Abstract

We developed a method for group delay and group delay dispersion measurements, based on location of interference resonance peaks. Such resonance peaks can be observed in transmittance or in reflectance when two mirrors are placed parallel to each other and separated by a thin air spacer. By using a novel approach, based on simultaneous processing of the data acquired for different spacer distances we obtained reliable results with high resolution. Measurements were performed both in transmittance and reflectance layouts depending on the reflectivity of the mirror to be measured. The developed method allows dispersion measurements of ultraviolet mirrors and ultra-broadband mirrors spanning more than one optical octave to be performed.

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  1. R. Szipöcs, K. Ferencz, C. Spielmann, and F. Krausz, “Chirped multilayer coatings for broadband dispersion control in femtosecond lasers,” Opt. Lett.19(3), 201–203 (1994).
    [CrossRef] [PubMed]
  2. R. Szipőcs and A. Köházi-Kis, “Theory and design of chirped dielectric laser mirrors,” Appl. Phys. B65(2), 115–135 (1997).
    [CrossRef]
  3. J.-C. Diels and W. Rudolph, Ultrashort laser pulse phenomena : fundamentals, techniques, and applications on a femtosecond time scale (Academic Press, 1996).
  4. D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun.56(3), 219–221 (1985).
    [CrossRef]
  5. A. Ashkin, G. Boyd, and J. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron.2(6), 109–124 (1966).
    [CrossRef]
  6. 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. B18(6), 882–885 (2001).
    [CrossRef]
  7. 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. B87(1), 5–12 (2007).
    [CrossRef]
  8. V. Pervak, I. Ahmad, M. K. Trubetskov, A. V. Tikhonravov, and F. Krausz, “Double-angle multilayer mirrors with smooth dispersion characteristics,” Opt. Express17(10), 7943–7951 (2009).
    [CrossRef] [PubMed]
  9. V. Pervak, O. Pronin, O. Razskazovskaya, J. Brons, I. B. Angelov, M. K. Trubetskov, A. V. Tikhonravov, and F. Krausz, “High-dispersive mirrors for high power applications,” Opt. Express20(4), 4503–4508 (2012).
    [CrossRef] [PubMed]
  10. V. Pervak, M. K. Trubetskov, and A. V. Tikhonravov, “Robust synthesis of dispersive mirrors,” Opt. Express19(3), 2371–2380 (2011).
    [CrossRef] [PubMed]
  11. M. Trubetskov, A. Tikhonravov, and V. Pervak, “Time-domain approach for designing dispersive mirrors based on the needle optimization technique. Theory,” Opt. Express16(25), 20637–20647 (2008).
    [CrossRef] [PubMed]
  12. M. K. Trubetskov, V. Pervak, and A. V. Tikhonravov, “Phase optimization of dispersive mirrors based on floating constants,” Opt. Express18(26), 27613–27618 (2010).
    [CrossRef] [PubMed]
  13. A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and A. A. Tikhonravov, “Application of advanced optimization concepts to the design of high quality optical coatings,” Proc. SPIE4829, 1061–1062 (2003).
    [CrossRef]
  14. O. Nohadani, J. R. Birge, F. X. Kärtner, and D. J. Bertsimas, “Robust chirped mirrors,” Appl. Opt.47(14), 2630–2636 (2008).
    [CrossRef] [PubMed]
  15. J. R. Birge, F. X. Kärtner, and O. Nohadani, “Improving thin-film manufacturing yield with robust optimization,” Appl. Opt.50(9), C36–C40 (2011).
    [CrossRef] [PubMed]
  16. V. Pervak, M. K. Trubetskov, and A. V. Tikhonravov, “Robust synthesis of dispersive mirrors,” Opt. Express19(3), 2371–2380 (2011).
    [CrossRef] [PubMed]
