Abstract

The typical phase correction term introduced in a diffraction grating-pair is rediscussed. It shows that the correction causes a conceptual difficulty in geometrical optics. A study reveals that Fraunhofer diffraction explains the correction and only mean-phase light rays are allowed for diffraction analysis. Besides, an equivalent phase formulation without correction is recommended.

© 2011 Optical Society of America

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  1. D. Strickland, and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
    [CrossRef]
  2. A. Dubietis, “G. Jonu sauskas, and A. Piskarskas, “Powerful femtosecond pulse generation by chirped and stretched pulse parametric amplification in BBO crystal,” Opt. Commun. 88, 437–440 (1992).
    [CrossRef]
  3. C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, “Compression of femtosecond optical pulses,” Appl. Phys. Lett. 40, 761–763 (1982).
    [CrossRef]
  4. R. L. Fork, C. H. Brito Cruz, P. C. Becker, and C. V. Shank, “Compression of optical pulses to six femtoseconds by using cubic phase compensation,” Opt. Lett. 12, 483–485 (1987).
    [CrossRef] [PubMed]
  5. R. E. Kennedy, A. B. Rulkov, S. V. Popov, and J. R. Taylor, “High-peak-power femtosecond pulse compression with polarization-maintaining ytterbium-doped fiber amplification,” Opt. Lett. 32, 1199–1201 (2007).
    [CrossRef] [PubMed]
  6. B. Schenkel, R. Paschotta, and U. Keller, “Pulse compression with supercontinuum generation in microstructure fibers,” J. Opt. Soc. Am. B 22, 687–693 (2005).
    [CrossRef]
  7. O. E. Martinez, “Achromatic phase matching for second harmonic generation of femtosecond pulses,” IEEE J. Quantum Electron. 25, 2464–2468 (1989).
    [CrossRef]
  8. G. Szabó, and Z. Bor, “Broadband frequency doubler for femtosecond pulses,” Appl. Phys. B 50, 51–54 (1990).
    [CrossRef]
  9. A. V. Smith, “Group-velocity-matched three-wave mixing in birefringent crystals,” Opt. Lett. 26, 719–721 (2001).
    [CrossRef]
  10. S. Ashihara, T. Shimura, and K. Kuroda, “Group-velocity matched second-harmonic generation in tilted quasiphase-matched gratings,” J. Opt. Soc. Am. B 20, 853–856 (2003).
    [CrossRef]
  11. T. Kobayashi, in Femtosecond Optical Frequency Comb: Principle, Operation and Applications, edited by J. Ye and S. T. Cundiff (Springer, Berlin, 2005), pp. 133–175.
    [CrossRef]
  12. E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. 5, 454–458 (1969).
    [CrossRef]
  13. J. D. McMullen, “Analysis of compression of frequency chirped optical pulses,” Appl. Opt. 18, 737–741 (1979).
    [CrossRef] [PubMed]
  14. I. P. Christov, and I. V. Tomov, “Large bandwidth pulse compression with diffraction gratings,” Opt. Commun. 58, 338–342 (1986).
    [CrossRef]
  15. S. D. Brorson, and H. A. Haus, “Geometrical limitations in grating pair pulse compression,” Appl. Opt. 27, 23–25 (1988).
    [CrossRef] [PubMed]
  16. O. E. Martinez, “Grating and prism compressors in the case of finite beam size,” J. Opt. Soc. Am. B 3, 929–934 (1986).
    [CrossRef]
  17. O. E. Martinez, “Matrix Formalism for Pulse Compressors,” IEEE J. Quantum Electron. 24, 2530–2536 (1988).
    [CrossRef]
  18. C. J. Mu, F. Tian, J. T. Bai, and X. Hou, “Matrix formulism calculation of dispersion in a grating compressor,” Acta Photonica Sinica 31, 1116–1119 (2002) (In Chinese).
  19. Z. G. Zhang, T. Yagi, and T. Arisawa, “Ray-tracing model for stretcher dispersion calculation,” Appl. Opt. 36, 3393–3399 (1997).
    [CrossRef] [PubMed]
  20. Z. G. Zhang, and H. Sun, “Calculation and evaluation of dispersions in a femtosecond pulse amplification system,” Acta Physica Sinica 50, 1080–1086 (2000) (In Chinese).
  21. S. D. Brorson, and H. A. Haus, “Diffraction gratings and geometrical optics,” J. Opt. Soc. Am. B 5, 247–248 (1988).
    [CrossRef]
  22. O. E. Martinez, “Pulse distortions in tilted pulse schemes for ultrashort pulses,” Opt. Commun. 59, 229–232 (1986).
    [CrossRef]
  23. S. Akturk, X. Gu, E. Zeek, and R. Trebino, “Pulse-front tilt caused by spatial and temporal chirp,” Opt. Express 12, 4399–4410 (2004).
    [CrossRef] [PubMed]
  24. J. J. Huang, and L. Y. Zhang, “Transformation of few-cycle ultrashort pulsed Gaussian beams by an angular disperser,” J. Phys. B 43, 175601 (2010).
    [CrossRef]
  25. S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, in Optics of Femtosecond Laser Pulses, edited by Y. Atanov (AIP, New York, 1992), pp. 205–206.
  26. M. Born, and E. Wolf, Principles of Optics (Cambridge University Press, 1999), pp. 446–453.

