Abstract

We combine powerful and well-proven needle-optimization technique with time-domain optimization approach in order to obtain a new efficient method of designing dispersive mirrors. We also propose a new optimization criterion targeted at reaching shortest possible pulses with maximum possible energy at the exit of a compressor containing such mirrors. Proposed optimization criterion includes two parameters allowing one to adjust the relative weights of the mentioned targets with a high flexibility. The obtained results are compared with solutions of the “classical” optimization approach based on the optimization of a merit function comparing theoretical reflectance and group delay dispersion with target ones. The new approach allows obtaining simpler solutions providing better characteristics of the output pulse.

© 2008 Optical Society of America

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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, 201-203 (1994).
    [CrossRef] [PubMed]
  2. V. Pervak, C. Tiesset, A. Sugita, S. Naumov, F. Krausz, and A. Apolonski, "High-dispersive mirrors for femtosecond lasers," Opt. Express 16, 10220-10233 (2008).
    [CrossRef] [PubMed]
  3. G. Steinmeyer, "Femtosecond dispersion compensation with multilayer coatings: toward the optical octave," Appl. Opt. 45, 1484-1490 (2006)
    [CrossRef] [PubMed]
  4. V. Yakovlev and G. Tempea, "Optimization of Chirped Mirrors," Appl. Opt. 41, 6514-6520 (2002).
    [CrossRef] [PubMed]
  5. 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]
  6. J. R. Birge and F. X. Kärtner, "Efficient optimization of multilayer coatings for ultrafast optics using analytic gradients of dispersion," Appl. Opt. 46, 2656-2662 (2007)
    [CrossRef] [PubMed]
  7. O. Nohadani, J. R. Birge, F. X. Kärtner, and D. J. Bertsimas, "Robust chirped mirrors," Appl. Opt. 47, 2630-2636 (2008)
    [CrossRef] [PubMed]
  8. R. Szipöcs, A. Köházi-Kis, S. Lakó, P. Apai, A. P. Kovács, G. Debell, L. Mott, A. W. Louderback, A. V. Tikhonravov, and M. K. Trubetskov, "Negative dispersion mirrors for dispersion control in femtosecond lasers: chirped dielectric mirrors and multi-cavity Gires-Tournois interferometers," Appl. Phys. B 70,S51-S57 (2000).
    [CrossRef]
  9. A. V. Tikhonravov, M. K. Trubetskov, U. Keller, and N. Matuschek, "Designing of coatings for femtosecond lasers with phase derivatives targets," Proc. SPIE 3738, 221-229 (1999).
    [CrossRef]
  10. A. Ozawa, J. Rauschenberger, Ch. Gohle, M. Herrmann, D. R. Walker, V. Pervak, A. Fernandez, R. Graf, A. Apolonski, R. Holzwarth, F. Krausz, T. W. Haensch, and Th. Udem, "High harmonic frequency comb for high resolution spectroscopy," Phys. Rev. Lett. 100, 253901 (2008).
    [CrossRef] [PubMed]
  11. P. Dombi, V. S. Yakovlev, K. O'Keeffe, T. Fuji, M. Lezius, and G. Tempea, "Pulse compression with time-domain optimized chirped mirrors," Opt. Express 13, 10888-10894 (2005).
    [CrossRef] [PubMed]
  12. Sh. Furman and A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Edition Frontieres, Gif-sur-Yvette, 1992).
  13. 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]
  14. 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]
  15. A. V. Tikhonravov, M. K. Trubetskov, V. Pervak, F. Krausz, and A. Apolonski, "Design, Fabrication and Reverse Engineering of Broad Band Chirped Mirrors," in Optical Interference Coatings, OSA Technical Digest (CD) (Optical Society of America, 2007), paper WB4.
  16. V. Pervak, S. Naumov, A. Cavalieri, X. Gu, M. K. Trubetskov, A. V. Tikhonravov, F. Krausz, and A. Apolonski, "Advanced Dispersive Optics for the VIS-IR Range," in Optical Interference Coatings, OSA Technical Digest (CD) (Optical Society of America, 2007), paper WA9.
  17. 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 (2006).
    [CrossRef]
  18. F. Abelès. "Recherches sur la propagation des ondes electromagnetique sinusoidales dans les milieux stratifies," Ann. de Physique 5, 596-640, 706-782 (1950).
  19. A. V. Tikhonravov and M. K. Trubetskov, OptiLayer Thin Film Software, http://www.optilayer.com.
  20. J. W. Cooley and J. W. Tukey, "An algorithm for the machine calculation of complex Fourier series," Math. Comput. 19, 297-301 (1965).
    [CrossRef]

