Abstract

Dispersive mirrors based on time-domain approach are compared with mirrors resulting from conventional phase target designs. Phase targets have been applied to complementary-pair dispersive mirrors, used for sub-5-fs pulse compression. While the phase approach has hither to afforded the best performance for the shortest pulses, our new approach, based on time-domain targets and tailored for a specific input spectrum, appears to provide comparable performance for pulse compression for a pulse duration 4.6 fs. Experimental studies using dispersive mirrors made to both designs are described.

©2009 Optical Society of America

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References

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  1. J. Diels and W. Rudolph, Ultra short laser pulse phenomena: fundamentals, techniques, and application on a femtosecond time scale, (Academic Press, 1995).
    [PubMed]
  2. T. Brabec and F. Krausz, “Intense few-cycle laser field: frontiers of nonlinear optics,” Rev. Mod. Phys. 72, 545–591 (2000).
    [Crossref]
  3. M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,“ Nature 414, 509–513 (2001).
    [Crossref] [PubMed]
  4. B. Schenkel, J. Biegert, U. Keller, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, S. De Silvestri, and O. Svelto, “Generation of 3.8-fs pulses from adaptive compression of a cascaded hollow fiber supercontinuum,” Opt. Lett. 28, 1987–1989 (2003).
    [Crossref] [PubMed]
  5. K. Yamane, Z. Zhang, K. Oka, R. Morita, M. Yamashita, and A. Suguro, “Optical pulse compression to 3.4 fs in the monocycle region by feedback phase compensation,” Opt. Lett. 28, 2258–2260 (2003).
    [Crossref] [PubMed]
  6. R. Szipöcs, K. Ferencz, C. Spielmann, and F. Krausz, “Chirped multilayer coatings for broadband dispersion control in femtosecond lasers,” Opt. Lett. 19, 201–203 (1994).
    [Crossref] [PubMed]
  7. V. Pervak, F. Krausz, and A. Apolonski “Dispersion control over the UV-VIS-NIR spectral range with HfO2/SiO2 chirped dielectric multilayers,” Opt. Lett. 32, 1183–1185 (2007).
    [Crossref] [PubMed]
  8. J. R. Birge, “Designing Phase-Sensitive Mirrors by Minimizing Complex Error Energy in the Frequency Domain,” in Optical Interference Coatings, OSA Technical Digest (CD) (Optical Society of America, 2007), paper WA9.
  9. V. Laude and P. Tournois, “Chirped mirror pairs for ultrabroadband dispersion control,” in Digest of Conference on Lasers and Electro-Optics (CLEO_US) (Optical Society of America, 1999) pp. 187–188.
  10. F. X. Kärtner, U. Morgner, R. Ell, T. Schibli, J. G. Fujimoto, E. P. Ippen, V. Scheuer, G. Angelow, and T. Tschudi, “Ultrabroadband double-chirped mirror pairs for generation of octave spectra,” J. Opt. Soc. Am. B 18, 882–885 (2001).
    [Crossref]
  11. V. Pervak, S. Naumov, G. Tempea, V. Yakovlev, F. Krausz, and A. Apolonski, “Synthesis and manufacturing the mirrors for ultrafast optics,” Proc. SPIE 5963, 490–500 (2005).
  12. V. Pervak, A. V. Tikhonravov, M. K. Trubetskov, S. Naumov, F. Krausz, and A. Apolonski, “1.5-octave chirped mirror for pulse compression down to sub-3 fs,” Appl. Phys. B. 87, 5–12 (2007).
    [Crossref]
  13. P. Baum, M. Breuer, E. Riedle, and G. Steinmeyer, “Brewster-angled chirped mirrors for broadband pulse compression without dispersion oscillations,” Opt. Lett. 31, 2220–2222 (2006).
    [Crossref] [PubMed]
  14. G. Steinmeyer, “Brewster-angled chirped mirrors for highfidelity dispersion compensation and bandwidths exceeding one optical octave,” Opt. Express 11, 2385–2396 (2003).
    [Crossref] [PubMed]
  15. F. X. Kärtner, N. Matuschek, T. Schibli, U. Keller, H. A. Haus, C. Heine, R. Morf, V. Scheuer, M. Tilsch, and T. Tschudi, “Design and fabrication of double-chirped mirrors,” Opt. Lett. 22, 831–833 (1997).
    [Crossref] [PubMed]
  16. F. X. Kartner, U. Morgner, R. Ell, T. Schibli, J. G. Fujimoto, E. P. Ippen, V. Scheuer, G. Angelow, and T. Tschudi, “Ultrabroadband double-chirped mirror pairs for generation of octave spectra,” J. Opt. Soc. Am. B 18, 882–885 (2001).
    [Crossref]
  17. N. Matuschek, F. X. Kärtner, and U. Keller, “Analytical design of double-chirped mirrors with customtailored dispersion characteristics,” IEEE J. Quantum Electron. 35, 129–137 (1999).
    [Crossref]
  18. N. Matuschek, L. Gallmann, D. H. Sutter, G. Steinmeyer, and U. Keller, “Back-side-coated chirped mirrors with ultrasmooth broadband dispersion characteristics,” Appl. Phys. B 71, 509–522 (2000).
    [Crossref]
  19. G. Tempea, V. Yakovlev, B. Bacovic, F. Krausz, and K. Ferencz, “Tilted-front-interface chirped mirrors,” J. Opt. Soc. Am. B 18, 1747–1750 (2001).
    [Crossref]
  20. P. Dombi, V. S. Yakovlev, K. O'Keeffe, T. Fuji, M. Lezius, and G. Tempea, “Pulse compression with timedomain optimized chirped mirrors,” Opt. Express 13, 10888–10894 (2005).
    [Crossref] [PubMed]
  21. M. K. Trubetskov, A. V. Tikhonravov, and V. Pervak, “Time-domain approach for designing dispersive mirrors based on the needle optimization technique. Theory,” Opt. Express 16, 20637–20647 (2008).
    [Crossref] [PubMed]
  22. A. V. Tikhonravov, M. K. Trubetskov, and G. W. DeBell, “Application of the needle optimization technique to the design of optical coatings,” Appl. Opt. 35, 5493–5508 (1996).
    [Crossref] [PubMed]
  23. A. V. Tikhonravov, M. K. Trubetskov, and G. W. DeBell, “Optical coating design approaches based on the needle optimization technique,” Appl. Opt. 46, 704–710 (2007).
    [Crossref] [PubMed]
  24. V. Pervak, F. Krausz, and A. Apolonski “Hafnium oxide films made by magnetron sputtering system,” Thin Solid Films 515, 7984–7989 (2007)
    [Crossref]

