Abstract

The grating and prism compressors are studied for the case of finite beam size by using the Kirchhoff–Fresnel integral and an amplitude transfer operator for the grating and prism. The results show that, even for well-collimated beams, pulse broadening may occur (mainly because of the wavelength dependence of the lateral walk-off). Methods to avoid the different types of distortions appearing in these systems are discussed.

© 1986 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. B. Treacy, IEEE J. Quantum Electron. QE-5, 454–458 (1969).
    [CrossRef]
  2. B. Nikolaus, D. Grischkowsky, Appl. Phys. Lett. 42, 1–2 (1983).
    [CrossRef]
  3. C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, W. J. Tomlinson, Appl. Phys. Lett. 40, 761–763 (1982).
    [CrossRef]
  4. A. M. Johnson, R. H. Stolen, W. M. Simpson, Appl. Phys. Lett. 44, 729–731 (1984).
    [CrossRef]
  5. W. J. Tomlinson, R. H. Stolen, C. V. Shank, J. Opt. Soc. Am. B 1, 139–143 (1984).
    [CrossRef]
  6. J. G. Fujimoto, A. M. Weiner, E. P. Ippen, Appl. Phys. Lett. 44, 832–834 (1984).
    [CrossRef]
  7. O. E. Martinez, J. P. Gordon, R. L. Fork, J. Opt. Soc. Am. A 1, 1003–1008 (1984).
    [CrossRef]
  8. J. D. McMullen, Appl. Opt. 18, 737–741 (1979).
    [CrossRef] [PubMed]
  9. J. M. Halbout, D. Grischkowsky, Appl. Phys. Lett. 45, 1281–1283 (1984).
    [CrossRef]
  10. W. K. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, J. A. Valdmanis, Appl. Phys. Lett. 46, 1120 (1985).
    [CrossRef]
  11. See, for example, R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).
  12. R. L. Fork, O. E. Martinez, J. P. Gordon, Opt. Lett. 9, 150–153 (1984).
    [CrossRef] [PubMed]
  13. M. Abramowitz, I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1970), p. 302.

1985 (1)

W. K. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, J. A. Valdmanis, Appl. Phys. Lett. 46, 1120 (1985).
[CrossRef]

1984 (6)

R. L. Fork, O. E. Martinez, J. P. Gordon, Opt. Lett. 9, 150–153 (1984).
[CrossRef] [PubMed]

A. M. Johnson, R. H. Stolen, W. M. Simpson, Appl. Phys. Lett. 44, 729–731 (1984).
[CrossRef]

W. J. Tomlinson, R. H. Stolen, C. V. Shank, J. Opt. Soc. Am. B 1, 139–143 (1984).
[CrossRef]

J. G. Fujimoto, A. M. Weiner, E. P. Ippen, Appl. Phys. Lett. 44, 832–834 (1984).
[CrossRef]

O. E. Martinez, J. P. Gordon, R. L. Fork, J. Opt. Soc. Am. A 1, 1003–1008 (1984).
[CrossRef]

J. M. Halbout, D. Grischkowsky, Appl. Phys. Lett. 45, 1281–1283 (1984).
[CrossRef]

1983 (1)

B. Nikolaus, D. Grischkowsky, Appl. Phys. Lett. 42, 1–2 (1983).
[CrossRef]

1982 (1)

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, W. J. Tomlinson, Appl. Phys. Lett. 40, 761–763 (1982).
[CrossRef]

1979 (1)

1969 (1)

E. B. Treacy, IEEE J. Quantum Electron. QE-5, 454–458 (1969).
[CrossRef]

Burckhardt, C. B.

See, for example, R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

Collier, R. J.

See, for example, R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

Downer, M. C.

W. K. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, J. A. Valdmanis, Appl. Phys. Lett. 46, 1120 (1985).
[CrossRef]

Fork, R. L.

W. K. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, J. A. Valdmanis, Appl. Phys. Lett. 46, 1120 (1985).
[CrossRef]

O. E. Martinez, J. P. Gordon, R. L. Fork, J. Opt. Soc. Am. A 1, 1003–1008 (1984).
[CrossRef]

R. L. Fork, O. E. Martinez, J. P. Gordon, Opt. Lett. 9, 150–153 (1984).
[CrossRef] [PubMed]

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, W. J. Tomlinson, Appl. Phys. Lett. 40, 761–763 (1982).
[CrossRef]

Fujimoto, J. G.

J. G. Fujimoto, A. M. Weiner, E. P. Ippen, Appl. Phys. Lett. 44, 832–834 (1984).
[CrossRef]

Gordon, J. P.

Grischkowsky, D.

J. M. Halbout, D. Grischkowsky, Appl. Phys. Lett. 45, 1281–1283 (1984).
[CrossRef]

B. Nikolaus, D. Grischkowsky, Appl. Phys. Lett. 42, 1–2 (1983).
[CrossRef]

Halbout, J. M.

J. M. Halbout, D. Grischkowsky, Appl. Phys. Lett. 45, 1281–1283 (1984).
[CrossRef]

Ippen, E. P.

