Abstract

We provide a detailed analytical expression of group-delay dispersion (GDD) and third-order dispersion (TOD) for a reflection grism-pair compressor without the first-order approximation of grating diffraction. The analytical expressions can be used to design a grism-pair compressor for compensating the dispersive material without ray tracing. Furthermore, the dispersion performance of the grism pair compressor, depending on compressor parameters, is comprehensively analyzed. Results are shown that we can adjust several parameters to obtain a certain GDD and TOD, such as the incidence angle of the beam, refractive index of the prism, grating constant, and the separation of the grism pair.

© 2012 Optical Society of America

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  1. N. V. Vysotina, N. N. Rosanov, and V. E. Yashin, “Modeling of systems for broadening of spectrum of petawatt laser pulses and for their nonlinear compression,” Opt. Spectrosc. 110, 973–981 (2011).
    [CrossRef]
  2. L. Kuznetsova, F. W. Wise, S. Kane, and J. Squier, “Chirped-pulse amplification near the gain-narrowing limit of Yb-doped fiber using a reflection grism compressor,” Appl. Phys. B 88, 515–518 (2007).
    [CrossRef]
  3. M. Aoyama, K. Yamakawa, Y. Akahane, J. Ma, N. Inoue, H. Ueda, and H. Kiriyama, “0.85 PW, 33 fs Ti:sapphire laser,” Opt. Lett. 28, 1594–1596 (2003).
    [CrossRef]
  4. M. Pittman, S. Ferré, J. P. Rousseau, L. Notebaert, J. P. Chambaret, and G. Chériaux, “Design and characterization of a near-diffraction-limited femtosecond 100 TW 10 Hz high-intensity laser system,” Appl. Phys. B 74, 529–535 (2002).
    [CrossRef]
  5. E. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. 5, 454–458 (1969).
    [CrossRef]
  6. R. Fork, O. Martinez, and J. Gordon, “Negative dispersion using pairs of prisms,” Opt. Lett. 9, 150–152 (1984).
    [CrossRef]
  7. R. L. Fork, C. Cruz, P. Becker, and C. V. Shank, “Compression of optical pulses to six femtoseconds by using cubic phase compensation,” Opt. Lett. 12, 483–485 (1987).
    [CrossRef]
  8. P. Tournois, “New diffraction grating pair with very linear dispersion for laser pulse compression,” Electron. Lett. 29, 1414–1415 (1993).
    [CrossRef]
  9. S. Kane and J. Squier, “Grism-pair stretcher compressor system for simultaneous second-and third-order dispersion compensation in chirped-pulse amplification,” J. Opt. Soc. Am. B 14, 661–665 (1997).
    [CrossRef]
  10. E. A. Gibson, D. M. Gaudiosi, H. C. Kapteyn, R. Jimenez, S. Kane, R. Huff, C. Durfee, and J. Squier, “Efficient reflection grisms for pulse compression and dispersion compensation of femtosecond pulses,” Opt. Lett. 31, 3363–3365 (2006).
    [CrossRef]
  11. S. Kane, R. Huff, J. Squier, E. Gibson, R. Jimenez, C. Durfee, F. Tortajada, H. Dinger, and B. Touzet, “Design and fabrication of efficient reflection grisms for pulse compression and dispersion compensation,” presented at the Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies (Optical Society of America, 2006), paper CThA5.
  12. S. Kane and J. Squier, “Grating compensation of third-order material dispersion in the normal dispersion regime: Sub-100-fs chirped-pulse amplification using a fiber stretcher and grating-pair compressor,” IEEE J. Quantum Electron. 31, 2052–2057 (1995).
    [CrossRef]
  13. D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 55, 447–449 (1985).
    [CrossRef]
  14. S. Kane, B. Touzet, C. Durfee, and J. Squier, “Analytical expressions and simplified formulas for GVD and TOD of reflection grism compressors,” presented at the Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies (Optical Society of America, 2008), paper JTuA66.
  15. K. Osvay, A. P. Kovács, G. Kurdi, Z. Heiner, M. Divall, J. Klebniczki, and I. E. Ferincz, “Measurement of non-compensated angular dispersion and the subsequent temporal lengthening of femtosecond pulses in a CPA laser,” Opt. Commun. 248, 201–209 (2005).
    [CrossRef]
  16. J. Zheng and H. Zacharias, “Design considerations for a compact grism stretcher for non-collinear optical parametric chirped-pulse amplification,” Appl. Phys. B 96, 445–452 (2009).
    [CrossRef]

