Abstract

We present an analytic design method for the reproducible fabrication of double-chirped mirrors to achieve simultaneously a high reflectivity and dispersion compensation over an extended bandwidth compared with those of standard quarter-wave Bragg mirrors. The mirrors are fabricated by ion beam sputtering. Use of these mirrors in a Ti:sapphire laser leads to 6.5-fs pulses directly out of the laser. The method can also be applied to the design of chirped-fiber gratings and general optical filters.

© 1997 Optical Society of America

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References

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  1. R. Szipöcs, K. Ferencz, C. Spielmann, and F. Krausz, Opt. Lett. 19, 201 (1994).
    [CrossRef]
  2. P. Laporta and V. Magni, Appl. Opt. 24, 2014 (1985).
    [CrossRef]
  3. N. Matuschek, F. X. Kärtner, and U. Keller, IEEE J. Quantum Electron. 33, 295 (1997).
    [CrossRef]
  4. R. E. Collin, Foundations for Microwave Engineering, 2nd ed. (McGraw-Hill, New York, 1992), Chaps. 3 and 5.
  5. A. B. Migdal, Qualitative Methods in Quantum Theory (Addison-Wesley, Reading, Mass., 1977), Chap. 3.
  6. R. Morf and R. E. Kunz, Proc. SPIE 1270, 11 (1990).
    [CrossRef]
  7. V. Scheuer, M. Tilsch, and T. Tschudi, Proc. SPIE 2253, 445 (1994).
    [CrossRef]
  8. M. Tilsch, V. Scheuer, and T. Tschudi, Proc. SPIE 2253, 414 (1994).
    [CrossRef]
  9. I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, G. Zhang, U. Keller, V. Scheuer, M. Tilsch, and T. Tschudi, “Self-starting 6.5-fs pulses from a Ti:sapphire laser,” Opt. Lett. (to be published).
  10. L. Xu, C. Spielmann, F. Krausz, and R. Szipöcs, Opt. Lett. 21, 1259 (1996).
    [CrossRef] [PubMed]
  11. R. Fluck, I. D. Jung, G. Zhang, F. X. Kärtner, and U. Keller, Opt. Lett. 21, 743 (1996).
    [CrossRef] [PubMed]
  12. U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers,” J. Sel. Topics Quantum Electron. (to be published).

1997 (1)

N. Matuschek, F. X. Kärtner, and U. Keller, IEEE J. Quantum Electron. 33, 295 (1997).
[CrossRef]

1996 (2)

1994 (3)

V. Scheuer, M. Tilsch, and T. Tschudi, Proc. SPIE 2253, 445 (1994).
[CrossRef]

M. Tilsch, V. Scheuer, and T. Tschudi, Proc. SPIE 2253, 414 (1994).
[CrossRef]

R. Szipöcs, K. Ferencz, C. Spielmann, and F. Krausz, Opt. Lett. 19, 201 (1994).
[CrossRef]

1990 (1)

R. Morf and R. E. Kunz, Proc. SPIE 1270, 11 (1990).
[CrossRef]

1985 (1)

Aus der Au, J.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers,” J. Sel. Topics Quantum Electron. (to be published).

Braun, B.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers,” J. Sel. Topics Quantum Electron. (to be published).

Collin, R. E.

R. E. Collin, Foundations for Microwave Engineering, 2nd ed. (McGraw-Hill, New York, 1992), Chaps. 3 and 5.

Ferencz, K.

Fluck, R.

R. Fluck, I. D. Jung, G. Zhang, F. X. Kärtner, and U. Keller, Opt. Lett. 21, 743 (1996).
[CrossRef] [PubMed]

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers,” J. Sel. Topics Quantum Electron. (to be published).

Hönninger, C.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers,” J. Sel. Topics Quantum Electron. (to be published).

Jung, I. D.