J. G. Fujimoto, A. M. Weiner, E. P. Ippen, Appl. Phys. Lett. 44, 832–834 (1984).
[CrossRef]

Johnson, A. M.

A. M. Johnson, R. H. Stolen, W. M. Simpson, Appl. Phys. Lett. 44, 729–731 (1984).
[CrossRef]

Knox, W. K.

W. K. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, J. A. Valdmanis, Appl. Phys. Lett. 46, 1120 (1985).
[CrossRef]

Lin, L. H.

See, for example, R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

Martinez, O. E.

McMullen, J. D.

Nikolaus, B.

B. Nikolaus, D. Grischkowsky, Appl. Phys. Lett. 42, 1–2 (1983).
[CrossRef]

Shank, C. V.

W. K. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, J. A. Valdmanis, Appl. Phys. Lett. 46, 1120 (1985).
[CrossRef]

W. J. Tomlinson, R. H. Stolen, C. V. Shank, J. Opt. Soc. Am. B 1, 139–143 (1984).
[CrossRef]

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, W. J. Tomlinson, Appl. Phys. Lett. 40, 761–763 (1982).
[CrossRef]

Simpson, W. M.

A. M. Johnson, R. H. Stolen, W. M. Simpson, Appl. Phys. Lett. 44, 729–731 (1984).
[CrossRef]

Stolen, R. H.

W. K. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, J. A. Valdmanis, Appl. Phys. Lett. 46, 1120 (1985).
[CrossRef]

A. M. Johnson, R. H. Stolen, W. M. Simpson, Appl. Phys. Lett. 44, 729–731 (1984).
[CrossRef]

W. J. Tomlinson, R. H. Stolen, C. V. Shank, J. Opt. Soc. Am. B 1, 139–143 (1984).
[CrossRef]

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, W. J. Tomlinson, Appl. Phys. Lett. 40, 761–763 (1982).
[CrossRef]

Tomlinson, W. J.

W. J. Tomlinson, R. H. Stolen, C. V. Shank, J. Opt. Soc. Am. B 1, 139–143 (1984).
[CrossRef]

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, W. J. Tomlinson, Appl. Phys. Lett. 40, 761–763 (1982).
[CrossRef]

Treacy, E. B.

E. B. Treacy, IEEE J. Quantum Electron. QE-5, 454–458 (1969).
[CrossRef]

Valdmanis, J. A.

W. K. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, J. A. Valdmanis, Appl. Phys. Lett. 46, 1120 (1985).
[CrossRef]

Weiner, A. M.

J. G. Fujimoto, A. M. Weiner, E. P. Ippen, Appl. Phys. Lett. 44, 832–834 (1984).
[CrossRef]

Yen, R.

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, W. J. Tomlinson, Appl. Phys. Lett. 40, 761–763 (1982).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (6)

J. M. Halbout, D. Grischkowsky, Appl. Phys. Lett. 45, 1281–1283 (1984).
[CrossRef]

W. K. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, J. A. Valdmanis, Appl. Phys. Lett. 46, 1120 (1985).
[CrossRef]

B. Nikolaus, D. Grischkowsky, Appl. Phys. Lett. 42, 1–2 (1983).
[CrossRef]

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, W. J. Tomlinson, Appl. Phys. Lett. 40, 761–763 (1982).
[CrossRef]

A. M. Johnson, R. H. Stolen, W. M. Simpson, Appl. Phys. Lett. 44, 729–731 (1984).
[CrossRef]

J. G. Fujimoto, A. M. Weiner, E. P. Ippen, Appl. Phys. Lett. 44, 832–834 (1984).
[CrossRef]

IEEE J. Quantum Electron. (1)

E. B. Treacy, IEEE J. Quantum Electron. QE-5, 454–458 (1969).
[CrossRef]

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

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

Opt. Lett. (1)

Other (2)

M. Abramowitz, I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1970), p. 302.

See, for example, R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

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 (4)

Fig. 1
Fig. 1

Diffraction grating. Definition of angles θ, γ and axes x1 and x2. Notice that x1 is normal to the input beam and x2 to the output beam. The y axis does not change. B, Prism disperser. Group-velocity dispersion introduced by the material itself is ignored. It would just introduce an additional frequency-dependent phase factor because of the transit through a distance e of material. This term can easily be added at the end if necessary.

Fig. 2
Fig. 2

Single-pair grating compressor. The different parameters are defined. The path indicated is for the central frequency at the beam center. BW, position of the waist of the input beam.

Fig. 3
Fig. 3

Ratio between the obtained and the optimum pulse widths as a function of the parameter N = λz/(πσ2) for different optimum compression factors C.

Fig. 4
Fig. 4

Two-pair compressor. Reflecting the beam back into the compressor is equivalent to placing a second pair that is inverted with respect to the first one. The solid line indicates the path for the central wavelength and the dashed line that for a different one. In this manner the compression factor is doubled and the lateral spectral walk-off compensated for.