2011

N. V. Vysotina, N. N. Rosanov, and V. E. Yashin, “Modeling of systems for broadening of spectrum of petawatt laser pulses and for their nonlinear compression,” Opt. Spectrosc. 110, 973–981 (2011).
[CrossRef]

2009

J. Zheng and H. Zacharias, “Design considerations for a compact grism stretcher for non-collinear optical parametric chirped-pulse amplification,” Appl. Phys. B 96, 445–452 (2009).
[CrossRef]

2007

L. Kuznetsova, F. W. Wise, S. Kane, and J. Squier, “Chirped-pulse amplification near the gain-narrowing limit of Yb-doped fiber using a reflection grism compressor,” Appl. Phys. B 88, 515–518 (2007).
[CrossRef]

2006

2005

K. Osvay, A. P. Kovács, G. Kurdi, Z. Heiner, M. Divall, J. Klebniczki, and I. E. Ferincz, “Measurement of non-compensated angular dispersion and the subsequent temporal lengthening of femtosecond pulses in a CPA laser,” Opt. Commun. 248, 201–209 (2005).
[CrossRef]

2003

2002

M. Pittman, S. Ferré, J. P. Rousseau, L. Notebaert, J. P. Chambaret, and G. Chériaux, “Design and characterization of a near-diffraction-limited femtosecond 100 TW 10 Hz high-intensity laser system,” Appl. Phys. B 74, 529–535 (2002).
[CrossRef]

1997

1995

S. Kane and J. Squier, “Grating compensation of third-order material dispersion in the normal dispersion regime: Sub-100-fs chirped-pulse amplification using a fiber stretcher and grating-pair compressor,” IEEE J. Quantum Electron. 31, 2052–2057 (1995).
[CrossRef]

1993

P. Tournois, “New diffraction grating pair with very linear dispersion for laser pulse compression,” Electron. Lett. 29, 1414–1415 (1993).
[CrossRef]

1987

1985

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 55, 447–449 (1985).
[CrossRef]

1984

1969

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

Akahane, Y.

Aoyama, M.

Becker, P.

Chambaret, J. P.

M. Pittman, S. Ferré, J. P. Rousseau, L. Notebaert, J. P. Chambaret, and G. Chériaux, “Design and characterization of a near-diffraction-limited femtosecond 100 TW 10 Hz high-intensity laser system,” Appl. Phys. B 74, 529–535 (2002).
[CrossRef]

Chériaux, G.

M. Pittman, S. Ferré, J. P. Rousseau, L. Notebaert, J. P. Chambaret, and G. Chériaux, “Design and characterization of a near-diffraction-limited femtosecond 100 TW 10 Hz high-intensity laser system,” Appl. Phys. B 74, 529–535 (2002).
[CrossRef]

Cruz, C.

Dinger, H.

S. Kane, R. Huff, J. Squier, E. Gibson, R. Jimenez, C. Durfee, F. Tortajada, H. Dinger, and B. Touzet, “Design and fabrication of efficient reflection grisms for pulse compression and dispersion compensation,” presented at the Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies (Optical Society of America, 2006), paper CThA5.

Divall, M.

K. Osvay, A. P. Kovács, G. Kurdi, Z. Heiner, M. Divall, J. Klebniczki, and I. E. Ferincz, “Measurement of non-compensated angular dispersion and the subsequent temporal lengthening of femtosecond pulses in a CPA laser,” Opt. Commun. 248, 201–209 (2005).
[CrossRef]

Durfee, C.

E. A. Gibson, D. M. Gaudiosi, H. C. Kapteyn, R. Jimenez, S. Kane, R. Huff, C. Durfee, and J. Squier, “Efficient reflection grisms for pulse compression and dispersion compensation of femtosecond pulses,” Opt. Lett. 31, 3363–3365 (2006).
[CrossRef]

S. Kane, R. Huff, J. Squier, E. Gibson, R. Jimenez, C. Durfee, F. Tortajada, H. Dinger, and B. Touzet, “Design and fabrication of efficient reflection grisms for pulse compression and dispersion compensation,” presented at the Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies (Optical Society of America, 2006), paper CThA5.

