Abstract

Dispersion delay lines (DDLs) are used for dispersion compensation in ultrafast optics. Note that the correct determination of the time delay of DDLs is based on the tautochronism principle: in an optical system consisting of refracting and reflecting elements the time delay between any two wavefronts is the same for all rays. But for diffraction gratings this principle is not valid; the time delay between the wavefronts of incident and diffracted waves for different light rays is different. However, fortunately, a pair of diffraction gratings can be combined so that the input and the output wavefronts of the system still satisfy the tautochronism principle. There are only two such grating systems: Treacy’s system and Martinez’s system. Both these systems are closely related to each other: in Martinez’s system one can see virtual Treacy’s system. Note that according to the tautochronism principle, dispersion Martinez’s system and virtual Treacy’s system are equal in value but opposite in sign.

© 2012 Optical Society of America

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References

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  1. “Group Delay Dispersion,” in Encyclopedia of Laser Physics and Technology, http://www.rp-photonics.com/group_delay_dispersion.html
  2. E. B. Treacy, “Compression of picosecond light pulse,” Phys. Lett. 28A, 34–35 (1968).
  3. E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. QE-5, 454–458 (1969).
  4. O. E. Martinez, “3000 Times grating compressor with positive group veloсity dispersion: application to fiber compensation in 1.3–1.6 μm region,” IEEE J. Quantum Electron. QE-23, 59–64 (1987).
    [CrossRef]
  5. O. E. Martinez, “Design of high-power ultrashort pulse amplifiers by expansion and recompression,” IEEE J. Quantum Electron. QE-23, 1385–1387 (1987).
    [CrossRef]
  6. A. V. Gitin, “Application of the Wigner function and matrix optics to describe variations in the shape of ultrashort laser pulses propagating through linear optical systems,” Quantum Electron. 36, 376–382 (2006).
    [CrossRef]
  7. G. S. Landsberg, Optics (Nauka, 1976) (in Russian).
  8. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).
  9. A. V. Gitin, “Geometrical method of calculation of a stretcher’s dispersion, which allows to consider influence of parameters of the optical system,” Quantum Electron. 38, 1021–1026 (2008).
    [CrossRef]
  10. W. B. Wetherell, “The calculation of image quality”, in Applied Optics and Optical Engineering, Vol. VIII (Academic, 1980, pp. 256–269.
  11. M. Nagibina, Interference and Diffraction of Light(Mashinostroenie, 1985) (in Russian).
  12. F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill, 1957).
  13. A. V. Gitin, “Zero-distance pulse front as a characteristic of the two-grating compressor,” Opt.Commun. 283, 1090–1095 (2010).
    [CrossRef]
  14. P. A. Naik and A. K. Sharma, “Calculation of higher order group velocity dispersion in a grating pulse stretcher/compressor using recursion method,” J. Opt. 29, 105–113 (2000).
  15. I. Walmsley, I. Waxer, and C. Dorrer, “The role of dispersion in ultrafast optics,” Rev. Sci. Instrum. 72, 1–29 (2001).
    [CrossRef]

2010 (1)

A. V. Gitin, “Zero-distance pulse front as a characteristic of the two-grating compressor,” Opt.Commun. 283, 1090–1095 (2010).
[CrossRef]

2008 (1)

A. V. Gitin, “Geometrical method of calculation of a stretcher’s dispersion, which allows to consider influence of parameters of the optical system,” Quantum Electron. 38, 1021–1026 (2008).
[CrossRef]

2006 (1)

A. V. Gitin, “Application of the Wigner function and matrix optics to describe variations in the shape of ultrashort laser pulses propagating through linear optical systems,” Quantum Electron. 36, 376–382 (2006).
[CrossRef]

2001 (1)

I. Walmsley, I. Waxer, and C. Dorrer, “The role of dispersion in ultrafast optics,” Rev. Sci. Instrum. 72, 1–29 (2001).
[CrossRef]

2000 (1)

P. A. Naik and A. K. Sharma, “Calculation of higher order group velocity dispersion in a grating pulse stretcher/compressor using recursion method,” J. Opt. 29, 105–113 (2000).

1987 (2)

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

O. E. Martinez, “Design of high-power ultrashort pulse amplifiers by expansion and recompression,” IEEE J. Quantum Electron. QE-23, 1385–1387 (1987).
[CrossRef]

1969 (1)

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

1968 (1)

E. B. Treacy, “Compression of picosecond light pulse,” Phys. Lett. 28A, 34–35 (1968).

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).

Dorrer, C.

I. Walmsley, I. Waxer, and C. Dorrer, “The role of dispersion in ultrafast optics,” Rev. Sci. Instrum. 72, 1–29 (2001).
[CrossRef]

Gitin, A. V.

A. V. Gitin, “Zero-distance pulse front as a characteristic of the two-grating compressor,” Opt.Commun. 283, 1090–1095 (2010).
[CrossRef]

A. V. Gitin, “Geometrical method of calculation of a stretcher’s dispersion, which allows to consider influence of parameters of the optical system,” Quantum Electron. 38, 1021–1026 (2008).
[CrossRef]

A. V. Gitin, “Application of the Wigner function and matrix optics to describe variations in the shape of ultrashort laser pulses propagating through linear optical systems,” Quantum Electron. 36, 376–382 (2006).
[CrossRef]

Jenkins, F. A.

F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill, 1957).

Landsberg, G. S.

G. S. Landsberg, Optics (Nauka, 1976) (in Russian).

Martinez, O. E.