2010

J. J. Huang, and L. Y. Zhang, “Transformation of few-cycle ultrashort pulsed Gaussian beams by an angular disperser,” J. Phys. B 43, 175601 (2010).
[CrossRef]

2007

R. E. Kennedy, A. B. Rulkov, S. V. Popov, and J. R. Taylor, “High-peak-power femtosecond pulse compression with polarization-maintaining ytterbium-doped fiber amplification,” Opt. Lett. 32, 1199–1201 (2007).
[CrossRef] [PubMed]

2005

B. Schenkel, R. Paschotta, and U. Keller, “Pulse compression with supercontinuum generation in microstructure fibers,” J. Opt. Soc. Am. B 22, 687–693 (2005).
[CrossRef]

2004

S. Akturk, X. Gu, E. Zeek, and R. Trebino, “Pulse-front tilt caused by spatial and temporal chirp,” Opt. Express 12, 4399–4410 (2004).
[CrossRef] [PubMed]

2003

S. Ashihara, T. Shimura, and K. Kuroda, “Group-velocity matched second-harmonic generation in tilted quasiphase-matched gratings,” J. Opt. Soc. Am. B 20, 853–856 (2003).
[CrossRef]

2002

C. J. Mu, F. Tian, J. T. Bai, and X. Hou, “Matrix formulism calculation of dispersion in a grating compressor,” Acta Photonica Sinica 31, 1116–1119 (2002) (In Chinese).

2001

A. V. Smith, “Group-velocity-matched three-wave mixing in birefringent crystals,” Opt. Lett. 26, 719–721 (2001).
[CrossRef]

2000

Z. G. Zhang, and H. Sun, “Calculation and evaluation of dispersions in a femtosecond pulse amplification system,” Acta Physica Sinica 50, 1080–1086 (2000) (In Chinese).

1997

Z. G. Zhang, T. Yagi, and T. Arisawa, “Ray-tracing model for stretcher dispersion calculation,” Appl. Opt. 36, 3393–3399 (1997).
[CrossRef] [PubMed]

1992

A. Dubietis, “G. Jonu sauskas, and A. Piskarskas, “Powerful femtosecond pulse generation by chirped and stretched pulse parametric amplification in BBO crystal,” Opt. Commun. 88, 437–440 (1992).
[CrossRef]

1990

G. Szabó, and Z. Bor, “Broadband frequency doubler for femtosecond pulses,” Appl. Phys. B 50, 51–54 (1990).
[CrossRef]

1989

O. E. Martinez, “Achromatic phase matching for second harmonic generation of femtosecond pulses,” IEEE J. Quantum Electron. 25, 2464–2468 (1989).
[CrossRef]