S. Kane, B. Touzet, C. Durfee, and J. Squier, “Analytical expressions and simplified formulas for GVD and TOD of reflection grism compressors,” presented at the Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies (Optical Society of America, 2008), paper JTuA66.

Ferincz, I. E.

K. Osvay, A. P. Kovács, G. Kurdi, Z. Heiner, M. Divall, J. Klebniczki, and I. E. Ferincz, “Measurement of non-compensated angular dispersion and the subsequent temporal lengthening of femtosecond pulses in a CPA laser,” Opt. Commun. 248, 201–209 (2005).
[CrossRef]

Ferré, S.

M. Pittman, S. Ferré, J. P. Rousseau, L. Notebaert, J. P. Chambaret, and G. Chériaux, “Design and characterization of a near-diffraction-limited femtosecond 100 TW 10 Hz high-intensity laser system,” Appl. Phys. B 74, 529–535 (2002).
[CrossRef]

Fork, R.

Fork, R. L.

Gaudiosi, D. M.

Gibson, E.

S. Kane, R. Huff, J. Squier, E. Gibson, R. Jimenez, C. Durfee, F. Tortajada, H. Dinger, and B. Touzet, “Design and fabrication of efficient reflection grisms for pulse compression and dispersion compensation,” presented at the Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies (Optical Society of America, 2006), paper CThA5.

Gibson, E. A.

Gordon, J.

Heiner, Z.

K. Osvay, A. P. Kovács, G. Kurdi, Z. Heiner, M. Divall, J. Klebniczki, and I. E. Ferincz, “Measurement of non-compensated angular dispersion and the subsequent temporal lengthening of femtosecond pulses in a CPA laser,” Opt. Commun. 248, 201–209 (2005).
[CrossRef]

Huff, R.

E. A. Gibson, D. M. Gaudiosi, H. C. Kapteyn, R. Jimenez, S. Kane, R. Huff, C. Durfee, and J. Squier, “Efficient reflection grisms for pulse compression and dispersion compensation of femtosecond pulses,” Opt. Lett. 31, 3363–3365 (2006).
[CrossRef]

S. Kane, R. Huff, J. Squier, E. Gibson, R. Jimenez, C. Durfee, F. Tortajada, H. Dinger, and B. Touzet, “Design and fabrication of efficient reflection grisms for pulse compression and dispersion compensation,” presented at the Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies (Optical Society of America, 2006), paper CThA5.

Inoue, N.

Jimenez, R.

E. A. Gibson, D. M. Gaudiosi, H. C. Kapteyn, R. Jimenez, S. Kane, R. Huff, C. Durfee, and J. Squier, “Efficient reflection grisms for pulse compression and dispersion compensation of femtosecond pulses,” Opt. Lett. 31, 3363–3365 (2006).
[CrossRef]

S. Kane, R. Huff, J. Squier, E. Gibson, R. Jimenez, C. Durfee, F. Tortajada, H. Dinger, and B. Touzet, “Design and fabrication of efficient reflection grisms for pulse compression and dispersion compensation,” presented at the Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies (Optical Society of America, 2006), paper CThA5.

Kane, S.

L. Kuznetsova, F. W. Wise, S. Kane, and J. Squier, “Chirped-pulse amplification near the gain-narrowing limit of Yb-doped fiber using a reflection grism compressor,” Appl. Phys. B 88, 515–518 (2007).
[CrossRef]

E. A. Gibson, D. M. Gaudiosi, H. C. Kapteyn, R. Jimenez, S. Kane, R. Huff, C. Durfee, and J. Squier, “Efficient reflection grisms for pulse compression and dispersion compensation of femtosecond pulses,” Opt. Lett. 31, 3363–3365 (2006).
[CrossRef]

S. Kane and J. Squier, “Grism-pair stretcher compressor system for simultaneous second-and third-order dispersion compensation in chirped-pulse amplification,” J. Opt. Soc. Am. B 14, 661–665 (1997).
[CrossRef]

S. Kane and J. Squier, “Grating compensation of third-order material dispersion in the normal dispersion regime: Sub-100-fs chirped-pulse amplification using a fiber stretcher and grating-pair compressor,” IEEE J. Quantum Electron. 31, 2052–2057 (1995).
[CrossRef]

S. Kane, R. Huff, J. Squier, E. Gibson, R. Jimenez, C. Durfee, F. Tortajada, H. Dinger, and B. Touzet, “Design and fabrication of efficient reflection grisms for pulse compression and dispersion compensation,” presented at the Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies (Optical Society of America, 2006), paper CThA5.

