Abstract

Based on the equations that describe the propagation of time and space pulses in dispersion and diffraction regimes, new analogies between the propagation parameters of both regimes are formulated.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. V. Bennett and B. H. Kolner, "Aberrations in temporal imaging," IEEE J. Quantum Electron. 37, 20-32 (2001).
    [CrossRef]
  2. B. H. Kolner, "Space-time duality and the theory of temporal imaging," IEEE J. Quantum Electron. 30, 1951-1963 (1994).
    [CrossRef]
  3. C. V. Bennett and B. H. Kolner, "Principles of parametric temporal imaging--part I: system configurations," IEEE J. Quantum Electron. 36, 430-437 (2000).
    [CrossRef]
  4. C. V. Bennett and B. H. Kolner, "Principles of parametric temporal imaging--Part II: system performance," IEEE J. Quantum Electron. 36, 649-655 (2000).
    [CrossRef]
  5. P. Naulleau and E. Leith, "Stretch, time lenses, and incoherent imaging," Appl. Opt. 34, 4119-4128 (1995).
    [CrossRef] [PubMed]
  6. S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, 1992).

2001

C. V. Bennett and B. H. Kolner, "Aberrations in temporal imaging," IEEE J. Quantum Electron. 37, 20-32 (2001).
[CrossRef]

2000

C. V. Bennett and B. H. Kolner, "Principles of parametric temporal imaging--part I: system configurations," IEEE J. Quantum Electron. 36, 430-437 (2000).
[CrossRef]

C. V. Bennett and B. H. Kolner, "Principles of parametric temporal imaging--Part II: system performance," IEEE J. Quantum Electron. 36, 649-655 (2000).
[CrossRef]

1995

1994

B. H. Kolner, "Space-time duality and the theory of temporal imaging," IEEE J. Quantum Electron. 30, 1951-1963 (1994).
[CrossRef]

1992

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, 1992).

Akhmanov, S. A.

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, 1992).

Bennett, C. V.

C. V. Bennett and B. H. Kolner, "Aberrations in temporal imaging," IEEE J. Quantum Electron. 37, 20-32 (2001).
[CrossRef]

C. V. Bennett and B. H. Kolner, "Principles of parametric temporal imaging--part I: system configurations," IEEE J. Quantum Electron. 36, 430-437 (2000).
[CrossRef]

C. V. Bennett and B. H. Kolner, "Principles of parametric temporal imaging--Part II: system performance," IEEE J. Quantum Electron. 36, 649-655 (2000).
[CrossRef]

Chirkin, A. S.

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, 1992).

Kolner, B. H.

C. V. Bennett and B. H. Kolner, "Aberrations in temporal imaging," IEEE J. Quantum Electron. 37, 20-32 (2001).
[CrossRef]

C. V. Bennett and B. H. Kolner, "Principles of parametric temporal imaging--part I: system configurations," IEEE J. Quantum Electron. 36, 430-437 (2000).
[CrossRef]

C. V. Bennett and B. H. Kolner, "Principles of parametric temporal imaging--Part II: system performance," IEEE J. Quantum Electron. 36, 649-655 (2000).
[CrossRef]

B. H. Kolner, "Space-time duality and the theory of temporal imaging," IEEE J. Quantum Electron. 30, 1951-1963 (1994).
[CrossRef]

Leith, E.

Naulleau, P.

Vysloukh, V. A.

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, 1992).

Appl. Opt.

IEEE J. Quantum Electron.

C. V. Bennett and B. H. Kolner, "Aberrations in temporal imaging," IEEE J. Quantum Electron. 37, 20-32 (2001).
[CrossRef]

B. H. Kolner, "Space-time duality and the theory of temporal imaging," IEEE J. Quantum Electron. 30, 1951-1963 (1994).
[CrossRef]

C. V. Bennett and B. H. Kolner, "Principles of parametric temporal imaging--part I: system configurations," IEEE J. Quantum Electron. 36, 430-437 (2000).
[CrossRef]

C. V. Bennett and B. H. Kolner, "Principles of parametric temporal imaging--Part II: system performance," IEEE J. Quantum Electron. 36, 649-655 (2000).
[CrossRef]

Other

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, 1992).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Geometric relations between the vectors associated with the propagation of the central spatial frequency k 0 .

Fig. 2
Fig. 2

Geometric relations between the vectors associated with the propagation of the spatial frequency k around k 0 .

Fig. 3
Fig. 3

Representation of the local variables r u = k 0 z k z 0 in Eq. (34) and α = k 0 k z 0 = tan γ .

Tables (1)

Tables Icon

Table 1 Equivalent Parameters in Space and Time

Equations (37)

Equations on this page are rendered with MathJax. Learn more.