1988

S. D. Brorson, and H. A. Haus, “Geometrical limitations in grating pair pulse compression,” Appl. Opt. 27, 23–25 (1988).
[CrossRef] [PubMed]

S. D. Brorson, and H. A. Haus, “Diffraction gratings and geometrical optics,” J. Opt. Soc. Am. B 5, 247–248 (1988).
[CrossRef]

O. E. Martinez, “Matrix Formalism for Pulse Compressors,” IEEE J. Quantum Electron. 24, 2530–2536 (1988).
[CrossRef]

1987

R. L. Fork, C. H. Brito Cruz, P. C. Becker, and C. V. Shank, “Compression of optical pulses to six femtoseconds by using cubic phase compensation,” Opt. Lett. 12, 483–485 (1987).
[CrossRef] [PubMed]

1986

O. E. Martinez, “Grating and prism compressors in the case of finite beam size,” J. Opt. Soc. Am. B 3, 929–934 (1986).
[CrossRef]

I. P. Christov, and I. V. Tomov, “Large bandwidth pulse compression with diffraction gratings,” Opt. Commun. 58, 338–342 (1986).
[CrossRef]

O. E. Martinez, “Pulse distortions in tilted pulse schemes for ultrashort pulses,” Opt. Commun. 59, 229–232 (1986).
[CrossRef]

1985

D. Strickland, and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

1982

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, “Compression of femtosecond optical pulses,” Appl. Phys. Lett. 40, 761–763 (1982).
[CrossRef]

1979

J. D. McMullen, “Analysis of compression of frequency chirped optical pulses,” Appl. Opt. 18, 737–741 (1979).
[CrossRef] [PubMed]

1969

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

Akturk, S.

S. Akturk, X. Gu, E. Zeek, and R. Trebino, “Pulse-front tilt caused by spatial and temporal chirp,” Opt. Express 12, 4399–4410 (2004).
[CrossRef] [PubMed]

Arisawa, T.

Z. G. Zhang, T. Yagi, and T. Arisawa, “Ray-tracing model for stretcher dispersion calculation,” Appl. Opt. 36, 3393–3399 (1997).
[CrossRef] [PubMed]

Ashihara, S.

S. Ashihara, T. Shimura, and K. Kuroda, “Group-velocity matched second-harmonic generation in tilted quasiphase-matched gratings,” J. Opt. Soc. Am. B 20, 853–856 (2003).
[CrossRef]

Bai, J. T.

C. J. Mu, F. Tian, J. T. Bai, and X. Hou, “Matrix formulism calculation of dispersion in a grating compressor,” Acta Photonica Sinica 31, 1116–1119 (2002) (In Chinese).

Becker, P. C.

R. L. Fork, C. H. Brito Cruz, P. C. Becker, and C. V. Shank, “Compression of optical pulses to six femtoseconds by using cubic phase compensation,” Opt. Lett. 12, 483–485 (1987).
[CrossRef] [PubMed]

Bor, Z.

G. Szabó, and Z. Bor, “Broadband frequency doubler for femtosecond pulses,” Appl. Phys. B 50, 51–54 (1990).
[CrossRef]

Brito Cruz, C. H.

R. L. Fork, C. H. Brito Cruz, P. C. Becker, and C. V. Shank, “Compression of optical pulses to six femtoseconds by using cubic phase compensation,” Opt. Lett. 12, 483–485 (1987).
[CrossRef] [PubMed]

Brorson, S. D.

S. D. Brorson, and H. A. Haus, “Diffraction gratings and geometrical optics,” J. Opt. Soc. Am. B 5, 247–248 (1988).
[CrossRef]

S. D. Brorson, and H. A. Haus, “Geometrical limitations in grating pair pulse compression,” Appl. Opt. 27, 23–25 (1988).
[CrossRef] [PubMed]

Christov, I. P.

I. P. Christov, and I. V. Tomov, “Large bandwidth pulse compression with diffraction gratings,” Opt. Commun. 58, 338–342 (1986).
[CrossRef]

Dubietis, A.