2008 (1)

2007 (4)

A. V. Tikhonravov, M. K. Trubetskov, and G. W. DeBell, “Optical coating design approaches based on the needle optimization technique,” Appl. Opt. 46, 704–710 (2007).
[Crossref] [PubMed]

V. Pervak, F. Krausz, and A. Apolonski “Dispersion control over the UV-VIS-NIR spectral range with HfO2/SiO2 chirped dielectric multilayers,” Opt. Lett. 32, 1183–1185 (2007).
[Crossref] [PubMed]

V. Pervak, A. V. Tikhonravov, M. K. Trubetskov, S. Naumov, F. Krausz, and A. Apolonski, “1.5-octave chirped mirror for pulse compression down to sub-3 fs,” Appl. Phys. B. 87, 5–12 (2007).
[Crossref]

V. Pervak, F. Krausz, and A. Apolonski “Hafnium oxide films made by magnetron sputtering system,” Thin Solid Films 515, 7984–7989 (2007)
[Crossref]

2006 (1)

2005 (2)

P. Dombi, V. S. Yakovlev, K. O'Keeffe, T. Fuji, M. Lezius, and G. Tempea, “Pulse compression with timedomain optimized chirped mirrors,” Opt. Express 13, 10888–10894 (2005).
[Crossref] [PubMed]

V. Pervak, S. Naumov, G. Tempea, V. Yakovlev, F. Krausz, and A. Apolonski, “Synthesis and manufacturing the mirrors for ultrafast optics,” Proc. SPIE 5963, 490–500 (2005).

