Abstract

A highly dispersive mirror for dispersion compensation in femtosecond lasers is designed by inverse spectral theory. The design of a simple quarter-wave Bragg reflector can be modified by moving the poles in the optical impedance found in the photonic stop band. These spectral quantities are used as independent variables in the numerical optimization because they have no effect on the location of the photonic stop band, and so the design requirements to obtain a high reflectivity and a specific delay spectrum are decoupled. The design was fabricated by ion-beam sputtering. A group delay dispersion of -300 fs2 was measured over a bandwidth of 28 nm, with a remaining reflectivity of greater than 99% in this range. The mirrors were used to make two Ti:sapphire lasers with 10- and 4-mm-long crystals, both of which generated near-transform-limited pulses of 35-fs duration. Because of the high dispersion of the mirrors, the laser cavities needed only five and three bounces from the mirrors, thus keeping reflection losses to a minimum.

© 1999 Optical Society of America

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References

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  1. K. Torizuka, M. Yamashita, “Third-order dispersion in a passively mode-locked continuous-wave dye laser,” J. Opt. Soc. Am. B 8, 2442–2448 (1991).
    [CrossRef]
  2. I. T. Sorokina, E. Sorokin, E. Wintner, A. Cassanho, H. P. Jenssen, R. Szipöcs, “Prismless passively mode-locked femtosecond Cr:LiSGaF laser,” Opt. Lett. 21, 1165–1167 (1996).
    [CrossRef] [PubMed]
  3. D. Kopf, G. Zhang, R. Fluck, M. Moser, U. Keller, “All-in-one dispersion-compensating saturable absorber mirror for compact femtosecond laser sources,” Opt. Lett. 21, 486–488 (1996).
    [CrossRef] [PubMed]
  4. M. Yamashita, K. Torizuka, T. Sato, “A chirp-compensation technique using incident angle changes of cavity mirrors in a femtosecond pulse laser,” IEEE J. Quantum Electron. 23, 2005–2007 (1987).
    [CrossRef]
  5. R. Szipöcs, K. Ferencz, C. Spielmann, F. Krausz, “Chirped multilayer coatings for broadband dispersion control in femtosecond lasers,” Opt. Lett. 19, 201–203 (1994).
    [CrossRef] [PubMed]
  6. F. X. Kärtner, N. Matuschek, T. Schibli, U. Keller, H. A. Haus, C. Heine, R. Morf, V. Scheuer, M. Tilsch, T. Tschudi, “Design and fabrication of double-chirped mirrors,” Opt. Lett. 22, 831–833 (1997).
    [CrossRef] [PubMed]
  7. R. Szipöcs, A. Köházi-Kis, “Theory and design of chirped dielectric laser mirrors,” Appl. Phys. B 65, 115–135 (1997).
    [CrossRef]
  8. I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, G. Zhang, U. Keller, V. Scheuer, M. Tilsch, T. Tschudi, “Self-starting 6.5-fs pulses from a Ti:sapphire laser,” Opt. Lett. 22, 1009–1011 (1997).
    [CrossRef] [PubMed]
  9. J. A. Dobrowolski, R. A. Kemp, “Refinements of optical multilayer systems with different optimization procedures,” Appl. Opt. 29, 2876–2893 (1990).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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  14. P. G. Verly, “Design of inhomogeneous and quasi-inhomogeneous optical coatings at the NRC,” in Inhomogeneous and Quasi-Homogeneous Optical Coatings, J. A. Dobrowolski, P. G. Verly, eds., Proc. SPIE2046, 36–42 (1993).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  23. G. Tempea, F. Krausz, C. Speilmann, K. Ferencz, “Dispersion control over 150 THz with chirped dielectric mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 193–196 (1998).
    [CrossRef]
  24. N. Matuschek, F. X. Kärtner, U. Keller, “Theory of double chirped mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 197–208 (1998).
    [CrossRef]
  25. I. T. Sorokina, E. Sorokin, E. Wintner, A. Cassanho, H. P. Jenssen, R. Szipöcs, “14-fs pulse generation in Kerr-lens mode-locked prismless Cr:LiSGaF and Cr:LiSAF lasers: observation of pulse self-frequency shift,” Opt. Lett. 22, 1716–1718 (1997).
    [CrossRef]
  26. K. Naganuma, K. Mogi, H. Yamada, “Group delay measurement using the Fourier transform of an interferometric cross correlation generated by white light,” Opt. Lett. 15, 393–395 (1990).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  29. F. Krausz, M. E. Fermann, T. Brabec, P. F. Curley, M. Hofer, M. H. Ober, C. Spielmann, E. Wintner, A. J. Schmidt, “Femtosecond solid state lasers,” IEEE J. Quantum Electron. 28, 2097–2122 (1992).
    [CrossRef]
  30. Z. Zhang, T. Yagi, “Observation of group delay dispersion as a function of the pulse width in a mode locked Ti:sapphire laser,” Appl. Phys. Lett. 63, 2993–2995 (1993).
    [CrossRef]