2008 (3)

V. Pervak, C. Tiesset, A. Sugita, S. Naumov, F. Krausz, and A. Apolonski, "High-dispersive mirrors for femtosecond lasers," Opt. Express 16, 10220-10233 (2008).
[CrossRef] [PubMed]

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

A. Ozawa, J. Rauschenberger, Ch. Gohle, M. Herrmann, D. R. Walker, V. Pervak, A. Fernandez, R. Graf, A. Apolonski, R. Holzwarth, F. Krausz, T. W. Haensch, and Th. Udem, "High harmonic frequency comb for high resolution spectroscopy," Phys. Rev. Lett. 100, 253901 (2008).
[CrossRef] [PubMed]

2007 (2)

2006 (2)

G. Steinmeyer, "Femtosecond dispersion compensation with multilayer coatings: toward the optical octave," Appl. Opt. 45, 1484-1490 (2006)
[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 (2006).
[CrossRef]

2005 (1)

2002 (1)

2001 (1)

2000 (1)

R. Szipöcs, A. Köházi-Kis, S. Lakó, P. Apai, A. P. Kovács, G. Debell, L. Mott, A. W. Louderback, A. V. Tikhonravov, and M. K. Trubetskov, "Negative dispersion mirrors for dispersion control in femtosecond lasers: chirped dielectric mirrors and multi-cavity Gires-Tournois interferometers," Appl. Phys. B 70,S51-S57 (2000).
[CrossRef]

1999 (1)

A. V. Tikhonravov, M. K. Trubetskov, U. Keller, and N. Matuschek, "Designing of coatings for femtosecond lasers with phase derivatives targets," Proc. SPIE 3738, 221-229 (1999).
[CrossRef]

1996 (1)

1994 (1)

1965 (1)

J. W. Cooley and J. W. Tukey, "An algorithm for the machine calculation of complex Fourier series," Math. Comput. 19, 297-301 (1965).
[CrossRef]

1950 (1)

F. Abelès. "Recherches sur la propagation des ondes electromagnetique sinusoidales dans les milieux stratifies," Ann. de Physique 5, 596-640, 706-782 (1950).

Abelès, F.

F. Abelès. "Recherches sur la propagation des ondes electromagnetique sinusoidales dans les milieux stratifies," Ann. de Physique 5, 596-640, 706-782 (1950).

Angelow, G.

Apai, P.

R. Szipöcs, A. Köházi-Kis, S. Lakó, P. Apai, A. P. Kovács, G. Debell, L. Mott, A. W. Louderback, A. V. Tikhonravov, and M. K. Trubetskov, "Negative dispersion mirrors for dispersion control in femtosecond lasers: chirped dielectric mirrors and multi-cavity Gires-Tournois interferometers," Appl. Phys. B 70,S51-S57 (2000).
[CrossRef]

Apolonski, A.

A. Ozawa, J. Rauschenberger, Ch. Gohle, M. Herrmann, D. R. Walker, V. Pervak, A. Fernandez, R. Graf, A. Apolonski, R. Holzwarth, F. Krausz, T. W. Haensch, and Th. Udem, "High harmonic frequency comb for high resolution spectroscopy," Phys. Rev. Lett. 100, 253901 (2008).
[CrossRef] [PubMed]

V. Pervak, C. Tiesset, A. Sugita, S. Naumov, F. Krausz, and A. Apolonski, "High-dispersive mirrors for femtosecond lasers," Opt. Express 16, 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. B 87, 5-12 (2006).
[CrossRef]

Bertsimas, D. J.

Birge, J. R.

Cooley, J. W.

J. W. Cooley and J. W. Tukey, "An algorithm for the machine calculation of complex Fourier series," Math. Comput. 19, 297-301 (1965).
[CrossRef]

Debell, G.