  17. T. V. Amotchkina, M. K. Trubetskov, V. Pervak, B. Romanov, and A. V. Tikhonravov, “On the reliability of reverse engineering results,” Appl. Opt.51(22), 5543–5551 (2012).
    [CrossRef] [PubMed]
  18. W. H. Knox, N. M. Pearson, K. D. Li, and C. A. Hirlimann, “Interferometric measurements of femtosecond group delay in optical components,” Opt. Lett.13(7), 574–576 (1988).
    [CrossRef] [PubMed]
  19. W. H. Knox, “Dispersion measurements for femtosecond-pulse generation and applications,” Appl. Phys. B58(3), 225–235 (1994).
    [CrossRef]
  20. A. Gosteva, M. Haiml, R. Paschotta, and U. Keller, “Noise-related resolution limit of dispersion measurements with white-light interferometers,” J. Opt. Soc. B22(9), 1868–1874 (2005).
    [CrossRef]
  21. M. Beck and I. A. Walmsley, “Measurement of group delay with high temporal and spectral resolution,” Opt. Lett.15(9), 492–494 (1990).
    [CrossRef] [PubMed]
  22. T. V. Amotchkina, A. V. Tikhonravov, M. K. Trubetskov, D. Grupe, A. Apolonski, and V. Pervak, “Measurement of group delay of dispersive mirrors with white-light interferometer,” Appl. Opt.48(5), 949–956 (2009).
    [CrossRef] [PubMed]
  23. K. Naganuma, K. Mogi, and H. Yamada, “Group-delay measurement using the Fourier transform of an interferometric cross correlation generated by white light,” Opt. Lett.15(7), 393–395 (1990).
    [CrossRef] [PubMed]
  24. S. Diddams and J.-C. Diels, “Dispersion measurements with white-light interferometry,” J. Opt. Soc. Am. B13(6), 1120–1129 (1996).
    [CrossRef]
  25. E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science320(5883), 1614–1617 (2008).
    [CrossRef] [PubMed]
  26. I. Pupeza, T. Eidam, J. Rauschenberger, B. Bernhardt, A. Ozawa, E. Fill, A. Apolonski, T. Udem, J. Limpert, Z. A. Alahmed, A. M. Azzeer, A. Tünnermann, T. W. Hänsch, and F. Krausz, “Power scaling of a high-repetition-rate enhancement cavity,” Opt. Lett.35(12), 2052–2054 (2010).
    [CrossRef] [PubMed]
  27. V. Pervak, C. Teisset, A. Sugita, S. Naumov, F. Krausz, and A. Apolonski, “High-dispersive mirrors for femtosecond lasers,” Opt. Express16(14), 10220–10233 (2008).
    [CrossRef] [PubMed]
  28. V. Pervak, I. Ahmad, S. A. Trushin, Z. Major, A. Apolonski, S. Karsch, and F. Krausz, “Chirped-pulse amplification of laser pulses with dispersive mirrors,” Opt. Express17(21), 19204–19212 (2009).
    [CrossRef] [PubMed]
  29. O. Pronin, J. Brons, C. Grasse, V. Pervak, G. Boehm, M.-C. Amann, V. L. Kalashnikov, A. Apolonski, and F. Krausz, “High-power 200 fs Kerr-lens mode-locked Yb:YAG thin-disk oscillator,” Opt. Lett.36(24), 4746–4748 (2011).
    [CrossRef] [PubMed]
  30. K. Osvay, G. Kurdi, J. Hebling, A. P. Kovács, Z. Bor, and R. Szipöcs, “Measurement of the group delay of laser mirrors by a Fabry-Perot interferometer,” Opt. Lett.20(22), 2339–2341 (1995).
    [CrossRef] [PubMed]
  31. H. A. Macleod, Thin-film optical filters (Taylor & Francis, 2010).
  32. D. R. Austin, T. Witting, and I. A. Walmsley, “High precision self-referenced phase retrieval of complex pulses with multiple-shearing spectral interferometry,” J. Opt. Soc. Am. B26(9), 1818–1830 (2009).
    [CrossRef]
  33. A. N. Tikhonov and V. I. Arsenin, Solutions of Ill-Posed Problems (Halsted Press, 1977).
  34. A. N. Tikhonov, A. Goncharsky, V. V. Stepanov, and A. G. Yagola, Numerical Methods for the Solution of Ill-posed Problems, Mathematics and Its Applications No. 328 (Kluwer Academic Publishers, 1995).
  35. J. H. Ahlberg, E. N. Nilson, and J. L. Walsh, The theory of splines and their applications (Academic Press, 1967).