1998 (3)

A. Ueda, H. Yoneda, K. Ueda, K. Waseda, M. Ohashi, “Two-dimensional measurement of optical parameters of superhigh-quality mirrors,” Laser Phys. 8, 697–702 (1998).

G. Tempea, F. Krausz, C. Speilmann, K. Ferencz, “Dispersion control over 150 THz with chirped dielectric mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 193–196 (1998).
[CrossRef]

N. Matuschek, F. X. Kärtner, U. Keller, “Theory of double chirped mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 197–208 (1998).
[CrossRef]

1997 (6)

1996 (2)

1994 (1)

1993 (2)

J. E. Roman, K. A. Winick, “Waveguide grating filters for dispersion compensation and pulse compression,” IEEE J. Quantum Electron. 29, 975–982 (1993).
[CrossRef]

Z. Zhang, T. Yagi, “Observation of group delay dispersion as a function of the pulse width in a mode locked Ti:sapphire laser,” Appl. Phys. Lett. 63, 2993–2995 (1993).
[CrossRef]

1992 (2)

T. Brabec, Ch. Spielmann, F. Krausz, “Limits of pulse shortening in solitary lasers,” Opt. Lett. 17, 748–750 (1992).
[CrossRef] [PubMed]

F. Krausz, M. E. Fermann, T. Brabec, P. F. Curley, M. Hofer, M. H. Ober, C. Spielmann, E. Wintner, A. J. Schmidt, “Femtosecond solid state lasers,” IEEE J. Quantum Electron. 28, 2097–2122 (1992).
[CrossRef]

1991 (2)

1990 (2)

1987 (1)

M. Yamashita, K. Torizuka, T. Sato, “A chirp-compensation technique using incident angle changes of cavity mirrors in a femtosecond pulse laser,” IEEE J. Quantum Electron. 23, 2005–2007 (1987).
[CrossRef]

1982 (1)

1977 (1)

L. Sossi, “On the synthesis of interference coatings,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 26, 28–36 (1977).

1974 (1)

L. Sossi, “A method for the synthesis of multilayer interference coatings,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 23, 229–237 (1974).

1967 (1)

Brabec, T.

F. Krausz, M. E. Fermann, T. Brabec, P. F. Curley, M. Hofer, M. H. Ober, C. Spielmann, E. Wintner, A. J. Schmidt, “Femtosecond solid state lasers,” IEEE J. Quantum Electron. 28, 2097–2122 (1992).
[CrossRef]

T. Brabec, Ch. Spielmann, F. Krausz, “Limits of pulse shortening in solitary lasers,” Opt. Lett. 17, 748–750 (1992).
[CrossRef] [PubMed]

Cassanho, A.

Chadan, K.

K. Chadan, P. C. Sabatier, Inverse Problems in Quantum Scattering Theory (Springer-Verlag, New York, 1989).
[CrossRef]

Curley, P. F.

F. Krausz, M. E. Fermann, T. Brabec, P. F. Curley, M. Hofer, M. H. Ober, C. Spielmann, E. Wintner, A. J. Schmidt, “Femtosecond solid state lasers,” IEEE J. Quantum Electron. 28, 2097–2122 (1992).
[CrossRef]

Delano, E.

