Abstract

A novel floating constants phase-optimization technique is developed and applied to the design of dispersive mirrors. This technique reduces the dispersive mirror’s sensitivity to layer thickness errors. To demonstrate the significant improvement in design stability, we theoretically and experimentally compare our new phase-optimization approach to the conventional one. The fabricated dispersive mirror has a reflectivity of >99.99% and provides an accurate dispersion control over a bandwidth of around 60 nm.

© 2010 OSA

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References

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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. 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(6), 882–885 (2001).
    [CrossRef]
  3. G. Steinmeyer, “Femtosecond dispersion compensation with multilayer coatings: toward the optical octave,” Appl. Opt. 45(7), 1484–1490 (2006).
    [CrossRef] [PubMed]
  4. G. Steinmeyer and G. Stibenz, “Generation of sub-4-fs pulses via compression of a white-light continuum using only chirped mirrors,” Appl. Phys. B 82(2), 175–181 (2006).
    [CrossRef]
  5. N. Matuschek, L. Gallmann, D. H. Sutter, G. Steinmeyer, and U. Keller, “Back-side-coated chirped mirrors with ultra-smooth broadband dispersion characteristics,” Appl. Phys. B 71(4), 509–522 (2000).
    [CrossRef]
  6. G. Steinmeyer, “Brewster-angled chirped mirrors for high-fidelity dispersion compensation and bandwidth exceeding one optical octave,” Opt. Express 11(19), 2385–2396 (2003).
    [CrossRef] [PubMed]
  7. D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56(3), 219–221 (1985).
    [CrossRef]
  8. A. Ashkin, G. D. Boyd, and J. M. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron. 2(6), 109–124 (1966).
    [CrossRef]
  9. P. Tournois, “Acousto-optic programmable dispersive filter for adaptive compensation of group delay time dispersion in laser systems,” Opt. Commun. 140(4-6), 245–249 (1997).
    [CrossRef]
  10. A. V. Tikhonravov, M. K. Trubetskov, and A. A. Tikhonravov, “To the design and theory of chirped mirrors,” In Optical Interference Coatings9, OSA Technical Digest Series, 293–295, (Optical Society of America, Washington DC, 1998).
  11. M. Trubetskov, “Design of dispersive mirrors for ultrafast applications,” Chin. Opt. Lett. 8(S1), 12–17 (2010).
    [CrossRef]
  12. 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(28), 5493–5508 (1996).
    [CrossRef] [PubMed]
  13. A. V. Tikhonravov, M. K. Trubetskov, and G. W. DeBell, “Optical coating design approaches based on the needle optimization technique,” Appl. Opt. 46(5), 704–710 (2007).
    [CrossRef] [PubMed]
  14. A. V. Tikhonravov, M. K. Trubetskov, and OptiLayer Thin Film Software, http://www.optilayer.com
  15. A. O'Keefe and D. A. G. Deacon, “Cavity ring-down Optical Spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum. 59(12), 2544 (1988).
    [CrossRef]
  16. P. Zalicki and R. N. Zare, “Cavity ring-down spectroscopy for quantitative absorption measurements,” J. Chem. Phys. 102(7), 2708–2717 (1995).
    [CrossRef]
  17. G. Berden, R. Peeters, and G. Meijer, “Cavity ring-down spectroscopy: Experimental schemes and applications,” Int. Rev. Phys. Chem. 19(4), 565–607 (2000).
    [CrossRef]
  18. 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]

2010 (1)

M. Trubetskov, “Design of dispersive mirrors for ultrafast applications,” Chin. Opt. Lett. 8(S1), 12–17 (2010).
[CrossRef]

2009 (1)

2007 (1)

2006 (2)

G. Steinmeyer, “Femtosecond dispersion compensation with multilayer coatings: toward the optical octave,” Appl. Opt. 45(7), 1484–1490 (2006).
[CrossRef] [PubMed]

G. Steinmeyer and G. Stibenz, “Generation of sub-4-fs pulses via compression of a white-light continuum using only chirped mirrors,” Appl. Phys. B 82(2), 175–181 (2006).
[CrossRef]

2003 (1)

2001 (1)

2000 (2)

N. Matuschek, L. Gallmann, D. H. Sutter, G. Steinmeyer, and U. Keller, “Back-side-coated chirped mirrors with ultra-smooth broadband dispersion characteristics,” Appl. Phys. B 71(4), 509–522 (2000).
[CrossRef]

G. Berden, R. Peeters, and G. Meijer, “Cavity ring-down spectroscopy: Experimental schemes and applications,” Int. Rev. Phys. Chem. 19(4), 565–607 (2000).
[CrossRef]

1997 (1)

P. Tournois, “Acousto-optic programmable dispersive filter for adaptive compensation of group delay time dispersion in laser systems,” Opt. Commun. 140(4-6), 245–249 (1997).
[CrossRef]

1996 (1)

1995 (1)

P. Zalicki and R. N. Zare, “Cavity ring-down spectroscopy for quantitative absorption measurements,” J. Chem. Phys. 102(7), 2708–2717 (1995).
[CrossRef]

1994 (1)

1988 (1)

A. O'Keefe and D. A. G. Deacon, “Cavity ring-down Optical Spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum. 59(12), 2544 (1988).
[CrossRef]

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

Amotchkina, T. V.