2003 (3)

2001 (4)

2000 (2)

T. Brabec and F. Krausz, “Intense few-cycle laser field: frontiers of nonlinear optics,” Rev. Mod. Phys. 72, 545–591 (2000).
[Crossref]

N. Matuschek, L. Gallmann, D. H. Sutter, G. Steinmeyer, and U. Keller, “Back-side-coated chirped mirrors with ultrasmooth broadband dispersion characteristics,” Appl. Phys. B 71, 509–522 (2000).
[Crossref]

1999 (1)

N. Matuschek, F. X. Kärtner, and U. Keller, “Analytical design of double-chirped mirrors with customtailored dispersion characteristics,” IEEE J. Quantum Electron. 35, 129–137 (1999).
[Crossref]

1997 (1)

1996 (1)

1994 (1)

Angelow, G.

Apolonski, A.

V. Pervak, F. Krausz, and A. Apolonski “Hafnium oxide films made by magnetron sputtering system,” Thin Solid Films 515, 7984–7989 (2007)
[Crossref]

V. Pervak, A. V. Tikhonravov, M. K. Trubetskov, S. Naumov, F. Krausz, and A. Apolonski, “1.5-octave chirped mirror for pulse compression down to sub-3 fs,” Appl. Phys. B. 87, 5–12 (2007).
[Crossref]

V. Pervak, F. Krausz, and A. Apolonski “Dispersion control over the UV-VIS-NIR spectral range with HfO2/SiO2 chirped dielectric multilayers,” Opt. Lett. 32, 1183–1185 (2007).
[Crossref] [PubMed]

V. Pervak, S. Naumov, G. Tempea, V. Yakovlev, F. Krausz, and A. Apolonski, “Synthesis and manufacturing the mirrors for ultrafast optics,” Proc. SPIE 5963, 490–500 (2005).

Bacovic, B.

Baum, P.

Biegert, J.

Birge, J. R.

J. R. Birge, “Designing Phase-Sensitive Mirrors by Minimizing Complex Error Energy in the Frequency Domain,” in Optical Interference Coatings, OSA Technical Digest (CD) (Optical Society of America, 2007), paper WA9.

Brabec, T.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,“ Nature 414, 509–513 (2001).
[Crossref] [PubMed]

T. Brabec and F. Krausz, “Intense few-cycle laser field: frontiers of nonlinear optics,” Rev. Mod. Phys. 72, 545–591 (2000).
[Crossref]

Breuer, M.

Corkum, P.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,“ Nature 414, 509–513 (2001).
[Crossref] [PubMed]

De Silvestri, S.

DeBell, G. W.

Diels, J.

J. Diels and W. Rudolph, Ultra short laser pulse phenomena: fundamentals, techniques, and application on a femtosecond time scale, (Academic Press, 1995).
[PubMed]

Dombi, P.

Drescher, M.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,“ Nature 414, 509–513 (2001).
[Crossref] [PubMed]

Ell, R.

Ferencz, K.

Fuji, T.

Fujimoto, J. G.

Gallmann, L.

N. Matuschek, L. Gallmann, D. H. Sutter, G. Steinmeyer, and U. Keller, “Back-side-coated chirped mirrors with ultrasmooth broadband dispersion characteristics,” Appl. Phys. B 71, 509–522 (2000).
[Crossref]

Haus, H. A.

Heine, C.

Heinzmann, U.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,“ Nature 414, 509–513 (2001).
[Crossref] [PubMed]

Hentschel, M.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,“ Nature 414, 509–513 (2001).
[Crossref] [PubMed]

Ippen, E. P.

Kartner, F. X.

Kärtner, F. X.

Keller, U.