Dobrowolski, J. A.

Dods, S. R. A.

Euteneuer, A.

Ferencz, K.

G. Tempea, F. Krausz, C. Speilmann, K. Ferencz, “Dispersion control over 150 THz with chirped dielectric mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 193–196 (1998).
[CrossRef]

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

Fermann, M. E.

F. Krausz, M. E. Fermann, T. Brabec, P. F. Curley, M. Hofer, M. H. Ober, C. Spielmann, E. Wintner, A. J. Schmidt, “Femtosecond solid state lasers,” IEEE J. Quantum Electron. 28, 2097–2122 (1992).
[CrossRef]

Fluck, R.

Fujimoto, J. G.

Haus, H. A.

Heine, C.

Hofer, M.

F. Krausz, M. E. Fermann, T. Brabec, P. F. Curley, M. Hofer, M. H. Ober, C. Spielmann, E. Wintner, A. J. Schmidt, “Femtosecond solid state lasers,” IEEE J. Quantum Electron. 28, 2097–2122 (1992).
[CrossRef]

Ippen, E. P.

Jenssen, H. P.

Jung, I. D.

Kärtner, F. X.

Kay, I.

I. Kay, H. E. Moses, Inverse Scattering Papers: 1955–1963 (Math Sciences, Brookline, Mass., 1982).

Keller, U.

Kemp, R. A.

Köházi-Kis, A.

R. Szipöcs, A. Köházi-Kis, “Theory and design of chirped dielectric laser mirrors,” Appl. Phys. B 65, 115–135 (1997).
[CrossRef]

R. Szipöcs, A. Köházi-Kis, “Design of dielectric high reflectors for dispersion control in femtosecond lasers,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 140–149 (1994).
[CrossRef]

Kopf, D.

Krausz, F.

G. Tempea, F. Krausz, C. Speilmann, K. Ferencz, “Dispersion control over 150 THz with chirped dielectric mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 193–196 (1998).
[CrossRef]

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

T. Brabec, Ch. Spielmann, F. Krausz, “Limits of pulse shortening in solitary lasers,” Opt. Lett. 17, 748–750 (1992).
[CrossRef] [PubMed]

F. Krausz, M. E. Fermann, T. Brabec, P. F. Curley, M. Hofer, M. H. Ober, C. Spielmann, E. Wintner, A. J. Schmidt, “Femtosecond solid state lasers,” IEEE J. Quantum Electron. 28, 2097–2122 (1992).
[CrossRef]

Laude, V.

V. Laude, P. Tournois, “Stochastic optimization of broadband dispersion controlled mirrors,” in Conference on Lasers and Electro-Optics Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 156–157.

Matuschek, N.

Mayer, E. J.

Möbius, J.

Mogi, K.

Morf, R.

Morier-Genoud, F.

Moser, M.

Moses, H. E.

I. Kay, H. E. Moses, Inverse Scattering Papers: 1955–1963 (Math Sciences, Brookline, Mass., 1982).

Naganuma, K.

Ober, M. H.

F. Krausz, M. E. Fermann, T. Brabec, P. F. Curley, M. Hofer, M. H. Ober, C. Spielmann, E. Wintner, A. J. Schmidt, “Femtosecond solid state lasers,” IEEE J. Quantum Electron. 28, 2097–2122 (1992).
[CrossRef]

Ogura, M.

Ohashi, M.

A. Ueda, H. Yoneda, K. Ueda, K. Waseda, M. Ohashi, “Two-dimensional measurement of optical parameters of superhigh-quality mirrors,” Laser Phys. 8, 697–702 (1998).

Piotrowski, S. H. C.

Roman, J. E.

J. E. Roman, K. A. Winick, “Waveguide grating filters for dispersion compensation and pulse compression,” IEEE J. Quantum Electron. 29, 975–982 (1993).
[CrossRef]

Rühle, W. W.

Sabatier, P. C.

K. Chadan, P. C. Sabatier, Inverse Problems in Quantum Scattering Theory (Springer-Verlag, New York, 1989).
[CrossRef]

Sato, T.

