Abstract

We precisely determine the dispersion of an optical cavity over a large spectral bandwidth using a broadband optical comb generated by a femtosecond laser. This approach permits the effective characterization of the next generation of mirrors that will offer high reflectivity, minimal absorption/scattering loss, and well-defined dispersion characteristics. Such mirrors are essential for constructing passive, high-finesse cavities capable of storing and enhancing ultrashort pulses and for exploring novel intracavity-based experiments in atomic and molecular spectroscopy and extreme nonlinear optics. We characterize both zero and negative group-delay-dispersion mirrors and compare their performance against the targeted coating design. The high sensitivity of this approach is demonstrated with a precise determination of the group-delay dispersion of air inside a 40-cm long optical cavity, demonstrating an accuracy better than 1 fs2.

© 2005 Optical Society of America

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References

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  1. T. Gherman, S. Kassi, A. Campargue, and D. Romanini, "Overtone spectroscopy in the blue region by cavity-enhanced absorption spectroscopy with a mode-locked femtosecond laser: application to acetylene,"Chem. Phys. Lett. 383, 353-358 (2004).
    [CrossRef]
  2. R. J. Jones, I. Thomann, and J. Ye, "Precision stabilization of femtosecond lasers to high-finesse optical cavities," Phys. Rev. A 69, 051803 (2004).
    [CrossRef]
  3. R. J. Jones and J. Ye, "Femtosecond pulse amplification by coherent addition in a passive optical cavity,"Opt. Lett. 27, 1848-1850 (2002).
    [CrossRef]
  4. G. P. A. Malcolm, M. Ebrahimzadeh, and A. I. Ferguson, "Efficient Frequency-Conversion of Mode-Locked Diode-Pumped Lasers and Tunable All-Solid-State Laser Sources," IEEE J. Quantum Electron. 28, 1172-1178 (1992).
    [CrossRef]
  5. R. J. Jones and J. Ye, "High-repetition rate, coherent femtosecond pulse amplification with an external passive optical cavity," Opt. Lett. 29, 2812-2814 (2004).
    [CrossRef] [PubMed]
  6. J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena : Fundamentals, Techniques, and Applications on a Femtosecond Timescale (Academic Press, San Diego, 1996).
  7. R. G. DeVoe, C. Fabre, K. Jungmann, J. Hoffnagle, and R. G. Brewer, "Precision Optical-Frequency-Difference Measurements," Phys. Rev. A 37, 1802-1805 (1988).
    [CrossRef] [PubMed]
  8. C. J. Hood, H. J. Kimble, and J. Ye, "Characterization of high-finesse mirrors: Loss, phase shifts, and mode structure in an optical cavity," Phys. Rev. A 64, 033804 (2001).
    [CrossRef]
  9. W. H. Knox, "Dispersion Measurements for Femtosecond-Pulse Generation and Applications," Appl. Phys. B 58, 225-235 (1994)
    [CrossRef]
  10. J. Reichert, R. Holzwarth, T. Udem, and T. W. Hänsch, "Measuring the frequency of light with mode-locked lasers," Opt. Commun. 172, 59-68 (1999).
    [CrossRef]
  11. J. C. Diels, R. J. Jones, and L. Arissian, in Femtosecond Optical Frequency Comb: Principle, Operation, and Applications, edited by J. Ye and S. T. Cundiff (Springer, 2005) pp. 333.
    [CrossRef]
  12. Advanced Thin Films provided all the custom-designed mirrors used in this work. Mentioning of manufacturer's name is for technical communications only and does not represent endorsement from NIST.
  13. M.Born, E. Wolf, "Principles of Optics: Electromagnetic theory of propagation, interference and diffraction," 7th ed. (Cambridge University Press, 1999) pp. 101.

Appl. Phys. B (1)

W. H. Knox, "Dispersion Measurements for Femtosecond-Pulse Generation and Applications," Appl. Phys. B 58, 225-235 (1994)
[CrossRef]

Chem. Phys. Lett. (1)

T. Gherman, S. Kassi, A. Campargue, and D. Romanini, "Overtone spectroscopy in the blue region by cavity-enhanced absorption spectroscopy with a mode-locked femtosecond laser: application to acetylene,"Chem. Phys. Lett. 383, 353-358 (2004).
[CrossRef]

IEEE J. Quantum Electron. (1)

