tR0/ν)/τ.

Tables (2)

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Table 1 Maximum Values of Red and Blue Shifts of the Spectral Maximum of the Gaussian-Shaped Pulse in the First Three Diffraction Ordersa

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Table 2 Maximum Values of Red and Blue Shifts of the Spectral Maximum of the Gaussian-Shaped Pulse for Different Values of the Pulse Bandwidth in the First Diffraction Order

Equations (22)

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V ( r , t ) = exp ( i ω t ) d U F ( r , ω ) , r R 3 ,
d I F ( r ; ω ) = | d U F ( r , ω ) | 2 = d S F ( r ; ω , ω ) ,
S F ( r ; ω 1 , ω 2 ) = U F ( r ; ω 1 ) U F * ( r ; ω 2 )
I F ( r ; t ) = | V ( r ; t ) | 2 = exp i ( ω 1 ω 2 ) t ] d S F ( r ; ω 1 , ω 2 ) .
d S F ( r ; ω 1 , ω 2 ) = d U F ( r ; ω 1 , ) d U F * ( r ; ω 2 , ) = 0 ω 1 ω 2 ,
I F ( r ) = d I F ( r ; ω ) .
d I F ( r , ω ) = | d U F ( r , ω ) | 2 = d I Q ( ω ) ( a / R 0 ) 2 sinc 2 ( ω υ a sin Θ ) ,
Q ( t ) = η exp [ 1 2 ( t τ ) 2 + i ω 0 t ] ,
I F ( r , ω ) = | U F ( r , ω ) | 2 = I τ 2 2 π exp { ( ω ω 0 ) τ ] 2 } [ ( a / R 0 ) ] 2 sinc 2 ( ω υ a sin Θ ) ,
I = | η | 2 .
I F ( r , ω ) norm = exp [ ( ω / γ ) 2 ] sinc 2 [ 2 π β ( ω + 1 ) ] .
I F ( r , ω 0 ) norm = sinc 2 ( ω 0 υ a sin Θ ) = sinc 2 ( 2 π β ) ,
sinc ( ω 0 υ a sin Θ ) = 0
β = a λ 0 sin Θ = n 2 , n = 0 , ± 1 , ± 2 .
I Q ( ω ) = 1 2 π Δ ω 2 exp { [ ( ω ω 0 ) / Δ ω ] 2 } ,
E F ( r ) = I F ( r , t ) d t ,
E F ( r ) = [ t = exp ( i ν t ) d t ] d S F ( r ; ω , ω ν ) .
δ ( ν ) = 1 2 π exp ( i ν t ) d t ,
E F ( r ) = 2 π d I F ( r , ω ) .
E F ( r ) = 2 π I F ( r , ω ) d ω = I τ 2 ( a / R 0 ) 2 exp { [ ( ω ω 0 ) τ ] 2 } × sinc 2 ( ω υ a sin Θ ) d ω .
I F ( r , t ) = I ( a / R 0 ) 2 | C ( r , t ) | 2 ,
C ( r , t ) = exp [ i ω ( t R 0 / ν ) ] τ 2 π exp [ 1 2 ( ω ω 0 ) 2 τ 2 ] sinc ( ω υ a sin Θ ) d ω .

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