M. Yamashita, K. Torizuka, T. Sato, “A chirp-compensation technique using incident angle changes of cavity mirrors in a femtosecond pulse laser,” IEEE J. Quantum Electron. 23, 2005–2007 (1987).
[CrossRef]

Scheuer, V.

Schibli, T.

Schmidt, A. J.

F. Krausz, M. E. Fermann, T. Brabec, P. F. Curley, M. Hofer, M. H. Ober, C. Spielmann, E. Wintner, A. J. Schmidt, “Femtosecond solid state lasers,” IEEE J. Quantum Electron. 28, 2097–2122 (1992).
[CrossRef]

Sorokin, E.

Sorokina, I. T.

Sossi, L.

L. Sossi, “On the synthesis of interference coatings,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 26, 28–36 (1977).

L. Sossi, “A method for the synthesis of multilayer interference coatings,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 23, 229–237 (1974).

Speilmann, C.

G. Tempea, F. Krausz, C. Speilmann, K. Ferencz, “Dispersion control over 150 THz with chirped dielectric mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 193–196 (1998).
[CrossRef]

Spielmann, C.

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

F. Krausz, M. E. Fermann, T. Brabec, P. F. Curley, M. Hofer, M. H. Ober, C. Spielmann, E. Wintner, A. J. Schmidt, “Femtosecond solid state lasers,” IEEE J. Quantum Electron. 28, 2097–2122 (1992).
[CrossRef]

Spielmann, Ch.

Sutter, D. H.

Szipöcs, R.

Tempea, G.

G. Tempea, F. Krausz, C. Speilmann, K. Ferencz, “Dispersion control over 150 THz with chirped dielectric mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 193–196 (1998).
[CrossRef]

Tilsch, M.

Torizuka, K.

K. Torizuka, M. Yamashita, “Third-order dispersion in a passively mode-locked continuous-wave dye laser,” J. Opt. Soc. Am. B 8, 2442–2448 (1991).
[CrossRef]

M. Yamashita, K. Torizuka, T. Sato, “A chirp-compensation technique using incident angle changes of cavity mirrors in a femtosecond pulse laser,” IEEE J. Quantum Electron. 23, 2005–2007 (1987).
[CrossRef]

Tournois, P.

V. Laude, P. Tournois, “Stochastic optimization of broadband dispersion controlled mirrors,” in Conference on Lasers and Electro-Optics Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 156–157.

Tschudi, T.

Ueda, A.

A. Ueda, H. Yoneda, K. Ueda, K. Waseda, M. Ohashi, “Two-dimensional measurement of optical parameters of superhigh-quality mirrors,” Laser Phys. 8, 697–702 (1998).

Ueda, K.

A. Ueda, H. Yoneda, K. Ueda, K. Waseda, M. Ohashi, “Two-dimensional measurement of optical parameters of superhigh-quality mirrors,” Laser Phys. 8, 697–702 (1998).

Verly, P. G.

P. G. Verly, “Design of inhomogeneous and quasi-inhomogeneous optical coatings at the NRC,” in Inhomogeneous and Quasi-Homogeneous Optical Coatings, J. A. Dobrowolski, P. G. Verly, eds., Proc. SPIE2046, 36–42 (1993).
[CrossRef]

Waseda, K.

A. Ueda, H. Yoneda, K. Ueda, K. Waseda, M. Ohashi, “Two-dimensional measurement of optical parameters of superhigh-quality mirrors,” Laser Phys. 8, 697–702 (1998).

Winick, K. A.

J. E. Roman, K. A. Winick, “Waveguide grating filters for dispersion compensation and pulse compression,” IEEE J. Quantum Electron. 29, 975–982 (1993).
[CrossRef]

Wintner, E.

Yagi, T.

Z. Zhang, T. Yagi, “Observation of group delay dispersion as a function of the pulse width in a mode locked Ti:sapphire laser,” Appl. Phys. Lett. 63, 2993–2995 (1993).
[CrossRef]

Yamada, H.

Yamashita, M.