2012 (2)

2011 (4)

2010 (2)

2009 (4)

2008 (4)

2007 (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. B87(1), 5–12 (2007).
[CrossRef]

2005 (1)

A. Gosteva, M. Haiml, R. Paschotta, and U. Keller, “Noise-related resolution limit of dispersion measurements with white-light interferometers,” J. Opt. Soc. B22(9), 1868–1874 (2005).
[CrossRef]

2003 (1)

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and A. A. Tikhonravov, “Application of advanced optimization concepts to the design of high quality optical coatings,” Proc. SPIE4829, 1061–1062 (2003).
[CrossRef]

2001 (1)

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. B18(6), 882–885 (2001).
[CrossRef]

1997 (1)

R. Szipőcs and A. Köházi-Kis, “Theory and design of chirped dielectric laser mirrors,” Appl. Phys. B65(2), 115–135 (1997).
[CrossRef]

1996 (1)

1995 (1)

1994 (2)

1990 (2)

1988 (1)

1985 (1)

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun.56(3), 219–221 (1985).
[CrossRef]

1966 (1)

A. Ashkin, G. Boyd, and J. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron.2(6), 109–124 (1966).
[CrossRef]

Ahmad, I.

Alahmed, Z. A.

Amann, M.-C.

Amotchkina, T. V.

Angelov, I. B.

Angelow, G.

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. B18(6), 882–885 (2001).
[CrossRef]

Apolonski, A.

Aquila, A. L.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science320(5883), 1614–1617 (2008).
[CrossRef] [PubMed]

Ashkin, A.

A. Ashkin, G. Boyd, and J. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron.2(6), 109–124 (1966).
[CrossRef]

Attwood, D. T.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science320(5883), 1614–1617 (2008).
[CrossRef] [PubMed]

Austin, D. R.

Azzeer, A. M.

Beck, M.

Bernhardt, B.

Bertsimas, D. J.

Birge, J. R.

Boehm, G.

Bor, Z.

Boyd, G.

A. Ashkin, G. Boyd, and J. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron.2(6), 109–124 (1966).
[CrossRef]

Brons, J.

Diddams, S.

Diels, J.-C.

Dziedzic, J.

A. Ashkin, G. Boyd, and J. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron.2(6), 109–124 (1966).
[CrossRef]

Eidam, T.

Ell, R.

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. B18(6), 882–885 (2001).
[CrossRef]

Ferencz, K.

Fill, E.

Fujimoto, J. G.

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. B18(6), 882–885 (2001).
[CrossRef]

Gagnon, J.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science320(5883), 1614–1617 (2008).
[CrossRef] [PubMed]

Gosteva, A.

A. Gosteva, M. Haiml, R. Paschotta, and U. Keller, “Noise-related resolution limit of dispersion measurements with white-light interferometers,” J. Opt. Soc. B22(9), 1868–1874 (2005).
[CrossRef]

Goulielmakis, E.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science320(5883), 1614–1617 (2008).
[CrossRef] [PubMed]

Grasse, C.

Grupe, D.

Gullikson, E. M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science320(5883), 1614–1617 (2008).
[CrossRef] [PubMed]

Haiml, M.

A. Gosteva, M. Haiml, R. Paschotta, and U. Keller, “Noise-related resolution limit of dispersion measurements with white-light interferometers,” J. Opt. Soc. B22(9), 1868–1874 (2005).
[CrossRef]

Hänsch, T. W.

Hebling, J.

Hirlimann, C. A.

Hofstetter, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science320(5883), 1614–1617 (2008).
[CrossRef] [PubMed]

Ippen, E. P.

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. B18(6), 882–885 (2001).
[CrossRef]

Kalashnikov, V. L.

Karsch, S.

Kärtner, F. X.

J. R. Birge, F. X. Kärtner, and O. Nohadani, “Improving thin-film manufacturing yield with robust optimization,” Appl. Opt.50(9), C36–C40 (2011).
[CrossRef] [PubMed]

O. Nohadani, J. R. Birge, F. X. Kärtner, and D. J. Bertsimas, “Robust chirped mirrors,” Appl. Opt.47(14), 2630–2636 (2008).
[CrossRef] [PubMed]

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. B18(6), 882–885 (2001).
[CrossRef]

Keller, U.

A. Gosteva, M. Haiml, R. Paschotta, and U. Keller, “Noise-related resolution limit of dispersion measurements with white-light interferometers,” J. Opt. Soc. B22(9), 1868–1874 (2005).
[CrossRef]

Kienberger, R.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science320(5883), 1614–1617 (2008).
[CrossRef] [PubMed]

Kleineberg, U.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science320(5883), 1614–1617 (2008).
[CrossRef] [PubMed]

Knox, W. H.