Angelow, G.

Apolonski, A.

Ashkin, A.

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

Berden, G.

G. Berden, R. Peeters, and G. Meijer, “Cavity ring-down spectroscopy: Experimental schemes and applications,” Int. Rev. Phys. Chem. 19(4), 565–607 (2000).
[CrossRef]

Boyd, G. D.

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

Deacon, D. A. G.

A. O'Keefe and D. A. G. Deacon, “Cavity ring-down Optical Spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum. 59(12), 2544 (1988).
[CrossRef]

DeBell, G. W.

Dziedzic, J. M.

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

Ell, R.

Ferencz, K.

Fujimoto, J. G.

Gallmann, L.

N. Matuschek, L. Gallmann, D. H. Sutter, G. Steinmeyer, and U. Keller, “Back-side-coated chirped mirrors with ultra-smooth broadband dispersion characteristics,” Appl. Phys. B 71(4), 509–522 (2000).
[CrossRef]

Grupe, D.

Ippen, E. P.

Kärtner, F. X.

Keller, U.

N. Matuschek, L. Gallmann, D. H. Sutter, G. Steinmeyer, and U. Keller, “Back-side-coated chirped mirrors with ultra-smooth broadband dispersion characteristics,” Appl. Phys. B 71(4), 509–522 (2000).
[CrossRef]

Krausz, F.

Matuschek, N.

N. Matuschek, L. Gallmann, D. H. Sutter, G. Steinmeyer, and U. Keller, “Back-side-coated chirped mirrors with ultra-smooth broadband dispersion characteristics,” Appl. Phys. B 71(4), 509–522 (2000).
[CrossRef]

Meijer, G.

G. Berden, R. Peeters, and G. Meijer, “Cavity ring-down spectroscopy: Experimental schemes and applications,” Int. Rev. Phys. Chem. 19(4), 565–607 (2000).
[CrossRef]

Morgner, U.

Mourou, G.

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

O'Keefe, A.

A. O'Keefe and D. A. G. Deacon, “Cavity ring-down Optical Spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum. 59(12), 2544 (1988).
[CrossRef]

Peeters, R.

G. Berden, R. Peeters, and G. Meijer, “Cavity ring-down spectroscopy: Experimental schemes and applications,” Int. Rev. Phys. Chem. 19(4), 565–607 (2000).
[CrossRef]

Pervak, V.

Scheuer, V.

Schibli, T.

Spielmann, C.

Steinmeyer, G.

G. Steinmeyer and G. Stibenz, “Generation of sub-4-fs pulses via compression of a white-light continuum using only chirped mirrors,” Appl. Phys. B 82(2), 175–181 (2006).
[CrossRef]

G. Steinmeyer, “Femtosecond dispersion compensation with multilayer coatings: toward the optical octave,” Appl. Opt. 45(7), 1484–1490 (2006).
[CrossRef] [PubMed]

G. Steinmeyer, “Brewster-angled chirped mirrors for high-fidelity dispersion compensation and bandwidth exceeding one optical octave,” Opt. Express 11(19), 2385–2396 (2003).
[CrossRef] [PubMed]

N. Matuschek, L. Gallmann, D. H. Sutter, G. Steinmeyer, and U. Keller, “Back-side-coated chirped mirrors with ultra-smooth broadband dispersion characteristics,” Appl. Phys. B 71(4), 509–522 (2000).
[CrossRef]

Stibenz, G.

G. Steinmeyer and G. Stibenz, “Generation of sub-4-fs pulses via compression of a white-light continuum using only chirped mirrors,” Appl. Phys. B 82(2), 175–181 (2006).
[CrossRef]

Strickland, D.

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

Sutter, D. H.

N. Matuschek, L. Gallmann, D. H. Sutter, G. Steinmeyer, and U. Keller, “Back-side-coated chirped mirrors with ultra-smooth broadband dispersion characteristics,” Appl. Phys. B 71(4), 509–522 (2000).
[CrossRef]

Szipöcs, R.

Tikhonravov, A. V.

Tournois, P.