S. Kane, B. Touzet, C. Durfee, and J. Squier, “Analytical expressions and simplified formulas for GVD and TOD of reflection grism compressors,” presented at the Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies (Optical Society of America, 2008), paper JTuA66.

Kapteyn, H. C.

Kiriyama, H.

Klebniczki, J.

K. Osvay, A. P. Kovács, G. Kurdi, Z. Heiner, M. Divall, J. Klebniczki, and I. E. Ferincz, “Measurement of non-compensated angular dispersion and the subsequent temporal lengthening of femtosecond pulses in a CPA laser,” Opt. Commun. 248, 201–209 (2005).
[CrossRef]

Kovács, A. P.

K. Osvay, A. P. Kovács, G. Kurdi, Z. Heiner, M. Divall, J. Klebniczki, and I. E. Ferincz, “Measurement of non-compensated angular dispersion and the subsequent temporal lengthening of femtosecond pulses in a CPA laser,” Opt. Commun. 248, 201–209 (2005).
[CrossRef]

Kurdi, G.

K. Osvay, A. P. Kovács, G. Kurdi, Z. Heiner, M. Divall, J. Klebniczki, and I. E. Ferincz, “Measurement of non-compensated angular dispersion and the subsequent temporal lengthening of femtosecond pulses in a CPA laser,” Opt. Commun. 248, 201–209 (2005).
[CrossRef]

Kuznetsova, L.

L. Kuznetsova, F. W. Wise, S. Kane, and J. Squier, “Chirped-pulse amplification near the gain-narrowing limit of Yb-doped fiber using a reflection grism compressor,” Appl. Phys. B 88, 515–518 (2007).
[CrossRef]

Ma, J.

Martinez, O.

Mourou, G.

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 55, 447–449 (1985).
[CrossRef]

Notebaert, L.

M. Pittman, S. Ferré, J. P. Rousseau, L. Notebaert, J. P. Chambaret, and G. Chériaux, “Design and characterization of a near-diffraction-limited femtosecond 100 TW 10 Hz high-intensity laser system,” Appl. Phys. B 74, 529–535 (2002).
[CrossRef]

Osvay, K.

K. Osvay, A. P. Kovács, G. Kurdi, Z. Heiner, M. Divall, J. Klebniczki, and I. E. Ferincz, “Measurement of non-compensated angular dispersion and the subsequent temporal lengthening of femtosecond pulses in a CPA laser,” Opt. Commun. 248, 201–209 (2005).
[CrossRef]

Pittman, M.

M. Pittman, S. Ferré, J. P. Rousseau, L. Notebaert, J. P. Chambaret, and G. Chériaux, “Design and characterization of a near-diffraction-limited femtosecond 100 TW 10 Hz high-intensity laser system,” Appl. Phys. B 74, 529–535 (2002).
[CrossRef]

Rosanov, N. N.

N. V. Vysotina, N. N. Rosanov, and V. E. Yashin, “Modeling of systems for broadening of spectrum of petawatt laser pulses and for their nonlinear compression,” Opt. Spectrosc. 110, 973–981 (2011).
[CrossRef]

Rousseau, J. P.

M. Pittman, S. Ferré, J. P. Rousseau, L. Notebaert, J. P. Chambaret, and G. Chériaux, “Design and characterization of a near-diffraction-limited femtosecond 100 TW 10 Hz high-intensity laser system,” Appl. Phys. B 74, 529–535 (2002).
[CrossRef]

Shank, C. V.

Squier, J.

