Abstract

A tensor method is presented to treat the transformation of pulsed nonideal beams in a four-dimension spatiotemporal domain. The equivalent beamwidth, mean pulse duration, divergence, spectrum width, radius of curvature, and pulsed beam quality factor for arbitrary-amplitude profile pulsed beams are introduced. The transformation rules of these parameters are derived by means of the four-dimension Huygens integral.

© 1993 Optical Society of America

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References

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  1. S. P. Dijaili, A. Dienes, J. S. Smith, IEEE J. Quantum Electron. 26, 1158 (1990).
    [CrossRef]
  2. A. G. Kostenbauder, IEEE J. Quantum Electron. 26, 1148 (1990).
    [CrossRef]
  3. Q. Lin, S. Wang, J. Alda, E. Bernabeu, “Transformation of pulsed Gaussian beams in four-dimension domain,” submitted to IEEE J. Quantum Electron.
  4. A. E. Siegman, Proc. Soc. Photo-Opt. Instrum. Eng. 1224, 2 (1990).
  5. A. E. Siegman, IEEE J. Quantum Electron. 27, 1146 (1991).
    [CrossRef]
  6. P. A. Bélanger, Opt. Lett. 16, 196 (1991).
    [CrossRef] [PubMed]
  7. M. J. Bastiaans, Optik 82, 173 (1989).
  8. J. Serna, R. Martinez-Herrero, P. M. Mejías, J. Opt. Soc. Am. A 8, 1094 (1991).
    [CrossRef]
  9. M. A. Porras, J. Alda, E. Bernabeu, Appl. Opt. 31, 6389 (1992).
    [CrossRef] [PubMed]
  10. Q. Lin, S. Wang, J. Alda, E. Bernabeu, Optik 85, 67 (1990).
  11. M. J. Bastiaans, Optik 88, 163 (1991).

1992 (1)

1991 (4)

1990 (4)

S. P. Dijaili, A. Dienes, J. S. Smith, IEEE J. Quantum Electron. 26, 1158 (1990).
[CrossRef]

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

A. E. Siegman, Proc. Soc. Photo-Opt. Instrum. Eng. 1224, 2 (1990).

Q. Lin, S. Wang, J. Alda, E. Bernabeu, Optik 85, 67 (1990).

1989 (1)

M. J. Bastiaans, Optik 82, 173 (1989).

Alda, J.

M. A. Porras, J. Alda, E. Bernabeu, Appl. Opt. 31, 6389 (1992).
[CrossRef] [PubMed]

Q. Lin, S. Wang, J. Alda, E. Bernabeu, Optik 85, 67 (1990).

Q. Lin, S. Wang, J. Alda, E. Bernabeu, “Transformation of pulsed Gaussian beams in four-dimension domain,” submitted to IEEE J. Quantum Electron.

Bastiaans, M. J.

M. J. Bastiaans, Optik 88, 163 (1991).

M. J. Bastiaans, Optik 82, 173 (1989).

Bélanger, P. A.

Bernabeu, E.

M. A. Porras, J. Alda, E. Bernabeu, Appl. Opt. 31, 6389 (1992).
[CrossRef] [PubMed]

Q. Lin, S. Wang, J. Alda, E. Bernabeu, Optik 85, 67 (1990).

Q. Lin, S. Wang, J. Alda, E. Bernabeu, “Transformation of pulsed Gaussian beams in four-dimension domain,” submitted to IEEE J. Quantum Electron.

Dienes, A.

S. P. Dijaili, A. Dienes, J. S. Smith, IEEE J. Quantum Electron. 26, 1158 (1990).
[CrossRef]

Dijaili, S. P.

S. P. Dijaili, A. Dienes, J. S. Smith, IEEE J. Quantum Electron. 26, 1158 (1990).
[CrossRef]

Kostenbauder, A. G.

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

Lin, Q.

Q. Lin, S. Wang, J. Alda, E. Bernabeu, Optik 85, 67 (1990).

Q. Lin, S. Wang, J. Alda, E. Bernabeu, “Transformation of pulsed Gaussian beams in four-dimension domain,” submitted to IEEE J. Quantum Electron.

Martinez-Herrero, R.

Mejías, P. M.

Porras, M. A.

Serna, J.

Siegman, A. E.

A. E. Siegman, IEEE J. Quantum Electron. 27, 1146 (1991).
[CrossRef]

A. E. Siegman, Proc. Soc. Photo-Opt. Instrum. Eng. 1224, 2 (1990).

Smith, J. S.

S. P. Dijaili, A. Dienes, J. S. Smith, IEEE J. Quantum Electron. 26, 1158 (1990).
[CrossRef]

Wang, S.

Q. Lin, S. Wang, J. Alda, E. Bernabeu, Optik 85, 67 (1990).

Q. Lin, S. Wang, J. Alda, E. Bernabeu, “Transformation of pulsed Gaussian beams in four-dimension domain,” submitted to IEEE J. Quantum Electron.

Appl. Opt. (1)

IEEE J. Quantum Electron. (3)

S. P. Dijaili, A. Dienes, J. S. Smith, IEEE J. Quantum Electron. 26, 1158 (1990).
[CrossRef]

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

A. E. Siegman, IEEE J. Quantum Electron. 27, 1146 (1991).
[CrossRef]

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

Opt. Lett. (1)

Optik (3)

M. J. Bastiaans, Optik 82, 173 (1989).

Q. Lin, S. Wang, J. Alda, E. Bernabeu, Optik 85, 67 (1990).

M. J. Bastiaans, Optik 88, 163 (1991).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

A. E. Siegman, Proc. Soc. Photo-Opt. Instrum. Eng. 1224, 2 (1990).

Other (1)

Q. Lin, S. Wang, J. Alda, E. Bernabeu, “Transformation of pulsed Gaussian beams in four-dimension domain,” submitted to IEEE J. Quantum Electron.

