Abstract

We propose a ray-tracing model that provides a clear physical picture and simple formulas for grating pair stretcher dispersion calculations. With this model we can easily demonstrate why and to what extent the stretcher and compressor are opposite quantitatively without using a Fourier transform. The dispersion calculation shows that the spherical aberration in the stretcher decreases fourth-order dispersion compared with an aberration-free stretcher. In a chirped pulse amplification system, this fourth order can help to reduce residual fourth-order dispersion. The effect of the finite beam size and the misalignment are also considered.

© 1997 Optical Society of America

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References

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  1. P. F. Curley, Ch. Spielmann, T. Brabec, F. Krausz, E. Wintner, A. J. Schmidt, “Operation of a femtosecond solitary laser in the vicinity of zero group-delay dispersion,” Opt. Lett. 18, 54–56 (1993).
    [CrossRef] [PubMed]
  2. M. T. Asaki, C-P. Huang, D. Garvey, J. Zhou, H. C. Kapteyn, M. M. Murnane, “Generation of 11-fs pulses from a self-mode-locked Ti:sapphire laser,” Opt. Lett. 18, 977–979 (1993).
    [CrossRef] [PubMed]
  3. B. Proctor, F. Wise, “Generation of 13-fs pulses from a modelocked Ti:Al2O3 laser with reduced third order dispersion,” Appl. Phys. Lett. 62, 470–472 (1993).
    [CrossRef]
  4. A. Stingl, M. Lenzner, Ch. Spielmann, F. Krausz, R. Szipöcs, “Sub-10-fs mirror-dispersion-controlled Ti:sapphire laser,” Opt. Lett. 20, 602–604 (1995).
    [CrossRef] [PubMed]
  5. M. Lenzner, Ch. Spielmann, E. Wintner, F. Krausz, A. J. Schmidt, “Sub-20-fs, kilohertz-repetition-rate Ti:sapphire amplifier,” Opt. Lett. 20, 1397–1399 (1995).
    [CrossRef] [PubMed]
  6. T. Joo, Y. Jia, G. R. Fleming, “Ti:sapphire regenerative amplifier for ultrashort high-power multikilohertz pulses without an external stretcher,” Opt. Lett. 20, 389–391 (1995).
    [CrossRef] [PubMed]
  7. J. Zhou, C. P. Huang, M. M. Murnane, H. C. Kapteyn, “Amplification of 26-fs, 2-TW pulses near the gain-narrowing limit in Ti:sapphire,” Opt. Lett. 20, 64–66 (1995).
    [CrossRef] [PubMed]
  8. K. Wynne, G. D. Reid, R. M. Hochstrasser, Regenerative amplification of 30 fs pulses in Ti:sapphire at 5 kHz,” Opt. Lett. 19, 895–897 (1994).
    [CrossRef]
  9. B. E. Lemoff, C. P. J. Barty, “Quintic-phase-limited, spatially uniform expansion and recompression of ultrashort optical pulses,” Opt. Lett. 18, 1651–1653 (1993).
    [CrossRef] [PubMed]
  10. C. P. J. Barty, T. Guo, C. Le Blanc, F. Raksi, C. Rose-Petruck, J. Squier, K. R. Wilson, V. V. Yakovlev, K. Yamakawa, “Generation of 18-fs, multiterawatt pulses by regenerative pulse shaping and chirped-pulse amplification,” Opt. Lett. 21, 668–670 (1996).
    [CrossRef] [PubMed]
  11. G. Cheriaux, P. Rousseau, F. Salin, J. P. Chambaret, B. Walker, L. F. Dimauro, “Aberration-free stretcher design for ultra-short pulse amplification,” Opt. Lett. 21, 414–416 (1996).
    [CrossRef] [PubMed]
  12. J. V. Rudd, G. Korn, S. Kane, J. Squier, G. Mourou, P. Bado, “Chirped-pulse amplification of 55-fs pulses at 1-kHz repetition rate in a Ti:Al2O3 regenerative amplifier,” Opt. Lett. 18, 2044–2046 (1993).
    [CrossRef]
  13. O. E. Martinez, “3000 times grating compressor with positive group velocity dispersion: application to fiber compensation in the 1.3–1.6 µm region,” IEEE J. Quantum Electron. QE-23, 59–64 (1987).
    [CrossRef]
  14. Z. Zhang, S. Harayama, T. Yagi, T. Arisawa, “Vertical chirp in grating stretcher and compressor,” Appl. Phys. Lett. 67, 176–178 (1995).
    [CrossRef]
  15. E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. QE-5, 454–458 (1969).
    [CrossRef]