B. Schenkel, J. Biegert, U. Keller, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, S. De Silvestri, and O. Svelto, “Generation of 3.8-fs pulses from adaptive compression of a cascaded hollow fiber supercontinuum,” Opt. Lett. 28, 1987–1989 (2003).
[Crossref] [PubMed]

N. Matuschek, L. Gallmann, D. H. Sutter, G. Steinmeyer, and U. Keller, “Back-side-coated chirped mirrors with ultrasmooth broadband dispersion characteristics,” Appl. Phys. B 71, 509–522 (2000).
[Crossref]

N. Matuschek, F. X. Kärtner, and U. Keller, “Analytical design of double-chirped mirrors with customtailored dispersion characteristics,” IEEE J. Quantum Electron. 35, 129–137 (1999).
[Crossref]

F. X. Kärtner, N. Matuschek, T. Schibli, U. Keller, H. A. Haus, C. Heine, R. Morf, V. Scheuer, M. Tilsch, and T. Tschudi, “Design and fabrication of double-chirped mirrors,” Opt. Lett. 22, 831–833 (1997).
[Crossref] [PubMed]

Kienberger, R.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,“ Nature 414, 509–513 (2001).
[Crossref] [PubMed]

Krausz, F.

V. Pervak, A. V. Tikhonravov, M. K. Trubetskov, S. Naumov, F. Krausz, and A. Apolonski, “1.5-octave chirped mirror for pulse compression down to sub-3 fs,” Appl. Phys. B. 87, 5–12 (2007).
[Crossref]

V. Pervak, F. Krausz, and A. Apolonski “Hafnium oxide films made by magnetron sputtering system,” Thin Solid Films 515, 7984–7989 (2007)
[Crossref]

V. Pervak, F. Krausz, and A. Apolonski “Dispersion control over the UV-VIS-NIR spectral range with HfO2/SiO2 chirped dielectric multilayers,” Opt. Lett. 32, 1183–1185 (2007).
[Crossref] [PubMed]

V. Pervak, S. Naumov, G. Tempea, V. Yakovlev, F. Krausz, and A. Apolonski, “Synthesis and manufacturing the mirrors for ultrafast optics,” Proc. SPIE 5963, 490–500 (2005).

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,“ Nature 414, 509–513 (2001).
[Crossref] [PubMed]

G. Tempea, V. Yakovlev, B. Bacovic, F. Krausz, and K. Ferencz, “Tilted-front-interface chirped mirrors,” J. Opt. Soc. Am. B 18, 1747–1750 (2001).
[Crossref]

T. Brabec and F. Krausz, “Intense few-cycle laser field: frontiers of nonlinear optics,” Rev. Mod. Phys. 72, 545–591 (2000).
[Crossref]

R. Szipöcs, K. Ferencz, C. Spielmann, and F. Krausz, “Chirped multilayer coatings for broadband dispersion control in femtosecond lasers,” Opt. Lett. 19, 201–203 (1994).
[Crossref] [PubMed]

Laude, V.

V. Laude and P. Tournois, “Chirped mirror pairs for ultrabroadband dispersion control,” in Digest of Conference on Lasers and Electro-Optics (CLEO_US) (Optical Society of America, 1999) pp. 187–188.

Lezius, M.

Matuschek, N.

N. Matuschek, L. Gallmann, D. H. Sutter, G. Steinmeyer, and U. Keller, “Back-side-coated chirped mirrors with ultrasmooth broadband dispersion characteristics,” Appl. Phys. B 71, 509–522 (2000).
[Crossref]

N. Matuschek, F. X. Kärtner, and U. Keller, “Analytical design of double-chirped mirrors with customtailored dispersion characteristics,” IEEE J. Quantum Electron. 35, 129–137 (1999).
[Crossref]

F. X. Kärtner, N. Matuschek, T. Schibli, U. Keller, H. A. Haus, C. Heine, R. Morf, V. Scheuer, M. Tilsch, and T. Tschudi, “Design and fabrication of double-chirped mirrors,” Opt. Lett. 22, 831–833 (1997).
[Crossref] [PubMed]

Milosevic, N.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,“ Nature 414, 509–513 (2001).
[Crossref] [PubMed]

Morf, R.

Morgner, U.

Morita, R.

Naumov, S.

V. Pervak, A. V. Tikhonravov, M. K. Trubetskov, S. Naumov, F. Krausz, and A. Apolonski, “1.5-octave chirped mirror for pulse compression down to sub-3 fs,” Appl. Phys. B. 87, 5–12 (2007).
[Crossref]

V. Pervak, S. Naumov, G. Tempea, V. Yakovlev, F. Krausz, and A. Apolonski, “Synthesis and manufacturing the mirrors for ultrafast optics,” Proc. SPIE 5963, 490–500 (2005).