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Equations (31)

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[ r ˜ 2 r ˜ 2 ] = [ A ˜ B ˜ C ˜ D ˜ ] [ r ˜ 1 r ˜ 1 ] ,
r ˜ 1 , 2 = [ r τ ] 1 , 2 = [ x y τ x τ y ] 1 , 2 , r ˜ 1 , 2 = [ r τ ] 1 , 2 = [ x y τ x τ y ] 1 , 2 .
τ 1 , 2 = [ τ x τ y ] 1 , 2 = [ λ o ν o ( t x - t o ) λ o ν o ( t y - t o ) ] 1 , 2 , τ 1 , 2 = [ τ x τ y ] 1 , 2 = [ ( ν o - ν c x ) / ν o ( ν o - ν c y ) / ν o ] 1 , 2 ,
U ( r ˜ ) = U ( r , τ ) = Ψ ( r ˜ ) exp [ i ϕ ( r ˜ ) ] .
U 2 ( r ˜ 2 ) = ( i λ o ) 2 1 Det ( B ˜ ) - U 1 ( r ˜ 1 ) × exp [ - i k o 2 ( r ˜ 1 T B ˜ - 1 A ˜ r ˜ 1 - 2 r ˜ 1 T B ˜ - 1 r ˜ 2 + r ˜ 2 T D ˜ B ˜ - 1 r ˜ 2 ] d r ˜ 1 ,
ω ˜ 2 = 4 - r ˜ r ˜ T U ( r ˜ ) 2 d r ˜ ,
- U ( r ˜ ) 2 d r ˜ = 1.
ω ˜ 2 = [ ω rr 2 ω r τ 2 ω τ r 2 ω τ 2 ] ,
ω ˜ 2 2 = A ˜ ω ˜ 2 2 A ˜ T + B ˜ θ ˜ 1 2 B ˜ T + A ˜ V ˜ 1 B ˜ T + B ˜ V ˜ 1 T A ˜ T ,
θ ˜ 2 = ( λ o π ) 2 - ( U ) ( U ) + d r ˜ ,
θ ˜ 2 = 4 λ o 2 - ξ ˜ ξ ˜ T U ( ξ ˜ ) 2 d ξ ˜ ,
U ( ξ ˜ ) = - U ( r ˜ ) exp ( i 2 π ξ ˜ T r ˜ ) d r ˜ .
V ˜ = i λ π - [ ( U ) ( U r ˜ ) + - ( U r ˜ ) ( U ) + ] d r ˜ ,
V ˜ = - 2 λ o π - U ( r ˜ ) 2 r ˜ [ ϕ ( r ˜ ) ] T d r ˜ ,
θ ˜ 2 2 = C ˜ ω ˜ 1 2 C ˜ T + D ˜ θ ˜ 1 2 D ˜ T + C ˜ V ˜ 1 D ˜ T + D ˜ V ˜ 1 T C ˜ T ,
V ˜ 2 = A ˜ ω ˜ 1 2 C ˜ T + B ˜ θ ˜ 1 2 D ˜ T + A ˜ V ˜ 1 D ˜ T + B ˜ V ˜ 1 T C ˜ T .
[ ω ˜ 2 2 V ˜ 2 V ˜ 2 T θ ˜ 2 2 ] = [ A ˜ B ˜ C ˜ D ˜ ] [ ω ˜ 1 2 V ˜ 1 V ˜ 1 T θ ˜ 1 2 ] [ A ˜ B ˜ C ˜ D ˜ ] T .
P = [ ω ˜ 2 V ˜ V ˜ T θ ˜ 2 ] .
P 2 = S P 1 S T ,
ω 2 θ 2 - ( V ) 2 = ( λ π ) 2 M 4 ,
ω ˜ 2 θ ˜ 2 - ( V ˜ ) 2 = ( λ o π ) 2 M ˜ 4 ,
A ˜ D ˜ T - B ˜ C ˜ T = ˜ ,
Tr ( M ˜ 1 4 ) = Tr ( M ˜ 2 4 ) .
U ( r ˜ ) = U o exp ( - i k o 2 r ˜ T Q ˜ - 1 r ˜ ) ,
Q ˜ - 1 = [ Q ˜ rr - 1 Q ˜ r τ - 1 Q ˜ τ r - 1 Q ˜ τ τ - 1 ] = Re ( Q ˜ - 1 ) - i Im ( Q ˜ - 1 ) .
ω ˜ 2 = 2 k o Im ( Q ˜ - 1 ) , θ ˜ 2 = Q ˜ - 1 ω ˜ 2 ( Q ˜ - 1 ) + ,             V ˜ = ω ˜ 2 Re ( Q ˜ - 1 ) ,
ω ˜ 2 ( θ ˜ 2 ) - ( V ˜ ) 2 = ( 2 k o ) 2 ˜ .
Tr ( M ˜ G 4 ) = 4
Re Q ˜ - 1 = ( ω ˜ 2 ) - 1 V ˜ ,
R ˜ - 1 = ( ω ˜ 2 ) - 1 V ˜ ,
M ˜ 4 = ( π λ o ) 2 ω ˜ 2 [ θ ˜ 2 - ω ˜ 2 ( R ˜ - 1 ) 2 ] .

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