R. Fluck, I. D. Jung, G. Zhang, F. X. Kärtner, and U. Keller, Opt. Lett. 21, 743 (1996).
[CrossRef] [PubMed]

I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, G. Zhang, U. Keller, V. Scheuer, M. Tilsch, and T. Tschudi, “Self-starting 6.5-fs pulses from a Ti:sapphire laser,” Opt. Lett. (to be published).

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers,” J. Sel. Topics Quantum Electron. (to be published).

Kärtner, F. X.

N. Matuschek, F. X. Kärtner, and U. Keller, IEEE J. Quantum Electron. 33, 295 (1997).
[CrossRef]

R. Fluck, I. D. Jung, G. Zhang, F. X. Kärtner, and U. Keller, Opt. Lett. 21, 743 (1996).
[CrossRef] [PubMed]

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers,” J. Sel. Topics Quantum Electron. (to be published).

I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, G. Zhang, U. Keller, V. Scheuer, M. Tilsch, and T. Tschudi, “Self-starting 6.5-fs pulses from a Ti:sapphire laser,” Opt. Lett. (to be published).

Keller, U.

N. Matuschek, F. X. Kärtner, and U. Keller, IEEE J. Quantum Electron. 33, 295 (1997).
[CrossRef]

R. Fluck, I. D. Jung, G. Zhang, F. X. Kärtner, and U. Keller, Opt. Lett. 21, 743 (1996).
[CrossRef] [PubMed]

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers,” J. Sel. Topics Quantum Electron. (to be published).

I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, G. Zhang, U. Keller, V. Scheuer, M. Tilsch, and T. Tschudi, “Self-starting 6.5-fs pulses from a Ti:sapphire laser,” Opt. Lett. (to be published).

Kopf, D.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers,” J. Sel. Topics Quantum Electron. (to be published).

Krausz, F.

Kunz, R. E.

R. Morf and R. E. Kunz, Proc. SPIE 1270, 11 (1990).
[CrossRef]

Laporta, P.

Magni, V.

Matuschek, N.

N. Matuschek, F. X. Kärtner, and U. Keller, IEEE J. Quantum Electron. 33, 295 (1997).
[CrossRef]

I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, G. Zhang, U. Keller, V. Scheuer, M. Tilsch, and T. Tschudi, “Self-starting 6.5-fs pulses from a Ti:sapphire laser,” Opt. Lett. (to be published).

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers,” J. Sel. Topics Quantum Electron. (to be published).

Migdal, A. B.

A. B. Migdal, Qualitative Methods in Quantum Theory (Addison-Wesley, Reading, Mass., 1977), Chap. 3.

Morf, R.

R. Morf and R. E. Kunz, Proc. SPIE 1270, 11 (1990).
[CrossRef]

Morier-Genoud, F.

I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, G. Zhang, U. Keller, V. Scheuer, M. Tilsch, and T. Tschudi, “Self-starting 6.5-fs pulses from a Ti:sapphire laser,” Opt. Lett. (to be published).

Scheuer, V.

M. Tilsch, V. Scheuer, and T. Tschudi, Proc. SPIE 2253, 414 (1994).
[CrossRef]

V. Scheuer, M. Tilsch, and T. Tschudi, Proc. SPIE 2253, 445 (1994).
[CrossRef]

I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, G. Zhang, U. Keller, V. Scheuer, M. Tilsch, and T. Tschudi, “Self-starting 6.5-fs pulses from a Ti:sapphire laser,” Opt. Lett. (to be published).

Spielmann, C.

Sutter, D. H.

I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, G. Zhang, U. Keller, V. Scheuer, M. Tilsch, and T. Tschudi, “Self-starting 6.5-fs pulses from a Ti:sapphire laser,” Opt. Lett. (to be published).

Szipöcs, R.

Tilsch, M.

M. Tilsch, V. Scheuer, and T. Tschudi, Proc. SPIE 2253, 414 (1994).
[CrossRef]

V. Scheuer, M. Tilsch, and T. Tschudi, Proc. SPIE 2253, 445 (1994).
[CrossRef]

I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, G. Zhang, U. Keller, V. Scheuer, M. Tilsch, and T. Tschudi, “Self-starting 6.5-fs pulses from a Ti:sapphire laser,” Opt. Lett. (to be published).