Köházi-Kis, A.

R. Szipőcs and A. Köházi-Kis, “Theory and design of chirped dielectric laser mirrors,” Appl. Phys. B65(2), 115–135 (1997).
[CrossRef]

Kovács, A. P.

Krausz, F.

V. Pervak, O. Pronin, O. Razskazovskaya, J. Brons, I. B. Angelov, M. K. Trubetskov, A. V. Tikhonravov, and F. Krausz, “High-dispersive mirrors for high power applications,” Opt. Express20(4), 4503–4508 (2012).
[CrossRef] [PubMed]

O. Pronin, J. Brons, C. Grasse, V. Pervak, G. Boehm, M.-C. Amann, V. L. Kalashnikov, A. Apolonski, and F. Krausz, “High-power 200 fs Kerr-lens mode-locked Yb:YAG thin-disk oscillator,” Opt. Lett.36(24), 4746–4748 (2011).
[CrossRef] [PubMed]

I. Pupeza, T. Eidam, J. Rauschenberger, B. Bernhardt, A. Ozawa, E. Fill, A. Apolonski, T. Udem, J. Limpert, Z. A. Alahmed, A. M. Azzeer, A. Tünnermann, T. W. Hänsch, and F. Krausz, “Power scaling of a high-repetition-rate enhancement cavity,” Opt. Lett.35(12), 2052–2054 (2010).
[CrossRef] [PubMed]

V. Pervak, I. Ahmad, S. A. Trushin, Z. Major, A. Apolonski, S. Karsch, and F. Krausz, “Chirped-pulse amplification of laser pulses with dispersive mirrors,” Opt. Express17(21), 19204–19212 (2009).
[CrossRef] [PubMed]

V. Pervak, I. Ahmad, M. K. Trubetskov, A. V. Tikhonravov, and F. Krausz, “Double-angle multilayer mirrors with smooth dispersion characteristics,” Opt. Express17(10), 7943–7951 (2009).
[CrossRef] [PubMed]

V. Pervak, C. Teisset, A. Sugita, S. Naumov, F. Krausz, and A. Apolonski, “High-dispersive mirrors for femtosecond lasers,” Opt. Express16(14), 10220–10233 (2008).
[CrossRef] [PubMed]

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science320(5883), 1614–1617 (2008).
[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. B87(1), 5–12 (2007).
[CrossRef]

R. Szipöcs, K. Ferencz, C. Spielmann, and F. Krausz, “Chirped multilayer coatings for broadband dispersion control in femtosecond lasers,” Opt. Lett.19(3), 201–203 (1994).
[CrossRef] [PubMed]

Kurdi, G.

Li, K. D.

Limpert, J.

Major, Z.

Mogi, K.

Morgner, U.

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. B18(6), 882–885 (2001).
[CrossRef]

Mourou, G.

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun.56(3), 219–221 (1985).
[CrossRef]

Naganuma, K.

Naumov, S.

V. Pervak, C. Teisset, A. Sugita, S. Naumov, F. Krausz, and A. Apolonski, “High-dispersive mirrors for femtosecond lasers,” Opt. Express16(14), 10220–10233 (2008).
[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. B87(1), 5–12 (2007).
[CrossRef]

Nohadani, O.

Osvay, K.

Ozawa, A.

Paschotta, R.

A. Gosteva, M. Haiml, R. Paschotta, and U. Keller, “Noise-related resolution limit of dispersion measurements with white-light interferometers,” J. Opt. Soc. B22(9), 1868–1874 (2005).
[CrossRef]

Pearson, N. M.

Pervak, V.