A. Dubietis, “G. Jonu sauskas, and A. Piskarskas, “Powerful femtosecond pulse generation by chirped and stretched pulse parametric amplification in BBO crystal,” Opt. Commun. 88, 437–440 (1992).
[CrossRef]

Fork, R. L.

R. L. Fork, C. H. Brito Cruz, P. C. Becker, and C. V. Shank, “Compression of optical pulses to six femtoseconds by using cubic phase compensation,” Opt. Lett. 12, 483–485 (1987).
[CrossRef] [PubMed]

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, “Compression of femtosecond optical pulses,” Appl. Phys. Lett. 40, 761–763 (1982).
[CrossRef]

Gu, X.

S. Akturk, X. Gu, E. Zeek, and R. Trebino, “Pulse-front tilt caused by spatial and temporal chirp,” Opt. Express 12, 4399–4410 (2004).
[CrossRef] [PubMed]

Haus, H. A.

S. D. Brorson, and H. A. Haus, “Diffraction gratings and geometrical optics,” J. Opt. Soc. Am. B 5, 247–248 (1988).
[CrossRef]

S. D. Brorson, and H. A. Haus, “Geometrical limitations in grating pair pulse compression,” Appl. Opt. 27, 23–25 (1988).
[CrossRef] [PubMed]

Hou, X.

C. J. Mu, F. Tian, J. T. Bai, and X. Hou, “Matrix formulism calculation of dispersion in a grating compressor,” Acta Photonica Sinica 31, 1116–1119 (2002) (In Chinese).

Huang, J. J.

J. J. Huang, and L. Y. Zhang, “Transformation of few-cycle ultrashort pulsed Gaussian beams by an angular disperser,” J. Phys. B 43, 175601 (2010).
[CrossRef]

Keller, U.

B. Schenkel, R. Paschotta, and U. Keller, “Pulse compression with supercontinuum generation in microstructure fibers,” J. Opt. Soc. Am. B 22, 687–693 (2005).
[CrossRef]

Kennedy, R. E.

R. E. Kennedy, A. B. Rulkov, S. V. Popov, and J. R. Taylor, “High-peak-power femtosecond pulse compression with polarization-maintaining ytterbium-doped fiber amplification,” Opt. Lett. 32, 1199–1201 (2007).
[CrossRef] [PubMed]

Kuroda, K.

S. Ashihara, T. Shimura, and K. Kuroda, “Group-velocity matched second-harmonic generation in tilted quasiphase-matched gratings,” J. Opt. Soc. Am. B 20, 853–856 (2003).
[CrossRef]

Martinez, O. E.

O. E. Martinez, “Achromatic phase matching for second harmonic generation of femtosecond pulses,” IEEE J. Quantum Electron. 25, 2464–2468 (1989).
[CrossRef]

O. E. Martinez, “Matrix Formalism for Pulse Compressors,” IEEE J. Quantum Electron. 24, 2530–2536 (1988).
[CrossRef]

O. E. Martinez, “Grating and prism compressors in the case of finite beam size,” J. Opt. Soc. Am. B 3, 929–934 (1986).
[CrossRef]

O. E. Martinez, “Pulse distortions in tilted pulse schemes for ultrashort pulses,” Opt. Commun. 59, 229–232 (1986).
[CrossRef]

McMullen, J. D.

J. D. McMullen, “Analysis of compression of frequency chirped optical pulses,” Appl. Opt. 18, 737–741 (1979).
[CrossRef] [PubMed]

Mourou, G.

D. Strickland, and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

Mu, C. J.

C. J. Mu, F. Tian, J. T. Bai, and X. Hou, “Matrix formulism calculation of dispersion in a grating compressor,” Acta Photonica Sinica 31, 1116–1119 (2002) (In Chinese).

Paschotta, R.

B. Schenkel, R. Paschotta, and U. Keller, “Pulse compression with supercontinuum generation in microstructure fibers,” J. Opt. Soc. Am. B 22, 687–693 (2005).
[CrossRef]

Popov, S. V.