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

O. E. Martinez, “Design of high-power ultrashort pulse amplifiers by expansion and recompression,” IEEE J. Quantum Electron. QE-23, 1385–1387 (1987).
[CrossRef]

Nagibina, M.

M. Nagibina, Interference and Diffraction of Light(Mashinostroenie, 1985) (in Russian).

Naik, P. A.

P. A. Naik and A. K. Sharma, “Calculation of higher order group velocity dispersion in a grating pulse stretcher/compressor using recursion method,” J. Opt. 29, 105–113 (2000).

Sharma, A. K.

P. A. Naik and A. K. Sharma, “Calculation of higher order group velocity dispersion in a grating pulse stretcher/compressor using recursion method,” J. Opt. 29, 105–113 (2000).

Treacy, E. B.

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

E. B. Treacy, “Compression of picosecond light pulse,” Phys. Lett. 28A, 34–35 (1968).

Walmsley, I.

I. Walmsley, I. Waxer, and C. Dorrer, “The role of dispersion in ultrafast optics,” Rev. Sci. Instrum. 72, 1–29 (2001).
[CrossRef]

Waxer, I.

I. Walmsley, I. Waxer, and C. Dorrer, “The role of dispersion in ultrafast optics,” Rev. Sci. Instrum. 72, 1–29 (2001).
[CrossRef]

Wetherell, W. B.

W. B. Wetherell, “The calculation of image quality”, in Applied Optics and Optical Engineering, Vol. VIII (Academic, 1980, pp. 256–269.

White, H. E.

F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill, 1957).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).

IEEE J. Quantum Electron. (3)

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

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

O. E. Martinez, “Design of high-power ultrashort pulse amplifiers by expansion and recompression,” IEEE J. Quantum Electron. QE-23, 1385–1387 (1987).
[CrossRef]

J. Opt. (1)

P. A. Naik and A. K. Sharma, “Calculation of higher order group velocity dispersion in a grating pulse stretcher/compressor using recursion method,” J. Opt. 29, 105–113 (2000).

Opt.Commun. (1)

A. V. Gitin, “Zero-distance pulse front as a characteristic of the two-grating compressor,” Opt.Commun. 283, 1090–1095 (2010).
[CrossRef]

Phys. Lett. (1)

E. B. Treacy, “Compression of picosecond light pulse,” Phys. Lett. 28A, 34–35 (1968).

Quantum Electron. (2)

A. V. Gitin, “Application of the Wigner function and matrix optics to describe variations in the shape of ultrashort laser pulses propagating through linear optical systems,” Quantum Electron. 36, 376–382 (2006).
[CrossRef]

A. V. Gitin, “Geometrical method of calculation of a stretcher’s dispersion, which allows to consider influence of parameters of the optical system,” Quantum Electron. 38, 1021–1026 (2008).
[CrossRef]

Rev. Sci. Instrum. (1)

I. Walmsley, I. Waxer, and C. Dorrer, “The role of dispersion in ultrafast optics,” Rev. Sci. Instrum. 72, 1–29 (2001).
[CrossRef]

Other (6)

“Group Delay Dispersion,” in Encyclopedia of Laser Physics and Technology, http://www.rp-photonics.com/group_delay_dispersion.html

W. B. Wetherell, “The calculation of image quality”, in Applied Optics and Optical Engineering, Vol. VIII (Academic, 1980, pp. 256–269.

M. Nagibina, Interference and Diffraction of Light(Mashinostroenie, 1985) (in Russian).

F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill, 1957).

G. S. Landsberg, Optics (Nauka, 1976) (in Russian).

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).

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Figures (7)

Fig. 1.
Fig. 1.

Tautochronism principle (а) in general case, (b) for the perfect optical system.

Fig. 2.
Fig. 2.

Parallel beam of monochromatic rays of width D, deflected by a diffraction grating. (a) The zero order (l=0):BA=AB, (b) the external first-order ((l=1):BA=AB+N·λ, (c) the internal first-order (l=1):BA=ABN·λ, where N=D/(dcosγ).

Fig. 3.
Fig. 3.

Treacy’s system and transformation in it: (a) plane monochromatic wave; (b) polychromatic ray. The red ray is shown by the double dash-and-dot line and the blue ray is shown by the dash-and-dot line.

Fig. 4.
Fig. 4.

Martinez’s system as a telescope with a negative unity angular magnification and transformation of a monochromatic plane wave in it: (a) 1=f, (b) 1<f. All rays from object point P which pass through the perfect optical system must pass through the image point P and light takes identically the same time traveling from the point P to the point P along all ray paths traversing the optical system.

Fig. 5.
Fig. 5.

Martinez’s system as an imaging optical system with a negative unity linear magnification and the transformation of the polychromatic ray in it: (a) l=f, (b) l<f.

Fig. 6.
Fig. 6.

Combined Treacy andMartinez system and its equivalent scheme.

Fig. 7.
Fig. 7.

Combining Treacy’s system and Martinez’s system with the help of their reference planes.

Equations (14)

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

U˜(ω)=Ftω{U(t)}andU(t)=Fωt1{U˜(ω)}.
U˜out(ω)=U˜in(ω)·f˜(ω).
f˜(ω)=exp[iφ(ω)]
φ(ω)=ωt,
t=OPLc.
OPL=γn(x,y,z)ds,
t=OPL.
d(sinγ+sinβ)=lλ,
tTr|FM|+|MM|=Z1+cos(γ+β)cosβ,
tVir.Tr(ω)=tTr(ω).
t=L+to,
t=L+tMar(ω)+tTr(ω).
tMar(ω)+tTr(ω)=to.
tMar(ω)=totVir.Tr(ω).

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