Tschudi, T.

M. Tilsch, V. Scheuer, and T. Tschudi, Proc. SPIE 2253, 414 (1994).
[CrossRef]

V. Scheuer, M. Tilsch, and T. Tschudi, Proc. SPIE 2253, 445 (1994).
[CrossRef]

I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, G. Zhang, U. Keller, V. Scheuer, M. Tilsch, and T. Tschudi, “Self-starting 6.5-fs pulses from a Ti:sapphire laser,” Opt. Lett. (to be published).

Weingarten, K. J.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers,” J. Sel. Topics Quantum Electron. (to be published).

Xu, L.

Zhang, G.

R. Fluck, I. D. Jung, G. Zhang, F. X. Kärtner, and U. Keller, Opt. Lett. 21, 743 (1996).
[CrossRef] [PubMed]

I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, G. Zhang, U. Keller, V. Scheuer, M. Tilsch, and T. Tschudi, “Self-starting 6.5-fs pulses from a Ti:sapphire laser,” Opt. Lett. (to be published).

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

N. Matuschek, F. X. Kärtner, and U. Keller, IEEE J. Quantum Electron. 33, 295 (1997).
[CrossRef]

Opt. Lett. (3)

Proc. SPIE (3)

R. Morf and R. E. Kunz, Proc. SPIE 1270, 11 (1990).
[CrossRef]

V. Scheuer, M. Tilsch, and T. Tschudi, Proc. SPIE 2253, 445 (1994).
[CrossRef]

M. Tilsch, V. Scheuer, and T. Tschudi, Proc. SPIE 2253, 414 (1994).
[CrossRef]

Other (4)

I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, G. Zhang, U. Keller, V. Scheuer, M. Tilsch, and T. Tschudi, “Self-starting 6.5-fs pulses from a Ti:sapphire laser,” Opt. Lett. (to be published).

R. E. Collin, Foundations for Microwave Engineering, 2nd ed. (McGraw-Hill, New York, 1992), Chaps. 3 and 5.

A. B. Migdal, Qualitative Methods in Quantum Theory (Addison-Wesley, Reading, Mass., 1977), Chap. 3.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers,” J. Sel. Topics Quantum Electron. (to be published).

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Figures (4)

Fig. 1
Fig. 1

A general Bragg structure can be decomposed into a series of symmetric index steps.

Fig. 2
Fig. 2

Comparison of the reflectivity and the group delay of chirped mirrors with 25 layer pairs with refractive indices nl=1.5, nh=2.5. The upper portion shows the enlarged top percent of the reflectivity. The dotted curves show the result for a simply chirped mirror. The dashed and solid curves show the result for double-chirped mirrors, where in addition to the chirp in the Bragg wave number kB the thickness of the high-index layers is also chirped over the first 12  layer pairs from zero to its maximum value for a linear chirp (dashed curves) and for a quadratic chirp (solid curves).

Fig. 3
Fig. 3

Schematic picture of the universal structure of a double-chirped mirror. AR, antireflection.

Fig. 4
Fig. 4

Designed and measured (a) reflectivity and (b) group delay of the fabricated double-chirped mirror as described in the text.

Equations (6)

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dAdm=-iδmAm-iκmBm,  dBdm=+iκmAm+iδmBm.
δm=-αm11-r2sinϕhm+ϕlm+r2 sinϕhm-ϕlm,  κm=-αm2r1-r2 sinϕhm,
αm=ηmsinhηm,
coshηm=-FRm,  sinhηm=FR2m-11/2,
FRm=11-r2cosϕhm+ϕlm-r2 cosϕhm-ϕlm.
dV/dm=-iXmI, X=δ-κ,  dI/dm=-iYmV, Y=δ+κ.

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