P. Tournois, “Acousto-optic programmable dispersive filter for adaptive compensation of group delay time dispersion in laser systems,” Opt. Commun. 140(4-6), 245–249 (1997).
[CrossRef]

Trubetskov, M.

M. Trubetskov, “Design of dispersive mirrors for ultrafast applications,” Chin. Opt. Lett. 8(S1), 12–17 (2010).
[CrossRef]

Trubetskov, M. K.

Tschudi, T.

Zalicki, P.

P. Zalicki and R. N. Zare, “Cavity ring-down spectroscopy for quantitative absorption measurements,” J. Chem. Phys. 102(7), 2708–2717 (1995).
[CrossRef]

Zare, R. N.

P. Zalicki and R. N. Zare, “Cavity ring-down spectroscopy for quantitative absorption measurements,” J. Chem. Phys. 102(7), 2708–2717 (1995).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. B (2)

G. Steinmeyer and G. Stibenz, “Generation of sub-4-fs pulses via compression of a white-light continuum using only chirped mirrors,” Appl. Phys. B 82(2), 175–181 (2006).
[CrossRef]

N. Matuschek, L. Gallmann, D. H. Sutter, G. Steinmeyer, and U. Keller, “Back-side-coated chirped mirrors with ultra-smooth broadband dispersion characteristics,” Appl. Phys. B 71(4), 509–522 (2000).
[CrossRef]

Chin. Opt. Lett. (1)

M. Trubetskov, “Design of dispersive mirrors for ultrafast applications,” Chin. Opt. Lett. 8(S1), 12–17 (2010).
[CrossRef]

IEEE J. Quantum Electron. (1)

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

Int. Rev. Phys. Chem. (1)

G. Berden, R. Peeters, and G. Meijer, “Cavity ring-down spectroscopy: Experimental schemes and applications,” Int. Rev. Phys. Chem. 19(4), 565–607 (2000).
[CrossRef]

J. Chem. Phys. (1)

P. Zalicki and R. N. Zare, “Cavity ring-down spectroscopy for quantitative absorption measurements,” J. Chem. Phys. 102(7), 2708–2717 (1995).
[CrossRef]

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

Opt. Commun. (2)

P. Tournois, “Acousto-optic programmable dispersive filter for adaptive compensation of group delay time dispersion in laser systems,” Opt. Commun. 140(4-6), 245–249 (1997).
[CrossRef]

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

Opt. Express (1)

Opt. Lett. (1)

Rev. Sci. Instrum. (1)

A. O'Keefe and D. A. G. Deacon, “Cavity ring-down Optical Spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum. 59(12), 2544 (1988).
[CrossRef]

Other (2)

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

A. V. Tikhonravov, M. K. Trubetskov, and A. A. Tikhonravov, “To the design and theory of chirped mirrors,” In Optical Interference Coatings9, OSA Technical Digest Series, 293–295, (Optical Society of America, Washington DC, 1998).

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Figures (4)

Fig. 1
Fig. 1

The theoretical (blue curve) and measured (red curve) transmittances of the conventional DM are shown in the left pane. In the right pane, the theoretical GDD at normal incidence (blue curve) and the theoretical GDD at 10° incidence with p-polarization (magenta curve) of the conventional DM are shown. Red crosses correspond to GDD measured with a white light interferometer (10° incidence, p-polarization). The green area shows a 68.3% probability corridor of GDD errors obtained by Monte-Carlo analysis.

Fig. 2
Fig. 2

Design structures of the DM designed by the conventional (left) and phase optimization (right) approaches.

Fig. 3
Fig. 3

The theoretical (blue curve) and measured (red curve) transmittances of the phase-optimized DM are shown in the left pane. In the right pane the theoretical GDD at normal incidence (blue curve) and the theoretical GDD at 10° incidence with p-polarization (magenta curve) of the phase-optimized DM are shown. Red crosses correspond to GDD measured with a white light interferometer (10° incidence, p-polarization). The green area shows 68.3% probability corridor of GDD errors obtained by Monte-Carlo analysis.

Fig. 4
Fig. 4

Theoretical GDD values (left pane) and phases (right pane) of the conventional (blue lines) DM and phase-optimized (red lines) DM.

Equations (3)

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φ ^ ( ω ) = ω 0 ω d ω 1 ω 0 ω 1 GDD ( ω 2 ) d ω 2 + C 1 ω + C 2 .
F ( X , C 1 , C 2 ) = 1 L m = 1 L [ ( R ( λ m ) R ( m ) Δ R ( m ) ) 2 + ( φ ( λ m ) φ ( m ) Δ φ ( m ) ) 2 ] ,
F ( X , C 1 , C 2 ) / C 1 = 0 , F ( X , C 1 , C 2 ) / C 2 = 0 .

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