R. E. Kennedy, A. B. Rulkov, S. V. Popov, and J. R. Taylor, “High-peak-power femtosecond pulse compression with polarization-maintaining ytterbium-doped fiber amplification,” Opt. Lett. 32, 1199–1201 (2007).
[CrossRef] [PubMed]

Rulkov, A. B.

R. E. Kennedy, A. B. Rulkov, S. V. Popov, and J. R. Taylor, “High-peak-power femtosecond pulse compression with polarization-maintaining ytterbium-doped fiber amplification,” Opt. Lett. 32, 1199–1201 (2007).
[CrossRef] [PubMed]

Schenkel, B.

B. Schenkel, R. Paschotta, and U. Keller, “Pulse compression with supercontinuum generation in microstructure fibers,” J. Opt. Soc. Am. B 22, 687–693 (2005).
[CrossRef]

Shank, C. V.

R. L. Fork, C. H. Brito Cruz, P. C. Becker, and C. V. Shank, “Compression of optical pulses to six femtoseconds by using cubic phase compensation,” Opt. Lett. 12, 483–485 (1987).
[CrossRef] [PubMed]

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, “Compression of femtosecond optical pulses,” Appl. Phys. Lett. 40, 761–763 (1982).
[CrossRef]

Shimura, T.

S. Ashihara, T. Shimura, and K. Kuroda, “Group-velocity matched second-harmonic generation in tilted quasiphase-matched gratings,” J. Opt. Soc. Am. B 20, 853–856 (2003).
[CrossRef]

Smith, A. V.

A. V. Smith, “Group-velocity-matched three-wave mixing in birefringent crystals,” Opt. Lett. 26, 719–721 (2001).
[CrossRef]

Stolen, R. H.

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, “Compression of femtosecond optical pulses,” Appl. Phys. Lett. 40, 761–763 (1982).
[CrossRef]

Strickland, D.

D. Strickland, and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

Sun, H.

Z. G. Zhang, and H. Sun, “Calculation and evaluation of dispersions in a femtosecond pulse amplification system,” Acta Physica Sinica 50, 1080–1086 (2000) (In Chinese).

Szabó, G.

G. Szabó, and Z. Bor, “Broadband frequency doubler for femtosecond pulses,” Appl. Phys. B 50, 51–54 (1990).
[CrossRef]

Taylor, J. R.

R. E. Kennedy, A. B. Rulkov, S. V. Popov, and J. R. Taylor, “High-peak-power femtosecond pulse compression with polarization-maintaining ytterbium-doped fiber amplification,” Opt. Lett. 32, 1199–1201 (2007).
[CrossRef] [PubMed]

Tian, F.

C. J. Mu, F. Tian, J. T. Bai, and X. Hou, “Matrix formulism calculation of dispersion in a grating compressor,” Acta Photonica Sinica 31, 1116–1119 (2002) (In Chinese).

Tomlinson, W. J.

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, “Compression of femtosecond optical pulses,” Appl. Phys. Lett. 40, 761–763 (1982).
[CrossRef]

Tomov, I. V.

I. P. Christov, and I. V. Tomov, “Large bandwidth pulse compression with diffraction gratings,” Opt. Commun. 58, 338–342 (1986).
[CrossRef]

Treacy, E. B.

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

Trebino, R.

S. Akturk, X. Gu, E. Zeek, and R. Trebino, “Pulse-front tilt caused by spatial and temporal chirp,” Opt. Express 12, 4399–4410 (2004).
[CrossRef] [PubMed]

Yagi, T.

Z. G. Zhang, T. Yagi, and T. Arisawa, “Ray-tracing model for stretcher dispersion calculation,” Appl. Opt. 36, 3393–3399 (1997).
[CrossRef] [PubMed]

Yen, R.

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, “Compression of femtosecond optical pulses,” Appl. Phys. Lett. 40, 761–763 (1982).
[CrossRef]

Zeek, E.