1996 (2)

1995 (5)

1994 (1)

1993 (5)

1987 (1)

O. E. Martinez, “3000 times grating compressor with positive group velocity dispersion: application to fiber compensation in the 1.3–1.6 µm region,” IEEE J. Quantum Electron. QE-23, 59–64 (1987).
[CrossRef]

1969 (1)

E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. QE-5, 454–458 (1969).
[CrossRef]

Arisawa, T.

Z. Zhang, S. Harayama, T. Yagi, T. Arisawa, “Vertical chirp in grating stretcher and compressor,” Appl. Phys. Lett. 67, 176–178 (1995).
[CrossRef]

Asaki, M. T.

Bado, P.

Barty, C. P. J.

Brabec, T.

Chambaret, J. P.

Cheriaux, G.

Curley, P. F.

Dimauro, L. F.

Fleming, G. R.

Garvey, D.

Guo, T.

Harayama, S.

Z. Zhang, S. Harayama, T. Yagi, T. Arisawa, “Vertical chirp in grating stretcher and compressor,” Appl. Phys. Lett. 67, 176–178 (1995).
[CrossRef]

Hochstrasser, R. M.

Huang, C. P.

Huang, C-P.

Jia, Y.

Joo, T.

Kane, S.

Kapteyn, H. C.

Korn, G.

Krausz, F.

Le Blanc, C.

Lemoff, B. E.

Lenzner, M.

Martinez, O. E.

O. E. Martinez, “3000 times grating compressor with positive group velocity dispersion: application to fiber compensation in the 1.3–1.6 µm region,” IEEE J. Quantum Electron. QE-23, 59–64 (1987).
[CrossRef]

Mourou, G.

Murnane, M. M.

Proctor, B.

B. Proctor, F. Wise, “Generation of 13-fs pulses from a modelocked Ti:Al2O3 laser with reduced third order dispersion,” Appl. Phys. Lett. 62, 470–472 (1993).
[CrossRef]

Raksi, F.

Reid, G. D.

Rose-Petruck, C.

Rousseau, P.

Rudd, J. V.

Salin, F.

Schmidt, A. J.

Spielmann, Ch.

Squier, J.

Stingl, A.

Szipöcs, R.

Treacy, E. B.

E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. QE-5, 454–458 (1969).
[CrossRef]

Walker, B.

Wilson, K. R.

Wintner, E.

Wise, F.

B. Proctor, F. Wise, “Generation of 13-fs pulses from a modelocked Ti:Al2O3 laser with reduced third order dispersion,” Appl. Phys. Lett. 62, 470–472 (1993).
[CrossRef]

Wynne, K.

Yagi, T.

Z. Zhang, S. Harayama, T. Yagi, T. Arisawa, “Vertical chirp in grating stretcher and compressor,” Appl. Phys. Lett. 67, 176–178 (1995).
[CrossRef]

Yakovlev, V. V.

Yamakawa, K.

Zhang, Z.

Z. Zhang, S. Harayama, T. Yagi, T. Arisawa, “Vertical chirp in grating stretcher and compressor,” Appl. Phys. Lett. 67, 176–178 (1995).
[CrossRef]

Zhou, J.

