Abstract

New time-resolved spatial parameters are given that characterize the behavior of pulsed beams along with their propagation laws through first-order optical systems. The analytical conditions that should be fulfilled so that the intensity-moment formalism remains valid are investigated. Their physical meaning is also discussed, along with the implications for the evolution of the spatial profile of a pulsed beam.

© 1995 Optical Society of America

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References

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  1. O. E. Martínez, IEEE J. Quantum Electron. 25, 196 (1989).
  2. A. G. Kostenbauder, IEEE J. Quantum Electron. 26, 1148 (1990).
    [Crossref]
  3. A. Caprara, G. C. Reali, Opt. Lett. 17, 414 (1992).
    [Crossref] [PubMed]
  4. T. Omatsu, T. Takase, K. Kuroda, Opt. Commun. 101, 199 (1993).
    [Crossref]
  5. A. E. Siegman, Lasers (Oxford U. Press, Oxford, 1986).
  6. O. E. Martínez, J. L. A. Chilla, Opt. Lett. 17, 1210 (1992).
    [Crossref] [PubMed]

1993 (1)

T. Omatsu, T. Takase, K. Kuroda, Opt. Commun. 101, 199 (1993).
[Crossref]

1992 (2)

1990 (1)

A. G. Kostenbauder, IEEE J. Quantum Electron. 26, 1148 (1990).
[Crossref]

1989 (1)

O. E. Martínez, IEEE J. Quantum Electron. 25, 196 (1989).

Caprara, A.

Chilla, J. L. A.

Kostenbauder, A. G.

A. G. Kostenbauder, IEEE J. Quantum Electron. 26, 1148 (1990).
[Crossref]

Kuroda, K.

T. Omatsu, T. Takase, K. Kuroda, Opt. Commun. 101, 199 (1993).
[Crossref]

Martínez, O. E.

O. E. Martínez, J. L. A. Chilla, Opt. Lett. 17, 1210 (1992).
[Crossref] [PubMed]

O. E. Martínez, IEEE J. Quantum Electron. 25, 196 (1989).

Omatsu, T.

T. Omatsu, T. Takase, K. Kuroda, Opt. Commun. 101, 199 (1993).
[Crossref]

Reali, G. C.

Siegman, A. E.

A. E. Siegman, Lasers (Oxford U. Press, Oxford, 1986).

Takase, T.

T. Omatsu, T. Takase, K. Kuroda, Opt. Commun. 101, 199 (1993).
[Crossref]

IEEE J. Quantum Electron. (2)

O. E. Martínez, IEEE J. Quantum Electron. 25, 196 (1989).

A. G. Kostenbauder, IEEE J. Quantum Electron. 26, 1148 (1990).
[Crossref]

Opt. Commun. (1)

T. Omatsu, T. Takase, K. Kuroda, Opt. Commun. 101, 199 (1993).
[Crossref]

Opt. Lett. (2)

Other (1)

A. E. Siegman, Lasers (Oxford U. Press, Oxford, 1986).

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Figures (1)

Fig. 1
Fig. 1

Geometry and notation used to illustrate the slice-to-slice approach. The condition for the independent time– slice propagation requires that {[p(x0, x)]maxL} be much smaller than the length of the pulse.

Equations (12)

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w n = ( 1 / F 0 ) w n | F ( x , w ) | 2 d x d w , n = 1 , 2 , ,
σ w 2 = ( w w ) 2 ,
σ w 2 ( x ) = ( 1 / F 0 x ) [ w w _ ( x ) ] 2 | F ( x , w ) | 2 d w .
F ( x , w , z ) = ( i w / c z ) 1 / 2 exp [ i ( w / c ) z ] F ( x 0 , w , 0 ) × exp [ i ( w / 2 c z ) ( x x 0 ) 2 ] d x 0 .
x 2 z 0 , t = ( 1 / I 0 ) x 2 | f ( x , t , z 0 ) | 2 d x ,
u 2 ( z 0 , t ) = ( c 2 / w 0 2 I 0 ) | f ( x , t , z 0 ) | 2 d x ,
x u ( z 0 , t ) = ( c / 2 i w 0 I 0 ) x [ ( f * ) f f * f ] d x ,
f out ( x , t ) = ( i / B ) 1 / 2 ( w / c ) 1 / 2 exp [ i ( w / 2 c B ) × ( A x 0 2 + D x 2 2 x 0 x ) ] F inp ( x 0 , w ) × exp [ i w ( t L / c ) ] d w d x 0 ,
f out ( x , t ) = ( i w 0 / B c ) 1 / 2 f inp ( x 0 , t L / c ) × exp [ i ( w 0 / 2 c B ) × ( A x 0 2 + D x 2 2 x 0 x ) ] d x 0 ,
[ p ( x 0 , x ) L ] [ σ w ( x 0 ) / c ] 1
x 2 ( t ) = A 2 x 2 i ( t L / c ) + B 2 u 2 i ( t L / c ) + 2 A B x u i ( t L / c ) ,
{ [ p ( x 0 , x ) ] max L } [ H + ( Q / 2 H ) + ( H 2 + Q ) 1 / 2 ] l ,

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