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.

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References

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

2010 (1)

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 (1)

2005 (1)

2004 (1)

2003 (1)

2002 (1)

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 (1)

2000 (1)

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 (1)

1992 (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]

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.

1990 (1)

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

1989 (1)

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

1988 (3)

1987 (1)

1986 (3)

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. Commnun. 59, 229–232 (1986).
[CrossRef]

1985 (1)

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

1982 (1)

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 (1)

1969 (1)

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

Akhmanov, S. A.

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.

Akturk, S.

Arisawa, T.

Ashihara, S.

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.

Bor, Z.

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

Born, M.

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

Brito Cruz, C. H.

Brorson, S. D.

Chirkin, A. S.

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.

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.

Haus, H. A.

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]

Jonu sauskas, G.

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]

Keller, U.

Kennedy, R. E.

Kobayashi, T.

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]

Kuroda, K.

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, “Pulse distortions in tilted pulse schemes for ultrashort pulses,” Opt. Commnun. 59, 229–232 (1986).
[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]

McMullen, J. D.

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.

Piskarskas, 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]

Popov, S. V.

Rulkov, A. B.

Schenkel, B.

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.

Smith, A. V.

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.

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.

Vysloukh, V. A.

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.

Wolf, E.

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

Yagi, T.

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.

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 (1)

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 (1)

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. (3)

Appl. Phys. B (1)

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

Appl. Phys. Lett. (1)

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. (3)

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 (4)

J. Phys. B (1)

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. Commnun. (1)

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

Opt. Commun. (3)

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 (1)

Opt. Lett. (3)

Optics of Femtosecond Laser Pulses (1)

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.

Other (2)

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

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]

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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)

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

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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