L. Kuznetsova, F. W. Wise, S. Kane, and J. Squier, “Chirped-pulse amplification near the gain-narrowing limit of Yb-doped fiber using a reflection grism compressor,” Appl. Phys. B 88, 515–518 (2007).
[CrossRef]

E. A. Gibson, D. M. Gaudiosi, H. C. Kapteyn, R. Jimenez, S. Kane, R. Huff, C. Durfee, and J. Squier, “Efficient reflection grisms for pulse compression and dispersion compensation of femtosecond pulses,” Opt. Lett. 31, 3363–3365 (2006).
[CrossRef]

S. Kane and J. Squier, “Grism-pair stretcher compressor system for simultaneous second-and third-order dispersion compensation in chirped-pulse amplification,” J. Opt. Soc. Am. B 14, 661–665 (1997).
[CrossRef]

S. Kane and J. Squier, “Grating compensation of third-order material dispersion in the normal dispersion regime: Sub-100-fs chirped-pulse amplification using a fiber stretcher and grating-pair compressor,” IEEE J. Quantum Electron. 31, 2052–2057 (1995).
[CrossRef]

S. Kane, R. Huff, J. Squier, E. Gibson, R. Jimenez, C. Durfee, F. Tortajada, H. Dinger, and B. Touzet, “Design and fabrication of efficient reflection grisms for pulse compression and dispersion compensation,” presented at the Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies (Optical Society of America, 2006), paper CThA5.

S. Kane, B. Touzet, C. Durfee, and J. Squier, “Analytical expressions and simplified formulas for GVD and TOD of reflection grism compressors,” presented at the Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies (Optical Society of America, 2008), paper JTuA66.

Strickland, D.

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 55, 447–449 (1985).
[CrossRef]

Tortajada, F.

S. Kane, R. Huff, J. Squier, E. Gibson, R. Jimenez, C. Durfee, F. Tortajada, H. Dinger, and B. Touzet, “Design and fabrication of efficient reflection grisms for pulse compression and dispersion compensation,” presented at the Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies (Optical Society of America, 2006), paper CThA5.

Tournois, P.

P. Tournois, “New diffraction grating pair with very linear dispersion for laser pulse compression,” Electron. Lett. 29, 1414–1415 (1993).
[CrossRef]

Touzet, B.

S. Kane, R. Huff, J. Squier, E. Gibson, R. Jimenez, C. Durfee, F. Tortajada, H. Dinger, and B. Touzet, “Design and fabrication of efficient reflection grisms for pulse compression and dispersion compensation,” presented at the Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies (Optical Society of America, 2006), paper CThA5.

S. Kane, B. Touzet, C. Durfee, and J. Squier, “Analytical expressions and simplified formulas for GVD and TOD of reflection grism compressors,” presented at the Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies (Optical Society of America, 2008), paper JTuA66.

Treacy, E.

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

Ueda, H.

Vysotina, N. V.

N. V. Vysotina, N. N. Rosanov, and V. E. Yashin, “Modeling of systems for broadening of spectrum of petawatt laser pulses and for their nonlinear compression,” Opt. Spectrosc. 110, 973–981 (2011).
[CrossRef]

Wise, F. W.

L. Kuznetsova, F. W. Wise, S. Kane, and J. Squier, “Chirped-pulse amplification near the gain-narrowing limit of Yb-doped fiber using a reflection grism compressor,” Appl. Phys. B 88, 515–518 (2007).
[CrossRef]

Yamakawa, K.

Yashin, V. E.

N. V. Vysotina, N. N. Rosanov, and V. E. Yashin, “Modeling of systems for broadening of spectrum of petawatt laser pulses and for their nonlinear compression,” Opt. Spectrosc. 110, 973–981 (2011).
[CrossRef]

Zacharias, H.

J. Zheng and H. Zacharias, “Design considerations for a compact grism stretcher for non-collinear optical parametric chirped-pulse amplification,” Appl. Phys. B 96, 445–452 (2009).
[CrossRef]

Zheng, J.

J. Zheng and H. Zacharias, “Design considerations for a compact grism stretcher for non-collinear optical parametric chirped-pulse amplification,” Appl. Phys. B 96, 445–452 (2009).
[CrossRef]

Appl. Phys. B

M. Pittman, S. Ferré, J. P. Rousseau, L. Notebaert, J. P. Chambaret, and G. Chériaux, “Design and characterization of a near-diffraction-limited femtosecond 100 TW 10 Hz high-intensity laser system,” Appl. Phys. B 74, 529–535 (2002).
[CrossRef]

L. Kuznetsova, F. W. Wise, S. Kane, and J. Squier, “Chirped-pulse amplification near the gain-narrowing limit of Yb-doped fiber using a reflection grism compressor,” Appl. Phys. B 88, 515–518 (2007).
[CrossRef]

J. Zheng and H. Zacharias, “Design considerations for a compact grism stretcher for non-collinear optical parametric chirped-pulse amplification,” Appl. Phys. B 96, 445–452 (2009).
[CrossRef]

Electron. Lett.