R. Szipöcs, A. Köházi-Kis, S. Lakó, P. Apai, A. P. Kovács, G. Debell, L. Mott, A. W. Louderback, A. V. Tikhonravov, and M. K. Trubetskov, "Negative dispersion mirrors for dispersion control in femtosecond lasers: chirped dielectric mirrors and multi-cavity Gires-Tournois interferometers," Appl. Phys. B 70,S51-S57 (2000).
[CrossRef]

DeBell, G. W.

Dombi, P.

Ell, R.

Ferencz, K.

Fernandez, A.

A. Ozawa, J. Rauschenberger, Ch. Gohle, M. Herrmann, D. R. Walker, V. Pervak, A. Fernandez, R. Graf, A. Apolonski, R. Holzwarth, F. Krausz, T. W. Haensch, and Th. Udem, "High harmonic frequency comb for high resolution spectroscopy," Phys. Rev. Lett. 100, 253901 (2008).
[CrossRef] [PubMed]

Fuji, T.

Fujimoto, J. G.

Gohle, Ch.

A. Ozawa, J. Rauschenberger, Ch. Gohle, M. Herrmann, D. R. Walker, V. Pervak, A. Fernandez, R. Graf, A. Apolonski, R. Holzwarth, F. Krausz, T. W. Haensch, and Th. Udem, "High harmonic frequency comb for high resolution spectroscopy," Phys. Rev. Lett. 100, 253901 (2008).
[CrossRef] [PubMed]

Graf, R.

A. Ozawa, J. Rauschenberger, Ch. Gohle, M. Herrmann, D. R. Walker, V. Pervak, A. Fernandez, R. Graf, A. Apolonski, R. Holzwarth, F. Krausz, T. W. Haensch, and Th. Udem, "High harmonic frequency comb for high resolution spectroscopy," Phys. Rev. Lett. 100, 253901 (2008).
[CrossRef] [PubMed]

Haensch, T. W.

A. Ozawa, J. Rauschenberger, Ch. Gohle, M. Herrmann, D. R. Walker, V. Pervak, A. Fernandez, R. Graf, A. Apolonski, R. Holzwarth, F. Krausz, T. W. Haensch, and Th. Udem, "High harmonic frequency comb for high resolution spectroscopy," Phys. Rev. Lett. 100, 253901 (2008).
[CrossRef] [PubMed]

Herrmann, M.

A. Ozawa, J. Rauschenberger, Ch. Gohle, M. Herrmann, D. R. Walker, V. Pervak, A. Fernandez, R. Graf, A. Apolonski, R. Holzwarth, F. Krausz, T. W. Haensch, and Th. Udem, "High harmonic frequency comb for high resolution spectroscopy," Phys. Rev. Lett. 100, 253901 (2008).
[CrossRef] [PubMed]

Holzwarth, R.

A. Ozawa, J. Rauschenberger, Ch. Gohle, M. Herrmann, D. R. Walker, V. Pervak, A. Fernandez, R. Graf, A. Apolonski, R. Holzwarth, F. Krausz, T. W. Haensch, and Th. Udem, "High harmonic frequency comb for high resolution spectroscopy," Phys. Rev. Lett. 100, 253901 (2008).
[CrossRef] [PubMed]

Ippen, E. P.

Kärtner, F. X.

Keller, U.

A. V. Tikhonravov, M. K. Trubetskov, U. Keller, and N. Matuschek, "Designing of coatings for femtosecond lasers with phase derivatives targets," Proc. SPIE 3738, 221-229 (1999).
[CrossRef]

Köházi-Kis, A.

R. Szipöcs, A. Köházi-Kis, S. Lakó, P. Apai, A. P. Kovács, G. Debell, L. Mott, A. W. Louderback, A. V. Tikhonravov, and M. K. Trubetskov, "Negative dispersion mirrors for dispersion control in femtosecond lasers: chirped dielectric mirrors and multi-cavity Gires-Tournois interferometers," Appl. Phys. B 70,S51-S57 (2000).
[CrossRef]

Kovács, A. P.

R. Szipöcs, A. Köházi-Kis, S. Lakó, P. Apai, A. P. Kovács, G. Debell, L. Mott, A. W. Louderback, A. V. Tikhonravov, and M. K. Trubetskov, "Negative dispersion mirrors for dispersion control in femtosecond lasers: chirped dielectric mirrors and multi-cavity Gires-Tournois interferometers," Appl. Phys. B 70,S51-S57 (2000).
[CrossRef]

Krausz, F.