K. Torizuka, M. Yamashita, “Third-order dispersion in a passively mode-locked continuous-wave dye laser,” J. Opt. Soc. Am. B 8, 2442–2448 (1991).
[CrossRef]

M. Yamashita, K. Torizuka, T. Sato, “A chirp-compensation technique using incident angle changes of cavity mirrors in a femtosecond pulse laser,” IEEE J. Quantum Electron. 23, 2005–2007 (1987).
[CrossRef]

Yoneda, H.

A. Ueda, H. Yoneda, K. Ueda, K. Waseda, M. Ohashi, “Two-dimensional measurement of optical parameters of superhigh-quality mirrors,” Laser Phys. 8, 697–702 (1998).

Zhang, G.

Zhang, Z.

Z. Zhang, T. Yagi, “Observation of group delay dispersion as a function of the pulse width in a mode locked Ti:sapphire laser,” Appl. Phys. Lett. 63, 2993–2995 (1993).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. B (1)

R. Szipöcs, A. Köházi-Kis, “Theory and design of chirped dielectric laser mirrors,” Appl. Phys. B 65, 115–135 (1997).
[CrossRef]

Appl. Phys. Lett. (1)

Z. Zhang, T. Yagi, “Observation of group delay dispersion as a function of the pulse width in a mode locked Ti:sapphire laser,” Appl. Phys. Lett. 63, 2993–2995 (1993).
[CrossRef]

Eesti NSV Tead. Akad. Toim. Fuus. Mat. (2)

L. Sossi, “A method for the synthesis of multilayer interference coatings,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 23, 229–237 (1974).

L. Sossi, “On the synthesis of interference coatings,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 26, 28–36 (1977).

IEEE J. Quantum Electron. (3)

J. E. Roman, K. A. Winick, “Waveguide grating filters for dispersion compensation and pulse compression,” IEEE J. Quantum Electron. 29, 975–982 (1993).
[CrossRef]

M. Yamashita, K. Torizuka, T. Sato, “A chirp-compensation technique using incident angle changes of cavity mirrors in a femtosecond pulse laser,” IEEE J. Quantum Electron. 23, 2005–2007 (1987).
[CrossRef]

F. Krausz, M. E. Fermann, T. Brabec, P. F. Curley, M. Hofer, M. H. Ober, C. Spielmann, E. Wintner, A. J. Schmidt, “Femtosecond solid state lasers,” IEEE J. Quantum Electron. 28, 2097–2122 (1992).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

G. Tempea, F. Krausz, C. Speilmann, K. Ferencz, “Dispersion control over 150 THz with chirped dielectric mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 193–196 (1998).
[CrossRef]

N. Matuschek, F. X. Kärtner, U. Keller, “Theory of double chirped mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 197–208 (1998).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Laser Phys. (1)

A. Ueda, H. Yoneda, K. Ueda, K. Waseda, M. Ohashi, “Two-dimensional measurement of optical parameters of superhigh-quality mirrors,” Laser Phys. 8, 697–702 (1998).

Opt. Lett. (9)

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

T. Brabec, Ch. Spielmann, F. Krausz, “Limits of pulse shortening in solitary lasers,” Opt. Lett. 17, 748–750 (1992).
[CrossRef] [PubMed]

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

E. J. Mayer, J. Möbius, A. Euteneuer, W. W. Rühle, R. Szipöcs, “Ultrabroadband chirped mirrors for femtosecond lasers,” Opt. Lett. 22, 528–530 (1997).
[CrossRef] [PubMed]

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

I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, G. Zhang, U. Keller, V. Scheuer, M. Tilsch, T. Tschudi, “Self-starting 6.5-fs pulses from a Ti:sapphire laser,” Opt. Lett. 22, 1009–1011 (1997).
[CrossRef] [PubMed]

I. T. Sorokina, E. Sorokin, E. Wintner, A. Cassanho, H. P. Jenssen, R. Szipöcs, “14-fs pulse generation in Kerr-lens mode-locked prismless Cr:LiSGaF and Cr:LiSAF lasers: observation of pulse self-frequency shift,” Opt. Lett. 22, 1716–1718 (1997).
[CrossRef]