2 E ̃ ( z , ω ) z 2 + β 2 ( ω ) E ̃ ( z , ω ) = 0 ,
β ( ω ) = ω μ ϵ ( ω ) = ω ν ( ω ) ,
E ( z , t ) = A ( z , t ) exp [ i ( ω 0 t β 0 z ) ] .
E ̃ ( z , ω ) = A ̃ ( z , ω ω 0 ) exp ( i β 0 z ) ,
E ̃ ( z , ω ) = F [ E ( z , t ) ] = + E ( z , t ) exp ( i ω t ) d t .
A ̃ ( z , ω ω 0 ) = A ̃ ( 0 , ω ω 0 ) exp [ i ( β ( ω ) β 0 ) z ] .
β ( ω ) = β 0 + β 1 ( ω ω 0 ) + β 2 2 ! ( ω ω 0 ) 2 + + β n n ! ( ω ω 0 ) n + ,
Ω ω 0 1 ,
A ̃ ( z , Ω ) = A ̃ ( 0 , Ω ) exp [ i ( β 1 Ω + β 2 2 ! Ω 2 + β 3 3 ! Ω 3 + β 4 4 ! Ω 4 + ) z ] .
A ̃ ( z , Ω ) z = i ( β 1 Ω + β 2 2 ! Ω 2 + β 3 3 ! Ω 3 + β 4 4 ! Ω 4 + ) A ̃ ( z , Ω )
A ( z , t ) z = β 1 A ( z , t ) t + i β 2 2 2 A ( z , t ) t 2 + β 3 3 ! 3 A ( z , t ) t 3 i β 4 4 ! 2 A ( z , t ) t 4 + .
τ = t β 1 z
ξ = z ,
A ( ξ , τ ) ξ i β 2 2 2 A ( ξ , τ ) τ 2 β 3 3 ! 3 A ( ξ , τ ) τ 2 + i β 4 4 ! 4 A ( ξ , τ ) τ 4 + = 0 ,
k 0 = k 0 + k z 0 = k x 0 x ̂ + k y 0 y ̂ + k z 0 z ̂ ,
F [ ( 2 + k 0 2 ) E ( r , z ) ] = ( k 2 + k 0 2 ) E ̃ ( k , z ) + 2 E ̃ ( k , z ) z 2 = 0 ,
E ̃ ( k , z ) = F { E ( r , z ) } = + E ( r , z ) exp ( i k r ) d r .
E ̃ ( k , z ) = E ̃ ( k , 0 ) exp [ i ( k 0 2 k 2 ) 1 2 z ]
E ( r , z ) = A ( r , z ) exp [ i ( k 0 r + k z 0 z ) ] .
E ̃ ( k , z ) = A ̃ ( k k 0 , z ) exp ( i k z 0 z ) .
A ̃ ( Δ k , z ) = A ̃ ( Δ k , 0 ) exp { i [ β ( k ) k z 0 ] z } ,
Δ k = k k 0 ,
β ( k ) = ( k 0 2 k 2 ) 1 2 = k ( k 0 2 k 2 1 ) 1 2 = k ν ( k ) ,
ν ( k ) = 1 k 0 2 k 2 1
β ( k ) = k z 0 ( 1 k 2 k 0 2 k z 0 2 ) 1 2 = n = 0 [ 1 n ! ( Δ k k ) n β ( k ) ] k = k 0 = k z 0 1 k z 0 k 0 Δ k 1 2 k z 0 [ Δ k 2 + 1 k z 0 2 ( k 0 Δ k ) 2 ] 1 2 k z 0 3 [ k 0 Δ k 3 + 1 k z 0 2 ( k 0 Δ k ) 3 ] 1 8 k z 0 3 [ Δ k 4 + 6 k z 0 2 ( k 0 Δ k ) 2 Δ k 2 + 5 k z 0 4 ( k 0 Δ k ) 4 ] + ,
β 0 ( k 0 ) = k z 0 ,
β 1 ( k 0 ) = k 0 k z 0 ,
β 2 ( k 0 ) = 1 k z 0 [ 1 + α 2 ( k 0 ) ] ,
β 3 ( k 0 ) = 3 k 0 k z 0 3 [ 1 + α 2 ( k 0 ) ] ,
β 4 ( k 0 ) = 3 k z 0 3 [ 1 + 6 α 2 ( k 0 ) + 5 α 4 ( k 0 ) ] ,
α ( k 0 ) = k 0 k z 0 cos ( θ )
β ( k ) = β 0 + β 1 Δ k + 1 2 ! β 2 Δ k 2 + 1 3 ! β 3 Δ k 3 + 1 4 ! β 4 Δ k 4 + ,
A ( r , z ) z = { 1 k z 0 k 0 i 2 k z 0 [ 2 + 1 k z 0 2 ( k 0 ) 2 ] + 1 2 k z 0 3 [ k 0 3 + 1 k z 0 2 ( k 0 ) 3 ] + i 8 k z 0 3 [ 4 + 6 k z 0 2 ( k 0 ) 2 2 + 5 k z 0 4 ( k 0 ) 4 ] + } A ( r , z ) ,
u = r + β 1 z = r k 0 k z 0 z ,
ξ = z ,
A ( u , z ) z = { i 2 k z 0 [ 2 + 1 k z 0 2 ( k 0 ) 2 ] + 1 2 k z 0 3 [ k 0 3 + 1 k z 0 2 ( k 0 ) 3 ] + i 8 k z 0 3 [ 4 + 6 k z 0 2 ( k 0 ) 2 2 + 5 k z 0 4 ( k 0 ) 4 ] + } A ( u , z ) ,
A ( u x , ξ ) ξ i β 2 2 ! 2 A ( u x , ξ ) u x 2 + β 3 3 ! 3 A ( u x , ξ ) u x 3 + i β 4 4 ! 4 A ( u x , ξ ) u x 4 + = 0 ,

Metrics