Appl. Phys. Lett. (2)

Z. Zhang, S. Harayama, T. Yagi, T. Arisawa, “Vertical chirp in grating stretcher and compressor,” Appl. Phys. Lett. 67, 176–178 (1995).
[CrossRef]

B. Proctor, F. Wise, “Generation of 13-fs pulses from a modelocked Ti:Al2O3 laser with reduced third order dispersion,” Appl. Phys. Lett. 62, 470–472 (1993).
[CrossRef]

IEEE J. Quantum Electron. (2)

O. E. Martinez, “3000 times grating compressor with positive group velocity dispersion: application to fiber compensation in the 1.3–1.6 µm region,” IEEE J. Quantum Electron. QE-23, 59–64 (1987).
[CrossRef]

E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. QE-5, 454–458 (1969).
[CrossRef]

Opt. Lett. (11)

P. F. Curley, Ch. Spielmann, T. Brabec, F. Krausz, E. Wintner, A. J. Schmidt, “Operation of a femtosecond solitary laser in the vicinity of zero group-delay dispersion,” Opt. Lett. 18, 54–56 (1993).
[CrossRef] [PubMed]

M. T. Asaki, C-P. Huang, D. Garvey, J. Zhou, H. C. Kapteyn, M. M. Murnane, “Generation of 11-fs pulses from a self-mode-locked Ti:sapphire laser,” Opt. Lett. 18, 977–979 (1993).
[CrossRef] [PubMed]

B. E. Lemoff, C. P. J. Barty, “Quintic-phase-limited, spatially uniform expansion and recompression of ultrashort optical pulses,” Opt. Lett. 18, 1651–1653 (1993).
[CrossRef] [PubMed]

K. Wynne, G. D. Reid, R. M. Hochstrasser, Regenerative amplification of 30 fs pulses in Ti:sapphire at 5 kHz,” Opt. Lett. 19, 895–897 (1994).
[CrossRef]

J. Zhou, C. P. Huang, M. M. Murnane, H. C. Kapteyn, “Amplification of 26-fs, 2-TW pulses near the gain-narrowing limit in Ti:sapphire,” Opt. Lett. 20, 64–66 (1995).
[CrossRef] [PubMed]

T. Joo, Y. Jia, G. R. Fleming, “Ti:sapphire regenerative amplifier for ultrashort high-power multikilohertz pulses without an external stretcher,” Opt. Lett. 20, 389–391 (1995).
[CrossRef] [PubMed]

A. Stingl, M. Lenzner, Ch. Spielmann, F. Krausz, R. Szipöcs, “Sub-10-fs mirror-dispersion-controlled Ti:sapphire laser,” Opt. Lett. 20, 602–604 (1995).
[CrossRef] [PubMed]

M. Lenzner, Ch. Spielmann, E. Wintner, F. Krausz, A. J. Schmidt, “Sub-20-fs, kilohertz-repetition-rate Ti:sapphire amplifier,” Opt. Lett. 20, 1397–1399 (1995).
[CrossRef] [PubMed]

G. Cheriaux, P. Rousseau, F. Salin, J. P. Chambaret, B. Walker, L. F. Dimauro, “Aberration-free stretcher design for ultra-short pulse amplification,” Opt. Lett. 21, 414–416 (1996).
[CrossRef] [PubMed]

C. P. J. Barty, T. Guo, C. Le Blanc, F. Raksi, C. Rose-Petruck, J. Squier, K. R. Wilson, V. V. Yakovlev, K. Yamakawa, “Generation of 18-fs, multiterawatt pulses by regenerative pulse shaping and chirped-pulse amplification,” Opt. Lett. 21, 668–670 (1996).
[CrossRef] [PubMed]

J. V. Rudd, G. Korn, S. Kane, J. Squier, G. Mourou, P. Bado, “Chirped-pulse amplification of 55-fs pulses at 1-kHz repetition rate in a Ti:Al2O3 regenerative amplifier,” Opt. Lett. 18, 2044–2046 (1993).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Single-mirror stretcher and compressor model for dispersion calculation.

Fig. 2
Fig. 2

Demonstration of a grating pair as either a compressor or a stretcher. λ l and λ s represent the long and short wavelength components, respectively.

Fig. 3
Fig. 3

Stretcher model with a folded telescope.

Fig. 4
Fig. 4

Derivative of the aberration term dA/dθ1 with respect to the relative diffraction angle θ1 for various grating positions.

Fig. 5
Fig. 5

Stretcher model with a misaligned folding mirror. ε represents the misalignment angle.

Fig. 6
Fig. 6

Normalized group delay dispersion (single pass, s 0 = s c = R/4, 1400-lines/mm grating groove density) as a function of wavelength for misalignment angles of -2°, 0°, and +2°. The dashed curve represents the group delay dispersion of the aberration-free stretcher.