S. Akturk, X. Gu, E. Zeek, and R. Trebino, “Pulse-front tilt caused by spatial and temporal chirp,” Opt. Express 12, 4399–4410 (2004).
[CrossRef] [PubMed]

Zhang, L. Y.

J. J. Huang, and L. Y. Zhang, “Transformation of few-cycle ultrashort pulsed Gaussian beams by an angular disperser,” J. Phys. B 43, 175601 (2010).
[CrossRef]

Zhang, Z. G.

Z. G. Zhang, and H. Sun, “Calculation and evaluation of dispersions in a femtosecond pulse amplification system,” Acta Physica Sinica 50, 1080–1086 (2000) (In Chinese).

Z. G. Zhang, T. Yagi, and T. Arisawa, “Ray-tracing model for stretcher dispersion calculation,” Appl. Opt. 36, 3393–3399 (1997).
[CrossRef] [PubMed]

Acta Photonica Sinica

C. J. Mu, F. Tian, J. T. Bai, and X. Hou, “Matrix formulism calculation of dispersion in a grating compressor,” Acta Photonica Sinica 31, 1116–1119 (2002) (In Chinese).

Acta Physica Sinica

Z. G. Zhang, and H. Sun, “Calculation and evaluation of dispersions in a femtosecond pulse amplification system,” Acta Physica Sinica 50, 1080–1086 (2000) (In Chinese).

Appl. Opt.

Z. G. Zhang, T. Yagi, and T. Arisawa, “Ray-tracing model for stretcher dispersion calculation,” Appl. Opt. 36, 3393–3399 (1997).
[CrossRef] [PubMed]

J. D. McMullen, “Analysis of compression of frequency chirped optical pulses,” Appl. Opt. 18, 737–741 (1979).
[CrossRef] [PubMed]

S. D. Brorson, and H. A. Haus, “Geometrical limitations in grating pair pulse compression,” Appl. Opt. 27, 23–25 (1988).
[CrossRef] [PubMed]

Appl. Phys. B

G. Szabó, and Z. Bor, “Broadband frequency doubler for femtosecond pulses,” Appl. Phys. B 50, 51–54 (1990).
[CrossRef]

Appl. Phys. Lett.

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, “Compression of femtosecond optical pulses,” Appl. Phys. Lett. 40, 761–763 (1982).
[CrossRef]

IEEE J. Quantum Electron.

O. E. Martinez, “Achromatic phase matching for second harmonic generation of femtosecond pulses,” IEEE J. Quantum Electron. 25, 2464–2468 (1989).
[CrossRef]

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

O. E. Martinez, “Matrix Formalism for Pulse Compressors,” IEEE J. Quantum Electron. 24, 2530–2536 (1988).
[CrossRef]

J. Opt. Soc. Am. B

O. E. Martinez, “Grating and prism compressors in the case of finite beam size,” J. Opt. Soc. Am. B 3, 929–934 (1986).
[CrossRef]

S. Ashihara, T. Shimura, and K. Kuroda, “Group-velocity matched second-harmonic generation in tilted quasiphase-matched gratings,” J. Opt. Soc. Am. B 20, 853–856 (2003).
[CrossRef]

B. Schenkel, R. Paschotta, and U. Keller, “Pulse compression with supercontinuum generation in microstructure fibers,” J. Opt. Soc. Am. B 22, 687–693 (2005).
[CrossRef]

S. D. Brorson, and H. A. Haus, “Diffraction gratings and geometrical optics,” J. Opt. Soc. Am. B 5, 247–248 (1988).
[CrossRef]

J. Phys. B

J. J. Huang, and L. Y. Zhang, “Transformation of few-cycle ultrashort pulsed Gaussian beams by an angular disperser,” J. Phys. B 43, 175601 (2010).
[CrossRef]

Opt. Commun.