Nisoli, M.

Oka, K.

O'Keeffe, K.

Pervak, V.

M. K. Trubetskov, A. V. Tikhonravov, and V. Pervak, “Time-domain approach for designing dispersive mirrors based on the needle optimization technique. Theory,” Opt. Express 16, 20637–20647 (2008).
[Crossref] [PubMed]

V. Pervak, F. Krausz, and A. Apolonski “Dispersion control over the UV-VIS-NIR spectral range with HfO2/SiO2 chirped dielectric multilayers,” Opt. Lett. 32, 1183–1185 (2007).
[Crossref] [PubMed]

V. Pervak, F. Krausz, and A. Apolonski “Hafnium oxide films made by magnetron sputtering system,” Thin Solid Films 515, 7984–7989 (2007)
[Crossref]

V. Pervak, A. V. Tikhonravov, M. K. Trubetskov, S. Naumov, F. Krausz, and A. Apolonski, “1.5-octave chirped mirror for pulse compression down to sub-3 fs,” Appl. Phys. B. 87, 5–12 (2007).
[Crossref]

V. Pervak, S. Naumov, G. Tempea, V. Yakovlev, F. Krausz, and A. Apolonski, “Synthesis and manufacturing the mirrors for ultrafast optics,” Proc. SPIE 5963, 490–500 (2005).

Reider, G. A.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,“ Nature 414, 509–513 (2001).
[Crossref] [PubMed]

Riedle, E.

Rudolph, W.

J. Diels and W. Rudolph, Ultra short laser pulse phenomena: fundamentals, techniques, and application on a femtosecond time scale, (Academic Press, 1995).
[PubMed]

Sansone, G.

Schenkel, B.

Scheuer, V.

Schibli, T.

Spielmann, C.

Spielmann, Ch.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,“ Nature 414, 509–513 (2001).
[Crossref] [PubMed]

Stagira, S.

Steinmeyer, G.

Suguro, A.

Sutter, D. H.

N. Matuschek, L. Gallmann, D. H. Sutter, G. Steinmeyer, and U. Keller, “Back-side-coated chirped mirrors with ultrasmooth broadband dispersion characteristics,” Appl. Phys. B 71, 509–522 (2000).
[Crossref]

Svelto, O.

Szipöcs, R.

Tempea, G.

Tikhonravov, A. V.

Tilsch, M.

Tournois, P.

V. Laude and P. Tournois, “Chirped mirror pairs for ultrabroadband dispersion control,” in Digest of Conference on Lasers and Electro-Optics (CLEO_US) (Optical Society of America, 1999) pp. 187–188.

Trubetskov, M. K.

Tschudi, T.

Vozzi, C.

Yakovlev, V.

V. Pervak, S. Naumov, G. Tempea, V. Yakovlev, F. Krausz, and A. Apolonski, “Synthesis and manufacturing the mirrors for ultrafast optics,” Proc. SPIE 5963, 490–500 (2005).

G. Tempea, V. Yakovlev, B. Bacovic, F. Krausz, and K. Ferencz, “Tilted-front-interface chirped mirrors,” J. Opt. Soc. Am. B 18, 1747–1750 (2001).
[Crossref]

Yakovlev, V. S.

Yamane, K.

Yamashita, M.

Zhang, Z.

Appl. Opt. (2)

Appl. Phys. B (1)

N. Matuschek, L. Gallmann, D. H. Sutter, G. Steinmeyer, and U. Keller, “Back-side-coated chirped mirrors with ultrasmooth broadband dispersion characteristics,” Appl. Phys. B 71, 509–522 (2000).
[Crossref]

Appl. Phys. B. (1)

V. Pervak, A. V. Tikhonravov, M. K. Trubetskov, S. Naumov, F. Krausz, and A. Apolonski, “1.5-octave chirped mirror for pulse compression down to sub-3 fs,” Appl. Phys. B. 87, 5–12 (2007).
[Crossref]

IEEE J. Quantum Electron. (1)

N. Matuschek, F. X. Kärtner, and U. Keller, “Analytical design of double-chirped mirrors with customtailored dispersion characteristics,” IEEE J. Quantum Electron. 35, 129–137 (1999).
[Crossref]

J. Opt. Soc. Am. B (3)

Nature (1)

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,“ Nature 414, 509–513 (2001).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Lett. (6)

Proc. SPIE (1)

V. Pervak, S. Naumov, G. Tempea, V. Yakovlev, F. Krausz, and A. Apolonski, “Synthesis and manufacturing the mirrors for ultrafast optics,” Proc. SPIE 5963, 490–500 (2005).