A. Ozawa, J. Rauschenberger, Ch. Gohle, M. Herrmann, D. R. Walker, V. Pervak, A. Fernandez, R. Graf, A. Apolonski, R. Holzwarth, F. Krausz, T. W. Haensch, and Th. Udem, "High harmonic frequency comb for high resolution spectroscopy," Phys. Rev. Lett. 100, 253901 (2008).
[CrossRef] [PubMed]

V. Pervak, C. Tiesset, A. Sugita, S. Naumov, F. Krausz, and A. Apolonski, "High-dispersive mirrors for femtosecond lasers," Opt. Express 16, 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. B 87, 5-12 (2006).
[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]

Lakó, S.

R. Szipöcs, A. Köházi-Kis, S. Lakó, P. Apai, A. P. Kovács, G. Debell, L. Mott, A. W. Louderback, A. V. Tikhonravov, and M. K. Trubetskov, "Negative dispersion mirrors for dispersion control in femtosecond lasers: chirped dielectric mirrors and multi-cavity Gires-Tournois interferometers," Appl. Phys. B 70,S51-S57 (2000).
[CrossRef]

Lezius, M.

Louderback, A. W.

R. Szipöcs, A. Köházi-Kis, S. Lakó, P. Apai, A. P. Kovács, G. Debell, L. Mott, A. W. Louderback, A. V. Tikhonravov, and M. K. Trubetskov, "Negative dispersion mirrors for dispersion control in femtosecond lasers: chirped dielectric mirrors and multi-cavity Gires-Tournois interferometers," Appl. Phys. B 70,S51-S57 (2000).
[CrossRef]

Matuschek, N.

A. V. Tikhonravov, M. K. Trubetskov, U. Keller, and N. Matuschek, "Designing of coatings for femtosecond lasers with phase derivatives targets," Proc. SPIE 3738, 221-229 (1999).
[CrossRef]

Morgner, U.

Mott, L.

R. Szipöcs, A. Köházi-Kis, S. Lakó, P. Apai, A. P. Kovács, G. Debell, L. Mott, A. W. Louderback, A. V. Tikhonravov, and M. K. Trubetskov, "Negative dispersion mirrors for dispersion control in femtosecond lasers: chirped dielectric mirrors and multi-cavity Gires-Tournois interferometers," Appl. Phys. B 70,S51-S57 (2000).
[CrossRef]

Naumov, S.

V. Pervak, C. Tiesset, A. Sugita, S. Naumov, F. Krausz, and A. Apolonski, "High-dispersive mirrors for femtosecond lasers," Opt. Express 16, 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. B 87, 5-12 (2006).
[CrossRef]

Nohadani, O.

O'Keeffe, K.

Ozawa, A.

A. Ozawa, J. Rauschenberger, Ch. Gohle, M. Herrmann, D. R. Walker, V. Pervak, A. Fernandez, R. Graf, A. Apolonski, R. Holzwarth, F. Krausz, T. W. Haensch, and Th. Udem, "High harmonic frequency comb for high resolution spectroscopy," Phys. Rev. Lett. 100, 253901 (2008).
[CrossRef] [PubMed]

Pervak, V.

A. Ozawa, J. Rauschenberger, Ch. Gohle, M. Herrmann, D. R. Walker, V. Pervak, A. Fernandez, R. Graf, A. Apolonski, R. Holzwarth, F. Krausz, T. W. Haensch, and Th. Udem, "High harmonic frequency comb for high resolution spectroscopy," Phys. Rev. Lett. 100, 253901 (2008).
[CrossRef] [PubMed]

V. Pervak, C. Tiesset, A. Sugita, S. Naumov, F. Krausz, and A. Apolonski, "High-dispersive mirrors for femtosecond lasers," Opt. Express 16, 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. B 87, 5-12 (2006).
[CrossRef]

Rauschenberger, J.

A. Ozawa, J. Rauschenberger, Ch. Gohle, M. Herrmann, D. R. Walker, V. Pervak, A. Fernandez, R. Graf, A. Apolonski, R. Holzwarth, F. Krausz, T. W. Haensch, and Th. Udem, "High harmonic frequency comb for high resolution spectroscopy," Phys. Rev. Lett. 100, 253901 (2008).
[CrossRef] [PubMed]

Scheuer, V.

Schibli, T.

Spielmann, C.

Steinmeyer, G.