O. E. Martinez, “Pulse distortions in tilted pulse schemes for ultrashort pulses,” Opt. Commun. 59, 229–232 (1986).
[CrossRef]

D. Strickland, and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

A. Dubietis, “G. Jonu sauskas, and A. Piskarskas, “Powerful femtosecond pulse generation by chirped and stretched pulse parametric amplification in BBO crystal,” Opt. Commun. 88, 437–440 (1992).
[CrossRef]

I. P. Christov, and I. V. Tomov, “Large bandwidth pulse compression with diffraction gratings,” Opt. Commun. 58, 338–342 (1986).
[CrossRef]

Opt. Express

S. Akturk, X. Gu, E. Zeek, and R. Trebino, “Pulse-front tilt caused by spatial and temporal chirp,” Opt. Express 12, 4399–4410 (2004).
[CrossRef] [PubMed]

Opt. Lett.

R. L. Fork, C. H. Brito Cruz, P. C. Becker, and C. V. Shank, “Compression of optical pulses to six femtoseconds by using cubic phase compensation,” Opt. Lett. 12, 483–485 (1987).
[CrossRef] [PubMed]

R. E. Kennedy, A. B. Rulkov, S. V. Popov, and J. R. Taylor, “High-peak-power femtosecond pulse compression with polarization-maintaining ytterbium-doped fiber amplification,” Opt. Lett. 32, 1199–1201 (2007).
[CrossRef] [PubMed]

A. V. Smith, “Group-velocity-matched three-wave mixing in birefringent crystals,” Opt. Lett. 26, 719–721 (2001).
[CrossRef]

Other

T. Kobayashi, in Femtosecond Optical Frequency Comb: Principle, Operation and Applications, edited by J. Ye and S. T. Cundiff (Springer, Berlin, 2005), pp. 133–175.
[CrossRef]

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, in Optics of Femtosecond Laser Pulses, edited by Y. Atanov (AIP, New York, 1992), pp. 205–206.

M. Born, and E. Wolf, Principles of Optics (Cambridge University Press, 1999), pp. 446–453.

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Figures (4)

Fig. 1
Fig. 1

Grating-pair arrangement for pulse compression (a) and schematic diagram of Treacy’s phase correction (b). Light path calculation starts and ends at the equiphase plane Z = 0 for the incident and output rays where the frequency ω′ is slightly smaller than ω. DD′, EE′, FF′, HH′ represent symmetrically sampled equiphase planes.

Fig. 2
Fig. 2

Principle of the diffraction grating where blazed grooves are simply shown for an analysis of the phase variation of a pencil of diffracted rays in one unit. Phase difference exist between the three sampled ray pairs 1 − 1, 2 − 2, 3 − 3. The incident and diffracted angles are the same as those of the second grating in Fig. 1(a).

Fig. 3
Fig. 3

Schematic show of a diffracted ray between two parallel gratings in which mean-phase points (denoted by a subscript S ) are illustrated as a reference for phase correction. Here, an illegal light path PABQ should be replaced by a correct representative path PA + A′SkQ′ where A locates at a mean-phase point.

Fig. 4
Fig. 4

Light paths of two frequencies inside a grating-pair similar to those in Fig. 1(a), where δθ is the angle between the diffracted directions of a ray ω and a referred ray ω0.

Equations (9)

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sin ( γ θ ) + sin ( γ ) = 2 π m c ω d
p = b [ 1 + cos ( θ ) ]
ϕ 0 ( ω ) = ω c b [ 1 + cos ( θ ) ] .
ϕ T ( ω ) = ω c b [ 1 + cos ( θ ) ] + R ( ω )
R ( ω ) = 2 π G d tan ( γ θ )
U ( ω , z ) = C x 0 x 1 F ( x ) exp [ i ω z ( x ) / c ] d x
U ( ω , z s ) = U 0 exp [ i ω z s / c ] , U 0 = C F | x 0 x 1 exp [ i ω z ( x ) / c ] d x | .
ϕ F ( ω ) = ϕ 0 ( ω ) 2 π δ / d .
ϕ ( ω ) = ω c b 0 [ cos ( θ ) + cos ( δ θ ) ] , b 0 = b ( ω = ω 0 ) .

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