Rev. Mod. Phys. (1)

T. Brabec and F. Krausz, “Intense few-cycle laser field: frontiers of nonlinear optics,” Rev. Mod. Phys. 72, 545–591 (2000).
[Crossref]

Thin Solid Films (1)

V. Pervak, F. Krausz, and A. Apolonski “Hafnium oxide films made by magnetron sputtering system,” Thin Solid Films 515, 7984–7989 (2007)
[Crossref]

Other (3)

J. Diels and W. Rudolph, Ultra short laser pulse phenomena: fundamentals, techniques, and application on a femtosecond time scale, (Academic Press, 1995).
[PubMed]

J. R. Birge, “Designing Phase-Sensitive Mirrors by Minimizing Complex Error Energy in the Frequency Domain,” in Optical Interference Coatings, OSA Technical Digest (CD) (Optical Society of America, 2007), paper WA9.

V. Laude and P. Tournois, “Chirped mirror pairs for ultrabroadband dispersion control,” in Digest of Conference on Lasers and Electro-Optics (CLEO_US) (Optical Society of America, 1999) pp. 187–188.

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Figures (10)

Fig.1.
Fig.1. Basic scheme of time-domain target approach.

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Fig. 2.
Fig. 2. The spectrum broadened in the hollow fiber after a Ti:Sa kHz laser was used as input for the time-domain design. The FTLP is 4.4 fs.

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Fig. 3.
Fig. 3. Physical thickness versus layer number of time-domain optimized DM.

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Fig. 4.
Fig. 4. Physical thickness versus layer number of complementary pair of DMs.

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Fig. 5.
Fig. 5. DM designed by using the complementary approach. The GD (three lower curves) and reflectivity (three upper curves) of the complementary pair of DMs are shown. The green curve is the average of the GD and reflectivity of two different DMs per bounce. The red and blue are the GD and reflectivity of two different DMs.

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Fig. 6.
Fig. 6. DM designed by using the time-domain approach. Orange shows the theoretical curve of the GD and reflectivity.

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Fig. 7.
Fig. 7. The pulse envelope of the FTLP is shown by the red curve, the blue curve shows the pulse after 8 bounces off the time-domain optimized DM, the green one – after 8 bounces off the complementary pair of DMs, the pink – after 8 bounces off one of the complementary pair of DMs. The time delay between the pulses is artificial.

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Fig. 8.
Fig. 8. Measurements of the GDD of 4.6-fs DMs. The green curve is the measured average GDD of the complementary pair of DMs per bounce. The red and blue ones are the GDD of each DM.

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Fig. 9.
Fig. 9. Measurement of the GDD of 4.6-fs DMs. The curve shows the measured GDD of the time-domain optimized DM.

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Fig. 10.
Fig. 10. Theoretical second-harmonic generation (SHG) interferometric autocorrelation corresponding to a 4.4-fs FTLP is shown in red; green and blue - the measured SHG interferometric autocorrelation function corresponds to a 4.6-fs pulse for the complementary pair of DM and time-domain optimized DM respectively.

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Equations (3)

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A out ( t ) = ( 2 π ) − 1 ∫ − ∞ + ∞ Â out ( ω ) exp ( i ω t ) d ω
Φ = ( E p ) − q ∫ − ∞ + ∞ ( t − t 0 ) 2 ∣ A out ( t ) ∣ p d t , q ≥ 1 ,
F = 1 L ∑ l = 1 L ( R p ( ω l ) − R ( l ) Δ R ( l ) ) 2 + ( GDD p ( ω l ) − GDD ( l ) ΔGDD ( l ) ) 2 .

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