Sugita, A.

Szipöcs, R.

R. Szipöcs, A. Köházi-Kis, S. Lakó, P. Apai, A. P. Kovács, G. Debell, L. Mott, A. W. Louderback, A. V. Tikhonravov, and M. K. Trubetskov, "Negative dispersion mirrors for dispersion control in femtosecond lasers: chirped dielectric mirrors and multi-cavity Gires-Tournois interferometers," Appl. Phys. B 70,S51-S57 (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]

Tempea, G.

Tiesset, C.

Tikhonravov, A. V.

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, 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 (2006).
[CrossRef]

R. Szipöcs, A. Köházi-Kis, S. Lakó, P. Apai, A. P. Kovács, G. Debell, L. Mott, A. W. Louderback, A. V. Tikhonravov, and M. K. Trubetskov, "Negative dispersion mirrors for dispersion control in femtosecond lasers: chirped dielectric mirrors and multi-cavity Gires-Tournois interferometers," Appl. Phys. B 70,S51-S57 (2000).
[CrossRef]

A. V. Tikhonravov, M. K. Trubetskov, U. Keller, and N. Matuschek, "Designing of coatings for femtosecond lasers with phase derivatives targets," Proc. SPIE 3738, 221-229 (1999).
[CrossRef]

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]

Trubetskov, M. K.

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, 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 (2006).
[CrossRef]

R. Szipöcs, A. Köházi-Kis, S. Lakó, P. Apai, A. P. Kovács, G. Debell, L. Mott, A. W. Louderback, A. V. Tikhonravov, and M. K. Trubetskov, "Negative dispersion mirrors for dispersion control in femtosecond lasers: chirped dielectric mirrors and multi-cavity Gires-Tournois interferometers," Appl. Phys. B 70,S51-S57 (2000).
[CrossRef]

A. V. Tikhonravov, M. K. Trubetskov, U. Keller, and N. Matuschek, "Designing of coatings for femtosecond lasers with phase derivatives targets," Proc. SPIE 3738, 221-229 (1999).
[CrossRef]

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]

Tschudi, T.

Tukey, J. W.

J. W. Cooley and J. W. Tukey, "An algorithm for the machine calculation of complex Fourier series," Math. Comput. 19, 297-301 (1965).
[CrossRef]

Udem, Th.

A. Ozawa, J. Rauschenberger, Ch. Gohle, M. Herrmann, D. R. Walker, V. Pervak, A. Fernandez, R. Graf, A. Apolonski, R. Holzwarth, F. Krausz, T. W. Haensch, and Th. Udem, "High harmonic frequency comb for high resolution spectroscopy," Phys. Rev. Lett. 100, 253901 (2008).
[CrossRef] [PubMed]

Walker, D. R.

A. Ozawa, J. Rauschenberger, Ch. Gohle, M. Herrmann, D. R. Walker, V. Pervak, A. Fernandez, R. Graf, A. Apolonski, R. Holzwarth, F. Krausz, T. W. Haensch, and Th. Udem, "High harmonic frequency comb for high resolution spectroscopy," Phys. Rev. Lett. 100, 253901 (2008).
[CrossRef] [PubMed]

Yakovlev, V.

Yakovlev, V. S.

Ann. de Physique (1)

F. Abelès. "Recherches sur la propagation des ondes electromagnetique sinusoidales dans les milieux stratifies," Ann. de Physique 5, 596-640, 706-782 (1950).

Appl. Opt. (6)

Appl. Phys. B (2)

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 (2006).
[CrossRef]

R. Szipöcs, A. Köházi-Kis, S. Lakó, P. Apai, A. P. Kovács, G. Debell, L. Mott, A. W. Louderback, A. V. Tikhonravov, and M. K. Trubetskov, "Negative dispersion mirrors for dispersion control in femtosecond lasers: chirped dielectric mirrors and multi-cavity Gires-Tournois interferometers," Appl. Phys. B 70,S51-S57 (2000).
[CrossRef]

J. Opt. Soc. Am. B (1)

Math. Comput. (1)

J. W. Cooley and J. W. Tukey, "An algorithm for the machine calculation of complex Fourier series," Math. Comput. 19, 297-301 (1965).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