T. V. Amotchkina, M. K. Trubetskov, V. Pervak, B. Romanov, and A. V. Tikhonravov, “On the reliability of reverse engineering results,” Appl. Opt.51(22), 5543–5551 (2012).
[CrossRef] [PubMed]

V. Pervak, O. Pronin, O. Razskazovskaya, J. Brons, I. B. Angelov, M. K. Trubetskov, A. V. Tikhonravov, and F. Krausz, “High-dispersive mirrors for high power applications,” Opt. Express20(4), 4503–4508 (2012).
[CrossRef] [PubMed]

V. Pervak, M. K. Trubetskov, and A. V. Tikhonravov, “Robust synthesis of dispersive mirrors,” Opt. Express19(3), 2371–2380 (2011).
[CrossRef] [PubMed]

V. Pervak, M. K. Trubetskov, and A. V. Tikhonravov, “Robust synthesis of dispersive mirrors,” Opt. Express19(3), 2371–2380 (2011).
[CrossRef] [PubMed]

O. Pronin, J. Brons, C. Grasse, V. Pervak, G. Boehm, M.-C. Amann, V. L. Kalashnikov, A. Apolonski, and F. Krausz, “High-power 200 fs Kerr-lens mode-locked Yb:YAG thin-disk oscillator,” Opt. Lett.36(24), 4746–4748 (2011).
[CrossRef] [PubMed]

M. K. Trubetskov, V. Pervak, and A. V. Tikhonravov, “Phase optimization of dispersive mirrors based on floating constants,” Opt. Express18(26), 27613–27618 (2010).
[CrossRef] [PubMed]

V. Pervak, I. Ahmad, M. K. Trubetskov, A. V. Tikhonravov, and F. Krausz, “Double-angle multilayer mirrors with smooth dispersion characteristics,” Opt. Express17(10), 7943–7951 (2009).
[CrossRef] [PubMed]

V. Pervak, I. Ahmad, S. A. Trushin, Z. Major, A. Apolonski, S. Karsch, and F. Krausz, “Chirped-pulse amplification of laser pulses with dispersive mirrors,” Opt. Express17(21), 19204–19212 (2009).
[CrossRef] [PubMed]

T. V. Amotchkina, A. V. Tikhonravov, M. K. Trubetskov, D. Grupe, A. Apolonski, and V. Pervak, “Measurement of group delay of dispersive mirrors with white-light interferometer,” Appl. Opt.48(5), 949–956 (2009).
[CrossRef] [PubMed]

V. Pervak, C. Teisset, A. Sugita, S. Naumov, F. Krausz, and A. Apolonski, “High-dispersive mirrors for femtosecond lasers,” Opt. Express16(14), 10220–10233 (2008).
[CrossRef] [PubMed]

M. Trubetskov, A. Tikhonravov, and V. Pervak, “Time-domain approach for designing dispersive mirrors based on the needle optimization technique. Theory,” Opt. Express16(25), 20637–20647 (2008).
[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. B87(1), 5–12 (2007).
[CrossRef]

Pronin, O.

Pupeza, I.

Rauschenberger, J.

Razskazovskaya, O.

Romanov, B.

Scheuer, V.

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. B18(6), 882–885 (2001).
[CrossRef]

Schibli, T.

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. B18(6), 882–885 (2001).
[CrossRef]

Schultze, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science320(5883), 1614–1617 (2008).
[CrossRef] [PubMed]

Spielmann, C.

Strickland, D.

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun.56(3), 219–221 (1985).
[CrossRef]

Sugita, A.

Szipocs, R.

R. Szipőcs and A. Köházi-Kis, “Theory and design of chirped dielectric laser mirrors,” Appl. Phys. B65(2), 115–135 (1997).
[CrossRef]

Szipöcs, R.

Teisset, C.

Tikhonravov, A.

Tikhonravov, A. A.

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and A. A. Tikhonravov, “Application of advanced optimization concepts to the design of high quality optical coatings,” Proc. SPIE4829, 1061–1062 (2003).
[CrossRef]

Tikhonravov, A. V.

V. Pervak, O. Pronin, O. Razskazovskaya, J. Brons, I. B. Angelov, M. K. Trubetskov, A. V. Tikhonravov, and F. Krausz, “High-dispersive mirrors for high power applications,” Opt. Express20(4), 4503–4508 (2012).
[CrossRef] [PubMed]

T. V. Amotchkina, M. K. Trubetskov, V. Pervak, B. Romanov, and A. V. Tikhonravov, “On the reliability of reverse engineering results,” Appl. Opt.51(22), 5543–5551 (2012).
[CrossRef] [PubMed]

V. Pervak, M. K. Trubetskov, and A. V. Tikhonravov, “Robust synthesis of dispersive mirrors,” Opt. Express19(3), 2371–2380 (2011).
[CrossRef] [PubMed]

