Abstract

It is shown that partially spectrally coherent pulses of light with controlled spectral coherence properties can be generated by temporal modulation of beams emitted by stationary light sources. A method for generation of spectrally Gaussian Schell-model-type pulses is presented.

© 2003 Optical Society of America

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References

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  1. P. P äkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F.Wyrowski, �??Partially coherent Gaussian pulses,�?? Opt. Commun. 204, 53�??58 (2002).
    [CrossRef]
  2. A. C. Schell, �??A technique for the determination of the radiation pattern of a partially coherent aperture,�?? IEEE Trans. Antennas Propag. AP-15, 187�??188 (1967).
    [CrossRef]
  3. J. T. Foley and M. S. Zubairy, �??The directionality of Gaussian Schell-model beams,�?? Opt. Commun. 26, 297�??300 (1976).
    [CrossRef]
  4. E. Wolf and E. Collett, �??Beams generated by Gaussian quasi-homogeneous sources,�?? Opt. Commun. 32, 27�??31 (1980).
    [CrossRef]
  5. F. Gori, �??Collett�??Wolf sources and multimode lasers,�?? Opt. Commun. 34, 301�??305 (1980).
    [CrossRef]
  6. A. T. Friberg and R. J. Sudol, �??Propagation parameters of Gaussian Schell-model beams,�?? Opt. Commun. 41, 383�??387 (1982).
    [CrossRef]
  7. J. Deschamps, D. Courjon, and J. Bulabois, �??Gaussian Schell-model sources: an example and some perspectives,�?? J. Opt. Soc. Am. 73, 256�??261 (1983).
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  8. A. T. Friberg and J. Turunen, �??Imaging of Gaussian Schell-model sources,�?? J. Opt. Soc. Am. A 5, 713�??720 (1988).
    [CrossRef]
  9. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995), p. 59.
  10. J. D. Farina, L. M. Narducci, and E. Collett, �??Generation of highly directional beams from a globally incoherent source,�?? Opt. Commun. 32, 203�??207 (1980).
    [CrossRef]
  11. Q. He, J. Turunen, and A. T. Friberg, �??Propagation and imaging experiments with Gaussian Schell-model sources,�?? Opt. Commun. 67, 245�??250 (1988).
    [CrossRef]

IEEE Trans. Antennas Propag.

A. C. Schell, �??A technique for the determination of the radiation pattern of a partially coherent aperture,�?? IEEE Trans. Antennas Propag. AP-15, 187�??188 (1967).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

J. D. Farina, L. M. Narducci, and E. Collett, �??Generation of highly directional beams from a globally incoherent source,�?? Opt. Commun. 32, 203�??207 (1980).
[CrossRef]

Q. He, J. Turunen, and A. T. Friberg, �??Propagation and imaging experiments with Gaussian Schell-model sources,�?? Opt. Commun. 67, 245�??250 (1988).
[CrossRef]

J. T. Foley and M. S. Zubairy, �??The directionality of Gaussian Schell-model beams,�?? Opt. Commun. 26, 297�??300 (1976).
[CrossRef]

E. Wolf and E. Collett, �??Beams generated by Gaussian quasi-homogeneous sources,�?? Opt. Commun. 32, 27�??31 (1980).
[CrossRef]

F. Gori, �??Collett�??Wolf sources and multimode lasers,�?? Opt. Commun. 34, 301�??305 (1980).
[CrossRef]

A. T. Friberg and R. J. Sudol, �??Propagation parameters of Gaussian Schell-model beams,�?? Opt. Commun. 41, 383�??387 (1982).
[CrossRef]

P. P äkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F.Wyrowski, �??Partially coherent Gaussian pulses,�?? Opt. Commun. 204, 53�??58 (2002).
[CrossRef]

Other

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995), p. 59.

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Figures (1)

Fig. 1.
Fig. 1.

(a) Pulse generation by chopping the collimated beam emitted by a stationary light source with a modulator. (b) Generation of partially coherent fields in the spatial frequency domain by spatial modulation of a field originating from an incoherent source.

Equations (22)

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Γ s ( τ ) = S s ( ω ) exp ( i ω τ ) d ω ,
γ s ( τ ) = Γ s ( τ ) Γ s ( 0 ) ,
Γ ( 0 , 0 ; t 1 , t 2 ) = Γ s ( 0 ) M * ( t 1 ) M ( t 2 ) γ s ( t 2 t 1 )
Γ ( z 1 , z 2 ; t 1 , t 2 ) = Γ s ( 0 ) M * ( t 1 z 1 c ) M ( t 2 z 2 c ) γ s ( t 2 t 1 ( z 2 z 1 ) c ) .
I ( z , t ) = Γ ( z , z ; t , t ) = Γ s ( 0 ) M ( t z c ) 2
γ ( z 1 , z 2 ; t 1 , t 2 ) = Γ ( z 1 , z 2 ; t 1 , t 2 ) [ I ( z 1 , t 1 ) I ( z 2 , t 2 ) ] 1 2
= γ s ( t 2 t 1 ( z 2 z 1 ) c ) exp [ iΔΦ ( z 1 , z 2 ; t 1 , t 2 ) ] ,
W ( z 1 , z 2 ; ω 1 , ω 2 ) = 1 ( 2 π ) 2 Γ ( z 1 , z 2 ; t 1 , t 2 ) exp [ i ( ω 1 t 1 ω 2 t 2 ) ] d t 1 d t 2 .
S ( z , ω ) = W ( z , z ; ω , ω )
μ ( z 1 , z 2 ; ω 1 , ω 2 ) = W ( z 1 , z 2 ; ω 1 , ω 2 ) [ S ( z 1 , ω 1 ) S ( z 2 , ω 2 ) ] 1 2 ,
S s ( ω ) = S 0 exp [ ( ω ω 0 ) 2 Ω s 2 ]
M ( t ) = exp ( t 2 2 T m 2 ) ,
Γ s ( τ ) = Γ 0 exp ( 1 4 Ω s 2 τ 2 ) exp ( i ω 0 τ ) ,
I ( z , t ) = Γ 0 exp [ ( t z c ) 2 T 2 ]
γ ( z 1 , z 2 ; t 1 , t 2 ) = exp { [ ( t 1 z 1 c ) ( t 2 z 2 c ) ] 2 2 T c 2 } ,
arg γ ( z 1 , z 2 , t 1 , t 2 ) = ω 0 [ ( t 1 z 1 c ) ( t 2 z 2 c ) ] ,
T = T m and T c = 2 Ω s .
S ( z , ω ) = exp [ ( ω ω 0 ) 2 Ω 2 ]
μ ( z 1 , z 2 ; ω 1 , ω 2 ) = exp [ ( ω 1 ω 2 ) 2 2 Ω c 2 ] ,
arg μ ( z 1 , z 2 ; ω 1 , ω 2 ) = ( ω 2 z 2 ω 1 z 1 ) c .
Ω 2 = 1 T 2 + 2 T c 2 = Ω s 2 + 1 T m 2
Ω c 2 = T c T 2 Ω 2 = 2 T m 2 ( 1 + 1 T m 2 Ω s 2 )

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