Abstract

Nonlinear chirped pulse compression can be theoretically achieved to any order by using a nonplane grating with adequate groove spacing. We evaluate the holographic recording of a grating that compensates to the quadratic chirp. A suitable design is found, and the building tolerances are analyzed.

© 1996 Optical Society of America

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References

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  1. I. P. Christov, “Generation and propagation of ultrashort optical pulses,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1991), Vol. 29, pp. 199–291.
    [CrossRef]
  2. J. M. Simon, S. A. Ledesma, C. C. Iemmi, D. E. Martinez, “General compressor for ultrashort pulses with nonlinear chirp,” Opt. Lett. 16, 1704–1706 (1991).
    [CrossRef] [PubMed]
  3. D. Marcuse, “Pulse distortion in single-mode fibers,”Appl. Opt. 19, 1653–1660 (1980).
    [CrossRef] [PubMed]

1991 (1)

1980 (1)

Appl. Opt. (1)

Opt. Lett. (1)

Other (1)

I. P. Christov, “Generation and propagation of ultrashort optical pulses,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1991), Vol. 29, pp. 199–291.
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Proposed compressor. The coordinate origin is at the center of grating G1, and f is the focal length of the parabolic mirror. Since the system is free of astigmatism, the center of the HOE must be at the Petzval sphere and hence it is shifted by z 0 in the z direction.

Fig. 2
Fig. 2

Location of the sources for recording. The coordinates of the recording sources are indicated. The arrows point in the directions of displacement for which the mistaken positioning was considered. In such cases the HOE was rotated to keep the Littrow incidence condition.

Fig. 3
Fig. 3

Solid curve represents both the original and well-corrected pulses. The dashed curve shows the incompletely corrected pulse when the hologram was recorded with a 3-mm error in the source location.

Fig. 4
Fig. 4

Pulse after fiber broadening. The origin of time is arbitrary.

Fig. 5
Fig. 5

Group front delays at the exit of the compressor for central frequency.

Tables (2)

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Table 1 Group Path Delays in Millimeters for the Principal Ray as a Function of Wavelength a

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Table 2 Lateral Deviations of the Principal Ray at the Exit of the Compressor as a Function of Wavelength at Single and Double Passes

Equations (12)

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x x 0 = D ( λ λ 0 ) .
τ c ( ω ) = d Φ / d ω = L c = L 0 2 ĝ ( ω ) c ,
τ f ( ω ) = z β 0 + z β 0 ( ω ω 0 ) + ½ z β 0 ( ω ω 0 ) 2 ,
g ( x x 0 ) = a ( x x 0 ) + b ( x x 0 ) 2 ,
a = β 0 z c 2 2 2 π D λ 0 2 , b = β 0 z c 2 2 2 π D 2 λ 0 3 β 0 z c 3 4 4 π 2 D 2 λ 0 4 .
d N / d x = 2 λ d g / d x ,
d N d x = 2 λ [ a + 2 b ( x x 0 ) ] .
d N d x = 2 a λ 0 + 2 ( 2 b λ 0 a D λ 0 2 ) ( x x 0 ) .
N λ c = ( O 1 P O 2 P ) ( O 1 A O 2 A ) = { [ ( x 1 x ) 2 + ( z 1 z ) 2 ] 1 / 2 [ ( x 1 x ) 2 + ( z 2 z ) 2 ] 1 / 2 } { [ ( x 1 x 0 ) 2 + ( z 1 z 0 ) 2 ] 1 / 2 [ ( x 2 x 0 ) 2 + ( z 2 z 0 ) 2 ] 1 / 2 } .
d N d x = 1 λ c [ ( α 1 α 2 ) a ( γ 1 γ 2 ) ] + 1 λ c [ ( a 2 + 1 ) ( 1 ρ 1 1 ρ 2 ) 2 b ( γ 1 γ 2 ) ( α 1 + a γ 1 ) 2 ρ 1 + ( α 2 + a γ 2 ) 2 ρ 2 ] ( x x 0 ) ,
a i = x i x 0 ρ i , γ i = z i z 0 ρ i , i = 1 , 2 .
Φ ( ω k ) Φ 0 = i = 1 k ( d Φ d ω ) i Δ ω = ( Δ path ) i c Δ ω ,

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