V. Pervak, M. K. Trubetskov, and A. V. Tikhonravov, “Robust synthesis of dispersive mirrors,” Opt. Express19(3), 2371–2380 (2011).
[CrossRef] [PubMed]

M. K. Trubetskov, V. Pervak, and A. V. Tikhonravov, “Phase optimization of dispersive mirrors based on floating constants,” Opt. Express18(26), 27613–27618 (2010).
[CrossRef] [PubMed]

V. Pervak, I. Ahmad, M. K. Trubetskov, A. V. Tikhonravov, and F. Krausz, “Double-angle multilayer mirrors with smooth dispersion characteristics,” Opt. Express17(10), 7943–7951 (2009).
[CrossRef] [PubMed]

T. V. Amotchkina, A. V. Tikhonravov, M. K. Trubetskov, D. Grupe, A. Apolonski, and V. Pervak, “Measurement of group delay of dispersive mirrors with white-light interferometer,” Appl. Opt.48(5), 949–956 (2009).
[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. B87(1), 5–12 (2007).
[CrossRef]

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and A. A. Tikhonravov, “Application of advanced optimization concepts to the design of high quality optical coatings,” Proc. SPIE4829, 1061–1062 (2003).
[CrossRef]

Trubetskov, M.

Trubetskov, M. K.

V. Pervak, O. Pronin, O. Razskazovskaya, J. Brons, I. B. Angelov, M. K. Trubetskov, A. V. Tikhonravov, and F. Krausz, “High-dispersive mirrors for high power applications,” Opt. Express20(4), 4503–4508 (2012).
[CrossRef] [PubMed]

T. V. Amotchkina, M. K. Trubetskov, V. Pervak, B. Romanov, and A. V. Tikhonravov, “On the reliability of reverse engineering results,” Appl. Opt.51(22), 5543–5551 (2012).
[CrossRef] [PubMed]

V. Pervak, M. K. Trubetskov, and A. V. Tikhonravov, “Robust synthesis of dispersive mirrors,” Opt. Express19(3), 2371–2380 (2011).
[CrossRef] [PubMed]

V. Pervak, M. K. Trubetskov, and A. V. Tikhonravov, “Robust synthesis of dispersive mirrors,” Opt. Express19(3), 2371–2380 (2011).
[CrossRef] [PubMed]

M. K. Trubetskov, V. Pervak, and A. V. Tikhonravov, “Phase optimization of dispersive mirrors based on floating constants,” Opt. Express18(26), 27613–27618 (2010).
[CrossRef] [PubMed]

V. Pervak, I. Ahmad, M. K. Trubetskov, A. V. Tikhonravov, and F. Krausz, “Double-angle multilayer mirrors with smooth dispersion characteristics,” Opt. Express17(10), 7943–7951 (2009).
[CrossRef] [PubMed]

T. V. Amotchkina, A. V. Tikhonravov, M. K. Trubetskov, D. Grupe, A. Apolonski, and V. Pervak, “Measurement of group delay of dispersive mirrors with white-light interferometer,” Appl. Opt.48(5), 949–956 (2009).
[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. B87(1), 5–12 (2007).
[CrossRef]

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and A. A. Tikhonravov, “Application of advanced optimization concepts to the design of high quality optical coatings,” Proc. SPIE4829, 1061–1062 (2003).
[CrossRef]

Trushin, S. A.

Tschudi, T.

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. B18(6), 882–885 (2001).
[CrossRef]

Tünnermann, A.

Udem, T.

Uiberacker, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science320(5883), 1614–1617 (2008).
[CrossRef] [PubMed]

Walmsley, I. A.

Witting, T.

Yakovlev, V. S.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science320(5883), 1614–1617 (2008).
[CrossRef] [PubMed]

Yamada, H.