Equations (44)

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

Δ θ = α Δ γ + β ω .
A ( ξ , ω ) = a ( x , ω ) exp ( i 2 π ξ x ) d x .
a ( x , ω ) = exp ( i 2 π ξ 0 x ) .
Δ γ sin ( Δ γ ) = ξ 0 λ,
A T ( ξ , ω ) = b 1 A ( ξ / α , ω ) .
a T ( x 2 , ω ) = b 1 exp ( i k β ω x 2 ) F 1 [ A T ( ξ / α ) ] = b 1 exp ( i k β ω x 2 ) a ( x 2 α ) ,
a ( x , y , ω ) = a i ( ω ) exp [ i k ( x 2 + y 2 ) 2 q ( d ) ] ,
q ( z ) = z + i π σ 2 / λ ,
a 2 ( x 2 , y 2 , ω ) = b 2 a i exp ( i k β ω x 2 ) exp [ i k ( x 2 2 α 2 + y 2 ) 2 q ( d ) ] .
sin γ + sin θ = m λ / d ,
α = cos γ 0 cos θ 0 ,
β = m 2 π c d cos θ 0 .
α = 1 ,
β = λ 2 π c d n d λ .
a ( x 3 , y 3 , z , ω ) = i λ z a ( x 2 , y 2 , 0 , ω ) × exp { i π λ z [ ( x 3 x 2 ) 2 + ( y 3 y 2 ) 2 ] } d x 2 d y 2 .
exp [ ( c 1 t 2 + 2 c 2 t + c 3 ) ] d t = ( π / c 1 ) 1 / 2 × exp [ ( c 2 2 c 1 c 3 ) / c 1 ] , Re ( c 1 ) > 0
c 1 = i [ k α 2 2 q ( d ) + k 2 z ] , c 2 = ( i k 2 z x 3 + i k β ω 2 ) , c 3 = i k x 3 2 2 z .
a ( x 3 , ω ) = b 3 a i exp ( i k x 3 2 2 z ) exp [ i k z q ( d ) 2 q ( d + α 2 z ) ( x 2 2 z 2 + β 2 ω 2 + 2 x β ω z ) ] .
Δ γ = β α ω + Δ θ α ,
α = 1 α , β = β α .
a 4 ( x 4 ) = b 4 exp ( i k β α ω x 4 ) a 3 ( x 4 / α ) ,
a 4 ( x 4 , ω ) = b 4 a i exp [ i k ( x 4 + α β w z ) 2 q ( d + α 2 z ) ] exp ( i k 2 β 2 w 2 z ) ,
a 4 ( x 4 , y , ω ) = b 4 a i exp ( i k β 2 2 w 2 z ) × exp { i k 2 [ ( x 4 + α β ω z ) q ( d + α 2 z ) + y 2 q ( d + z ) ] } .
d 2 ϕ d ω 2 = τ 2 4 = 2 a 0 = k β 2 z .
α 2 = 1.
a ( x , y , z , ω ) = b 5 a i exp ( i k β 2 ω 2 2 z ) × exp { i k 2 [ ( x + β ω z ) 2 + y 2 ] q ( d + z + z ) } .
ϕ ( z ) = k β 2 ω 2 z 2 k β 2 ω 2 z 2 ( d + z + z ) z ( d + z + z ) 2 + π 2 σ 4 / λ 2 .
( d + z + z ) z ( d + z + z ) 2 + π 2 σ 4 / λ 2 1.
( d + z + z ) π σ 2 λ ,
z π σ 2 λ .
a ( x , y , ω ) = b a i exp ( i k β 2 ω 2 z / 2 ) exp { [ ( x + β ω z ) 2 + y 2 ] / σ 2 } .
A i ( t ) = exp [ t 2 ( 1 i δ ) / τ 2 ] .
a i ( ω ) = [ π / ( 1 + i δ ) ] 1 / 2 exp ( ω 2 τ 0 2 4 ) exp ( i ω 2 τ 0 2 δ 4 ) ,
τ 0 2 = τ 2 1 + δ 2 .
a ( x , y , ω ) = ( π / 1 + i δ ) exp { [ τ 0 2 ω 2 4 + ( x + β ω z ) 2 + y 2 σ 2 ] } .
A ( x , y , t ) = b exp { [ x 2 ( 1 + u ) σ 2 + y 2 σ 2 ] exp [ t 2 τ 0 2 ( 1 + u ) ] } × exp [ i u x t ( 1 + u ) β z ] ,
u = 4 β 2 z 2 τ 0 2 σ 2 .
τ f = τ 0 ( 1 + u ) 1 / 2 .
2 π Δ ν = u x ( 1 + u ) β z .
τ f τ 0 = σ x σ y .
τ f τ 0 = ( 1 + δ N ) = 1 + ( C 2 1 ) 1 / 2 N ,
C = ( 1 + δ 2 ) 1 / 2 = τ 2 / τ 0 2
N = λ z π σ 2
a ( x , y , ω ) = a i b exp ( i k β 2 ω 2 z ) × exp { i k 2 [ x 2 q ( d + z 1 + z 2 + 2 α 2 z ) + y 2 q ( d + z 1 + z 2 + 2 z ) ] } ,

Metrics