D. Kopf, G. Zhang, R. Fluck, M. Moser, U. Keller, “All-in-one dispersion-compensating saturable absorber mirror for compact femtosecond laser sources,” Opt. Lett. 21, 486–488 (1996).
[CrossRef] [PubMed]

I. T. Sorokina, E. Sorokin, E. Wintner, A. Cassanho, H. P. Jenssen, R. Szipöcs, “Prismless passively mode-locked femtosecond Cr:LiSGaF laser,” Opt. Lett. 21, 1165–1167 (1996).
[CrossRef] [PubMed]

Other (5)

V. Laude, P. Tournois, “Stochastic optimization of broadband dispersion controlled mirrors,” in Conference on Lasers and Electro-Optics Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 156–157.

P. G. Verly, “Design of inhomogeneous and quasi-inhomogeneous optical coatings at the NRC,” in Inhomogeneous and Quasi-Homogeneous Optical Coatings, J. A. Dobrowolski, P. G. Verly, eds., Proc. SPIE2046, 36–42 (1993).
[CrossRef]

R. Szipöcs, A. Köházi-Kis, “Design of dielectric high reflectors for dispersion control in femtosecond lasers,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 140–149 (1994).
[CrossRef]

I. Kay, H. E. Moses, Inverse Scattering Papers: 1955–1963 (Math Sciences, Brookline, Mass., 1982).

K. Chadan, P. C. Sabatier, Inverse Problems in Quantum Scattering Theory (Springer-Verlag, New York, 1989).
[CrossRef]

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Figures (13)

Fig. 1
Fig. 1

Quarter-wave buried Bragg reflector, Λ = 790 nm.

Fig. 2
Fig. 2

Optical impedance of the multilayer of Fig. 1 showing photonic stop band and poles in |Z|.

Fig. 3
Fig. 3

Refractive-index profile of the optimized system, after the poles have been moved as shown in Fig. 4 and as summarized in Table 1.

Fig. 4
Fig. 4

Delay spectrum of 4 mm of sapphire (times -1), and the delay spectra of the auxiliary and optimized systems. The photonic stop band and the location of the poles before and after optimization are also shown.

Fig. 5
Fig. 5

GDD spectrum of 4 mm of sapphire (times -1), and the GDD spectrum of the optimized system.

Fig. 6
Fig. 6

Optimized delay spectrum, and the delay and reflectivity spectra after the graded system was replaced by a Herpin equivalent (HE).

Fig. 7
Fig. 7

Optimized GDD spectrum, and the GDD and reflectivity spectra after the graded system was replaced by a Herpin equivalent (HE).

Fig. 8
Fig. 8

Magnitude of the optical electric field inside the mirror at the two extremes of the reflection band. For both wavelengths the wave incident from the left-hand side has unit intensity. The short wavelength has the usual exponential decay in amplitude, but the long wavelength is delayed by both resonance and increased depth of penetration.

Fig. 9
Fig. 9

Expected delay and reflectivity of the binary multilayer compared with the measured spectra. The error bars on the expected delay (and reflectivity) indicate ±1 standard deviation in the delay (and reflectivity) as a result of random errors in all the layers. The layer errors had a uniform distribution bounded by ±1 nm.

Fig. 10
Fig. 10

Expected GDD and reflectivity compared with the measured spectrum. The error bars show the standard deviation in the expected GDD with random layer errors as described in Fig. 9.

Fig. 11
Fig. 11

Optical layout of the laser with five intracavity bounces from the dispersive mirrors.

Fig. 12
Fig. 12

Measured spectrum of the pulse from the laser with the 4-mm Ti:sapphire crystal compared with the mirror GDD spectrum.

Fig. 13
Fig. 13

Autocorrelation trace of the pulse from the laser with the 4-mm Ti:sapphire crystal.

Tables (1)

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Table 1 Spectral Data of Auxiliary and Optimized Multilayers

Equations (3)

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Zk=1+Γk1-Γk,
τ=-d argΓdω.
Z˜k=Zauxk+jk n0m=1M1/ρ˜mk˜m2-k2-1/ρmkm2-k2,

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