Appl. Opt. (4)

Appl. Phys. B (3)

R. Szipőcs and A. Köházi-Kis, “Theory and design of chirped dielectric laser mirrors,” Appl. Phys. B65(2), 115–135 (1997).
[CrossRef]

W. H. Knox, “Dispersion measurements for femtosecond-pulse generation and applications,” Appl. Phys. B58(3), 225–235 (1994).
[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. B87(1), 5–12 (2007).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. Ashkin, G. Boyd, and J. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron.2(6), 109–124 (1966).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Opt. Soc. B (2)

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. B18(6), 882–885 (2001).
[CrossRef]

A. Gosteva, M. Haiml, R. Paschotta, and U. Keller, “Noise-related resolution limit of dispersion measurements with white-light interferometers,” J. Opt. Soc. B22(9), 1868–1874 (2005).
[CrossRef]

Opt. Commun. (1)

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun.56(3), 219–221 (1985).
[CrossRef]

Opt. Express (8)

V. Pervak, O. Pronin, O. Razskazovskaya, J. Brons, I. B. Angelov, M. K. Trubetskov, A. V. Tikhonravov, and F. Krausz, “High-dispersive mirrors for high power applications,” Opt. Express20(4), 4503–4508 (2012).
[CrossRef] [PubMed]

V. Pervak, I. Ahmad, S. A. Trushin, Z. Major, A. Apolonski, S. Karsch, and F. Krausz, “Chirped-pulse amplification of laser pulses with dispersive mirrors,” Opt. Express17(21), 19204–19212 (2009).
[CrossRef] [PubMed]

M. K. Trubetskov, V. Pervak, and A. V. Tikhonravov, “Phase optimization of dispersive mirrors based on floating constants,” Opt. Express18(26), 27613–27618 (2010).
[CrossRef] [PubMed]

V. Pervak, M. K. Trubetskov, and A. V. Tikhonravov, “Robust synthesis of dispersive mirrors,” Opt. Express19(3), 2371–2380 (2011).
[CrossRef] [PubMed]

V. Pervak, M. K. Trubetskov, and A. V. Tikhonravov, “Robust synthesis of dispersive mirrors,” Opt. Express19(3), 2371–2380 (2011).
[CrossRef] [PubMed]

V. Pervak, I. Ahmad, M. K. Trubetskov, A. V. Tikhonravov, and F. Krausz, “Double-angle multilayer mirrors with smooth dispersion characteristics,” Opt. Express17(10), 7943–7951 (2009).
[CrossRef] [PubMed]

V. Pervak, C. Teisset, A. Sugita, S. Naumov, F. Krausz, and A. Apolonski, “High-dispersive mirrors for femtosecond lasers,” Opt. Express16(14), 10220–10233 (2008).
[CrossRef] [PubMed]

M. Trubetskov, A. Tikhonravov, and V. Pervak, “Time-domain approach for designing dispersive mirrors based on the needle optimization technique. Theory,” Opt. Express16(25), 20637–20647 (2008).
[CrossRef] [PubMed]

Opt. Lett. (7)

O. Pronin, J. Brons, C. Grasse, V. Pervak, G. Boehm, M.-C. Amann, V. L. Kalashnikov, A. Apolonski, and F. Krausz, “High-power 200 fs Kerr-lens mode-locked Yb:YAG thin-disk oscillator,” Opt. Lett.36(24), 4746–4748 (2011).
[CrossRef] [PubMed]

I. Pupeza, T. Eidam, J. Rauschenberger, B. Bernhardt, A. Ozawa, E. Fill, A. Apolonski, T. Udem, J. Limpert, Z. A. Alahmed, A. M. Azzeer, A. Tünnermann, T. W. Hänsch, and F. Krausz, “Power scaling of a high-repetition-rate enhancement cavity,” Opt. Lett.35(12), 2052–2054 (2010).
[CrossRef] [PubMed]

K. Osvay, G. Kurdi, J. Hebling, A. P. Kovács, Z. Bor, and R. Szipöcs, “Measurement of the group delay of laser mirrors by a Fabry-Perot interferometer,” Opt. Lett.20(22), 2339–2341 (1995).
[CrossRef] [PubMed]

W. H. Knox, N. M. Pearson, K. D. Li, and C. A. Hirlimann, “Interferometric measurements of femtosecond group delay in optical components,” Opt. Lett.13(7), 574–576 (1988).
[CrossRef] [PubMed]

K. Naganuma, K. Mogi, and H. Yamada, “Group-delay measurement using the Fourier transform of an interferometric cross correlation generated by white light,” Opt. Lett.15(7), 393–395 (1990).
[CrossRef] [PubMed]

M. Beck and I. A. Walmsley, “Measurement of group delay with high temporal and spectral resolution,” Opt. Lett.15(9), 492–494 (1990).
[CrossRef] [PubMed]