A. Ozawa, J. Rauschenberger, Ch. Gohle, M. Herrmann, D. R. Walker, V. Pervak, A. Fernandez, R. Graf, A. Apolonski, R. Holzwarth, F. Krausz, T. W. Haensch, and Th. Udem, "High harmonic frequency comb for high resolution spectroscopy," Phys. Rev. Lett. 100, 253901 (2008).
[CrossRef] [PubMed]

Proc. SPIE (1)

A. V. Tikhonravov, M. K. Trubetskov, U. Keller, and N. Matuschek, "Designing of coatings for femtosecond lasers with phase derivatives targets," Proc. SPIE 3738, 221-229 (1999).
[CrossRef]

Other (4)

Sh. Furman and A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Edition Frontieres, Gif-sur-Yvette, 1992).

A. V. Tikhonravov, M. K. Trubetskov, V. Pervak, F. Krausz, and A. Apolonski, "Design, Fabrication and Reverse Engineering of Broad Band Chirped Mirrors," in Optical Interference Coatings, OSA Technical Digest (CD) (Optical Society of America, 2007), paper WB4.

V. Pervak, S. Naumov, A. Cavalieri, X. Gu, M. K. Trubetskov, A. V. Tikhonravov, F. Krausz, and A. Apolonski, "Advanced Dispersive Optics for the VIS-IR Range," in Optical Interference Coatings, OSA Technical Digest (CD) (Optical Society of America, 2007), paper WA9.

A. V. Tikhonravov and M. K. Trubetskov, OptiLayer Thin Film Software, http://www.optilayer.com.

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Figures (10)

Fig. 1.
Fig. 1.

Left: Spectral density and GDD of the input pulse. Right: Input pulse intensity in a temporal representation (phase modulation is ideally compensated).

Fig. 2.
Fig. 2.

Layer thicknesses of the 100 layer chirp mirror obtained with “classical” approach.

Fig. 3.
Fig. 3.

GDD (left axis) and reflectance (right axis) of the 100-layer chirp mirror obtained with “classical” approach. Crosses designate specified target values.

Fig. 4.
Fig. 4.

Output pulse intensity (green line) and input bandwidth limited pulse intensity envelope (red curve) for the 100-layer chirp-mirror design obtained with “classical” design approach. Pulse intensity after 12 bounces from this mirror is shown with blue line.

Fig. 5.
Fig. 5.

Layer thicknesses of the 64-layer chirp mirror obtained with the help of the time-domain approach.

Fig. 6.
Fig. 6.

GDD (left axis) and reflectance (right axis) of the 64-layer chirp mirror obtained with the time domain approach.

Fig. 7.
Fig. 7.

Bandwidth limited input pulse envelope (red curve), the envelope of the output pulse after one reflection (green curve), and the envelope of the output pulse (blue curve) after 12 bounces for the 64-layer chirp mirror obtained by time-domain needle optimization.

Fig. 8.
Fig. 8.

Influence of variations of input pulse spectral distribution on the envelope of the output pulse after 12 bounces: left — design obtained with “classical” approach, right — design obtained with time-domain optimization.

Fig. 9.
Fig. 9.

Influence of 0.5% relative errors in layer thicknesses: left — design obtained with “classical” approach, right — design obtained with time-domain optimization.

Fig. 10.
Fig. 10.

Influence of 0.3 nm absolute errors in layer thicknesses: left — design obtained with “classical” approach, right — design obtained with time-domain optimization.

Tables (1)

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Table 1. Cauchy formula coefficients for the substrate and layer materials, wavelength in the Cauchy formula should be expressed in microns.

Equations (6)

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A ̂ in ( ω ) = I in ( ω ) exp ( i φ in ( ω ) ) .
A ̂ out ( ω ) = [ r ( ω ) ] n A ̂ in ( ω ) ,
A out ( t ) = ( 2 π ) 1 + A ̂ out ( ω ) exp ( i ω t ) d ω .
Δ 2 = ( E p ) 1 + ( t t 0 ) 2 A out ( t ) p d t , t 0 = ( E p ) 1 + t A out ( t ) p d t , E p = + A out ( t ) p d t .
Φ = ( E p ) q + ( t t 0 ) 2 A out ( t ) p d t , q 1 .
F = 1 L l = 1 L ( R ( ω l ) R ( l ) Δ R ( l ) ) 2 + ( GDD ( ω l ) GDD ( l ) Δ GDD ( l ) ) 2 .

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