P. Tournois, “New diffraction grating pair with very linear dispersion for laser pulse compression,” Electron. Lett. 29, 1414–1415 (1993).
[CrossRef]

IEEE J. Quantum Electron.

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

S. Kane and J. Squier, “Grating compensation of third-order material dispersion in the normal dispersion regime: Sub-100-fs chirped-pulse amplification using a fiber stretcher and grating-pair compressor,” IEEE J. Quantum Electron. 31, 2052–2057 (1995).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 55, 447–449 (1985).
[CrossRef]

K. Osvay, A. P. Kovács, G. Kurdi, Z. Heiner, M. Divall, J. Klebniczki, and I. E. Ferincz, “Measurement of non-compensated angular dispersion and the subsequent temporal lengthening of femtosecond pulses in a CPA laser,” Opt. Commun. 248, 201–209 (2005).
[CrossRef]

Opt. Lett.

Opt. Spectrosc.

N. V. Vysotina, N. N. Rosanov, and V. E. Yashin, “Modeling of systems for broadening of spectrum of petawatt laser pulses and for their nonlinear compression,” Opt. Spectrosc. 110, 973–981 (2011).
[CrossRef]

Other

S. Kane, B. Touzet, C. Durfee, and J. Squier, “Analytical expressions and simplified formulas for GVD and TOD of reflection grism compressors,” presented at the Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies (Optical Society of America, 2008), paper JTuA66.

S. Kane, R. Huff, J. Squier, E. Gibson, R. Jimenez, C. Durfee, F. Tortajada, H. Dinger, and B. Touzet, “Design and fabrication of efficient reflection grisms for pulse compression and dispersion compensation,” presented at the Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies (Optical Society of America, 2006), paper CThA5.

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Figures (7)

Fig. 1.
Fig. 1.

Layout and ray tracing of a reflection grism-pair compressor. θi is the incidence angle, α is the apex angle of the prism, θd is the diffraction angle, and θ is the refraction angle.

Fig. 2.
Fig. 2.

TOD/GDD ratio as a function of the refractive index in different regions. Solid line is the ratio of the grism. Dashed line is the ratio in the air-space region between the grisms. Dotted line is the ratio inside the prism glass.

Fig. 3.
Fig. 3.

TOD/GDD ratio as a function of wavelength at different incidence angle and corresponding time delay.

Fig. 4.
Fig. 4.

TOD/GDD ratio and the resulting spectral time delay for different grating constants as a function of wavelength.

Fig. 5.
Fig. 5.

TOD/GDD ratio and the spectral time delay as a function of the apex angle of prism.

Fig. 6.
Fig. 6.

TOD/GDD ratio as a function of the separation of grism-pair and corresponding time delay.

Fig. 7.
Fig. 7.

TOD/GDD ratio and the corresponding time delay as a function of the insertion Δ at the first prism.

Equations (8)

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

ϕ(ω)=ϕ0+ϕ1(ωω0)+12ϕ2(ωω0)2+16ϕ3(ωω0)3+
GDD=d2ϕdω2=nLpcsinβp(2dβpdω+ωd2βpdω2)ωnLpccosβp(dβpdω)2,
TOD=d3ϕdω3=3nLpccosβp[(dβpdω)2+ωdβpdωd2βpdω2]nLpcsinβp[3d2βpdω2+ωd3βpdω3ω(dβpdω)3].
GDDprismωnLpc(dβPdω)2=12m2Lpλ3πnc2d2cos2θd,
TODprism3nLpc[(dβdω)2+ωdβpdω·d2βpdω2]=GDDprism×3λ2πc(1+23mλsinθdndcos2θd).
GDDair=12m2Laλ3cos2(αθd)πc2d2cos2θdcos2,
TODair=GDDair×3λ2πc[1+23mλsinαndcos2θdcos(αθd)23mλsinθcos(αθd)dcosθdcos2θ].
ξgrism=(TODprism+TODair)/(GDDprism+GDDair).

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