R. Szipöcs, K. Ferencz, C. Spielmann, and F. Krausz, “Chirped multilayer coatings for broadband dispersion control in femtosecond lasers,” Opt. Lett.19(3), 201–203 (1994).
[CrossRef] [PubMed]

Proc. SPIE (1)

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and A. A. Tikhonravov, “Application of advanced optimization concepts to the design of high quality optical coatings,” Proc. SPIE4829, 1061–1062 (2003).
[CrossRef]

Science (1)

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science320(5883), 1614–1617 (2008).
[CrossRef] [PubMed]

Other (5)

H. A. Macleod, Thin-film optical filters (Taylor & Francis, 2010).

A. N. Tikhonov and V. I. Arsenin, Solutions of Ill-Posed Problems (Halsted Press, 1977).

A. N. Tikhonov, A. Goncharsky, V. V. Stepanov, and A. G. Yagola, Numerical Methods for the Solution of Ill-posed Problems, Mathematics and Its Applications No. 328 (Kluwer Academic Publishers, 1995).

J. H. Ahlberg, E. N. Nilson, and J. L. Walsh, The theory of splines and their applications (Academic Press, 1967).

J.-C. Diels and W. Rudolph, Ultrashort laser pulse phenomena : fundamentals, techniques, and applications on a femtosecond time scale (Academic Press, 1996).

Supplementary Material (1)

» Media 1: AVI (2642 KB)     

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Figures (7)

Fig. 1
Fig. 1

Measurement setup for transmission mode (a) and for reflection mode (b) (the distance between mirrors is exaggerated). Simulated transmittance peaks (c) and reflectance resonances (d) for the system consisting of a 80-layer DM, 10- µm air spacer, and a partially-transmitting Al mirror having virtually zero GDD.

Fig. 2
Fig. 2

Single-frame excerpt from video recording (Media 1) of resonance positions changes (a) with spacer thickness (b). Joining data from the measurements with different spacer thicknesses into a combined grid for data processing (c).

Fig. 3
Fig. 3

Results of GD and GDD reconstruction in case of location of reflectance minima with a high accuracy (0.002 nm) ((a) – GD and (b) – GDD) and in case of a typical CCD spectrometer accuracy of 0.37nm ((c) – GD and (d) – GDD).

Fig. 4
Fig. 4

GD (a) and GDD (b) obtained with RSI in transmittance mode (green curves), WLI results (red curves) and theoretical data (blue curves). Comparison of GD (c) and GDD (d) results obtained with RSI in transmittance mode (green curves) and in reflectance mode (red curves).

Fig. 5
Fig. 5

Result of a typical reflectance scan (blue curves) in the ranges 650-1060 nm (a) and 850-1350 nm (b). Red vertical lines indicate positions of reflectance peaks. Measured data is represented in intensity non-normalized units. Obtained GD (c) and GDD (d) of the ultra-broadband 96-layer mirror (green curves) and theoretical data (red curves) for comparison.

Fig. 6
Fig. 6

GD (a) and GDD (b) evaluated from reflectance measurements for a mirror working in the ultraviolet (green curves) along with the corresponding theoretical predictions (red lines).

Fig. 7
Fig. 7

GD (a, c) and GDD (b, d) RSI measurements for a high-dispersive mirror in a wide band 940-1100 nm (a, b) and in working range 1000-1040 nm (c, d) (green curves). Blue curves correspond to the theoretical GD and GDD, red curves – to WLI measurements.

Equations (8)

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

T= T m T [1 ( R m R + ) 1/2 ] 2 [ 1+ 4 ( R m R + ) 1/2 [1 ( R m R + ) 1/2 ] 2 sin 2 ( φ m +φ 2 δ ) ] 1 ,
δ=ω d s n s cos θ s /c.
φ m +φ 2 δ=πk,k=1,
Δ φ j φ j+1 φ j = 2 d s n s cos θ s c ( ω j+1 ω j )2π.
GD j = 2 d s n s cos θ s c + 2π Δ ω j ,Δ ω j = ω j+1 ω j ,
GD j+1 GD j =2π( 1/Δ ω j+1 1/Δ ω j ).
Ab = u
GD(ω)= a i + b i (ω x i )+ c i (ω x i ) 2 + d i (ω x i ) 3 ,ω[ x i , x i+1 ).

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