Fig. 7
Fig. 7

Output angle deviation from an incident angle for misalignment angles of -4°, -2°, 0°, +2°, and +4°.

Fig. 8
Fig. 8

Ray-tracing paths for an open grating–telescope stretcher. Dashed curve and lines represent the image part of the mirror, grating, and paths when the telescope is folded.

Equations (57)

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τ=dΦdω=pc=b1+cos θc,
sin γ+sinγ-θ=λ/d,
diΦdωi=di-1dωi-1pc.
p=PA+ACB+BE+EQ=4R-b1+cos θ,
PA=R,
ACB=2R-b,
BE=R-bcos θ,
EQ=R1-cos θ,
τ=dΦdω=4Rc-b1+cos θc.
γ-θ=γ-θ0+θ1.
p=p0+p1+p2+p3+p4+p5,
p0=PB=l0,
p1=BD=l1,
p2=DEH=l3-l2,
p3=HI=HA-AI=l4-b,
p4=IJ=p3 cosθ0+θ4,
p5=JQ=LO-KM-MO=R-l4 cosθ+θ4+R-s4cos θ0.
b=s4-sccosγ-θ0cosγ-θ0-θ4=R1-sin ϕ4sin θ4-scRcosγ-θ0cosγ-θ0-θ4=Gcosγ-θ0-θ4,
G=R1-sin ϕ4sin θ4-scRcosγ-θ0
s4=R-s1.
b=R-s1-sccosγ-θ0cosγ-θ0-θ4.
b0=R-s1-sc=2f-s1-sc
p0=l0=R1-1-s1Rcos θ0,
p1=Rsinθ1-ϕ1sin θ1,
p2=Rsinθ3-ϕ3sin θ3+sinθ1-ϕ1sin θ2,
p3=Rsinθ3-ϕ3sin θ4-b,
p=R2-1-s1Rcos θ0+sinθ1-ϕ11sin θ1+1sin θ2+sinθ3-ϕ31sin θ3+1sin θ4+sin ϕ4sin θ4 cos θ0-1-sin ϕ4sin θ4-scR×cosγ-θ0cosγ-θ0-θ41+cosθ0+θ4.
C=2-1-s1Rcos θ0,
A=sinθ1-ϕ11sin θ1+1sin θ2+sinθ3-ϕ3×1sin θ3+1sin θ4+sin ϕ4sin θ4 cos θ0,
D=1-sin ϕ4cos θ4-scRcosγ-θ0cosγ-θ0-θ4×1+cosθ0+θ4=bR1+cosθ0+θ4.
p=RC+A-D.
ϕ1=θ1,
ϕ2=-ϕ1=-θ1,
θ2=-θ1,
ϕ4=-ϕ3=0,
θ4=θ1.
p=R4-cos θ0-b1+cosθ0+θ1.
p=3R-R cos θ0.
Δs1=σ2cosγ-θ0-θ1cos γ sin θ1,
p=R1-1-s1Rcos θ0+sinθ1-ϕ11sin θ1+1sin θ2+sinθ3-ϕ31sin θ3+1sin θ4-sin ϕ4sin θ4 cos θ0-1-sin ϕ4sin θ4-scR×cosγ-θ0cosγ-θ0-θ41+cosθ0+θ4+12+sin ϕ2sin θ2cos εcosθ3+ε1-sin θ3sin θ3,
θ3=θ3+2ε.
Am=12+sin ϕ2sin θ2cos εcosθ3+ε1-sin θ3sin θ3.
pm=RC+A+Am-D.
sin ϕ1=1-s1Rsin θ1,
ϕ2=-ϕ1,
θ2=θ1-2ϕ1,
s2R=1-sin ϕ2sin θ2,
l1=Rsinθ1-ϕ1sin θ1,
l2=Rsinθ1-ϕ1sin θ2.
θ3=-θ2,
s3R=1+s2R,
sin ϕ3=1-s3Rsin θ3,
ϕ4=-ϕ3,
θ4=θ3-2ϕ3,
s4R=1-sin ϕ4sin θ4,
l3=Rsinθ3-ϕ3sin θ3,
l4=Rsinθ3-ϕ3sin θ4.

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