G. P. A. Malcolm, M. Ebrahimzadeh, and A. I. Ferguson, "Efficient Frequency-Conversion of Mode-Locked Diode-Pumped Lasers and Tunable All-Solid-State Laser Sources," IEEE J. Quantum Electron. 28, 1172-1178 (1992).
[CrossRef]

Opt. Commun. (1)

J. Reichert, R. Holzwarth, T. Udem, and T. W. Hänsch, "Measuring the frequency of light with mode-locked lasers," Opt. Commun. 172, 59-68 (1999).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (3)

R. G. DeVoe, C. Fabre, K. Jungmann, J. Hoffnagle, and R. G. Brewer, "Precision Optical-Frequency-Difference Measurements," Phys. Rev. A 37, 1802-1805 (1988).
[CrossRef] [PubMed]

C. J. Hood, H. J. Kimble, and J. Ye, "Characterization of high-finesse mirrors: Loss, phase shifts, and mode structure in an optical cavity," Phys. Rev. A 64, 033804 (2001).
[CrossRef]

R. J. Jones, I. Thomann, and J. Ye, "Precision stabilization of femtosecond lasers to high-finesse optical cavities," Phys. Rev. A 69, 051803 (2004).
[CrossRef]

Other (4)

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena : Fundamentals, Techniques, and Applications on a Femtosecond Timescale (Academic Press, San Diego, 1996).

J. C. Diels, R. J. Jones, and L. Arissian, in Femtosecond Optical Frequency Comb: Principle, Operation, and Applications, edited by J. Ye and S. T. Cundiff (Springer, 2005) pp. 333.
[CrossRef]

Advanced Thin Films provided all the custom-designed mirrors used in this work. Mentioning of manufacturer's name is for technical communications only and does not represent endorsement from NIST.

M.Born, E. Wolf, "Principles of Optics: Electromagnetic theory of propagation, interference and diffraction," 7th ed. (Cambridge University Press, 1999) pp. 101.

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Figures (4)

Fig. 1.
Fig. 1.

Experimental scheme for intracavity dispersion measurement using a mode-locked femtosecond laser. The frequency locking error signal is obtained via frequency modulation generated by the electro-optic modulator (EOM), with the light detected in cavity reflection and after spectral selection. The cavity transmission spectrum is recorded to determine the cavity FSR.

Fig. 2.
Fig. 2.

Principle of intracavity dispersion measurement using a mode-locked laser. (a) Cavity transmission spectra obtained with two different values of the laser f rep. The peak at 830 nm is the result of locking the average frequency of the selected comb to the cavity modes there. (b) The inverted parabola indicates the cavity FSR versus wavelength, due to the net cavity dispersion. Different settings of the laser f rep, as shown by straight horizontal lines, allow different sections of cavity modes to become overlapped with the frequency comb, resulting in changes in the cavity transmission. The shaded area between f rep1 and the cavity FSR curve illustrates that the integral of the difference between these two curves over the frequency interval separating the two transmission peaks is zero (see Eq. (1)). (c) Cartoon showing the walk-off effect between the frequency comb and the non-uniformly spaced cavity modes. Near the locking frequency, the detuning between the laser f rep and the cavity FSR cause the optical comb modes to walk-off from the cavity modes. Away from the locking region, the frequency-dependent cavity FSR causes the optical comb to realign with the cavity modes such that the m th comb component is once again resonant with the m th cavity mode.

Fig. 3.
Fig. 3.

(a) Cavity-based measurement of the GDD of zero-GDD mirrors used as an input coupler. Three independent measurements are shown. The design theory curve is shown as a dashed line. (b) Cavity-based measurement of the GDD of zero-(open circles) and negative-GDD (filled circles) high reflectors. Data from three independent measurements are shown for the zero-GDD mirror and a single data set is shown for the negative-GDD mirror. Also included are the design curves for both types of mirrors. Due to the sensitivity on layer thickness of the GTI structure, the range obtained from 20 theoretical curves corresponding to a 0.5% RMS variation in the layer thickness is shown. .

Fig. 4.
Fig. 4.

Cavity-based measurement of the dispersion of air versus theory. The theory curve is derived using the Sellmeier equation for the air refractive index and multiplying it by the cavity length. This curve illustrates that the disagreement between the measurement method and theory across the entire spectrum is less than 1 fs2.

Equations (2)

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0 = υ t υ l [ FSR ( υ ) F rep ( υ t , υ l ) 1 ] d υ .
FSR ( υ ) = F rep ( υ t , υ l ) + ( υ t υ l ) d d υ t F rep ( υ t , υ l ) .

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