Abstract

We demonstrate a new method to simultaneously measure spectrally resolved dispersion and losses (finesse) of a passive optical cavity over the entire bandwidth of an optical frequency comb. To this end, we record and analyze the spectral Moiré pattern between the perfectly equidistant frequency comb emitted from a Ti:Sapphire laser and the longitudinal modes of the passive cavity as a function of the laser’s carrier-envelope-offset phase slippage ϕ CE. In the group-delay dispersion measurement of additionally introduced optical elements we verify a 2fs2 accuracy in a 2THz resolution bandwidth and find good agreement of the measured performance and the target design of a high reflectance dielectric mirror. The sensitivity of the method is essentially equivalent to a cavity ring down technique allowing us also to readily observe signatures of atmospheric gas species.

© 2006 Optical Society of America

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References

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  1. Th. Udem, R. Holzwarth, and T. W. Hänsch, "Optical frequency metrology," Nature (London) 416, 233-237 (2002).
    [CrossRef]
  2. E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U.Kleineberg, U. Heinzmann, M. Drescher, F. Krausz, "Direct measurement of light waves," Science 305, 1267-1269 (2004).
    [CrossRef] [PubMed]
  3. S. T. Cundiff and J. Ye, "Colloquium: Femtosecond optical frequency combs," Rev. Mod. Phys. 75, 325-342, (2003).
    [CrossRef]
  4. Ch. Gohle, Th. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz and T. W. Hänsch, "A frequency comb in the extreme ultraviolet," Nature (London) 436, 234-237 (2005).
    [CrossRef]
  5. R. J. Jones, K. D. Moll, M. J. Thorpe and J. Ye, "Phase-Coherent Frequency Combs in the Vacuum Ultraviolet via High-Harmonic Generation inside a Femtosecond Enhancement Cavity," Phys. Rev. Lett. 94, 193201 (2005).
    [CrossRef] [PubMed]
  6. 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]
  7. A. P. Kovács, K. Osvay, Z. Bor and R. Szipöcs, "Group-delay measurement on laser mirrors by spectrally resolved white-light interferometry," Opt. Lett. 20, 788-90, (1995).
    [CrossRef] [PubMed]
  8. 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]
  9. 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]
  10. M. J. Thorpe, R. J. Jones, K. D. Moll, J. Ye, and R. Lalezari, "Precise measurements of optical cavity dispersion and mirror coating properties via femtosecond combs," Opt. Express 13, 882-888 (2005).
    [CrossRef] [PubMed]
  11. For example A. E. Siegmann, "Lasers," Chapter 11, 416 (1986).
  12. T. W. Hansch and B. Couillaud, "Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity," Opt. Commun. 35, 441-444 (1980).
    [CrossRef]
  13. M. J. Weber, "CRC Handbook of Laser Science and Technology, Volume IV Optical Materials: Part 2," CRC Press (1986).
  14. J. Zhang, Z. H. Li and L. J. Wang, "Precision measurement of the refractive index of air with frequency combs," Opt. Lett. 30, 3314-3316 (2005).
    [CrossRef]
  15. L. S. Rothman et al., "The HITRAN 2004 molecular spectroscopic database," J. Quant. Spect. Rad. Trans. 96, 139-204, (2005).
    [CrossRef]
  16. M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi and J. Ye, "Broadband Cavity Ringdown Spectroscopy for Sensitive and Rapid Molecular Detection," Science 311, 1595-1599 (2006).
    [CrossRef] [PubMed]

2006 (1)

M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi and J. Ye, "Broadband Cavity Ringdown Spectroscopy for Sensitive and Rapid Molecular Detection," Science 311, 1595-1599 (2006).
[CrossRef] [PubMed]

2005 (5)

Ch. Gohle, Th. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz and T. W. Hänsch, "A frequency comb in the extreme ultraviolet," Nature (London) 436, 234-237 (2005).
[CrossRef]

R. J. Jones, K. D. Moll, M. J. Thorpe and J. Ye, "Phase-Coherent Frequency Combs in the Vacuum Ultraviolet via High-Harmonic Generation inside a Femtosecond Enhancement Cavity," Phys. Rev. Lett. 94, 193201 (2005).
[CrossRef] [PubMed]

M. J. Thorpe, R. J. Jones, K. D. Moll, J. Ye, and R. Lalezari, "Precise measurements of optical cavity dispersion and mirror coating properties via femtosecond combs," Opt. Express 13, 882-888 (2005).
[CrossRef] [PubMed]

J. Zhang, Z. H. Li and L. J. Wang, "Precision measurement of the refractive index of air with frequency combs," Opt. Lett. 30, 3314-3316 (2005).
[CrossRef]

L. S. Rothman et al., "The HITRAN 2004 molecular spectroscopic database," J. Quant. Spect. Rad. Trans. 96, 139-204, (2005).
[CrossRef]

2004 (2)

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U.Kleineberg, U. Heinzmann, M. Drescher, F. Krausz, "Direct measurement of light waves," Science 305, 1267-1269 (2004).
[CrossRef] [PubMed]

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]

2003 (1)

S. T. Cundiff and J. Ye, "Colloquium: Femtosecond optical frequency combs," Rev. Mod. Phys. 75, 325-342, (2003).
[CrossRef]

2001 (1)

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]

1988 (1)

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]

1980 (1)

T. W. Hansch and B. Couillaud, "Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity," Opt. Commun. 35, 441-444 (1980).
[CrossRef]

Brewer, R. G.

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]

Couillaud, B.

T. W. Hansch and B. Couillaud, "Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity," Opt. Commun. 35, 441-444 (1980).
[CrossRef]

Cundiff, S. T.

S. T. Cundiff and J. Ye, "Colloquium: Femtosecond optical frequency combs," Rev. Mod. Phys. 75, 325-342, (2003).
[CrossRef]

DeVoe, R. G.

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]

Fabre, C.

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]

Gohle, Ch.

Ch. Gohle, Th. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz and T. W. Hänsch, "A frequency comb in the extreme ultraviolet," Nature (London) 436, 234-237 (2005).
[CrossRef]

Hansch, T. W.

T. W. Hansch and B. Couillaud, "Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity," Opt. Commun. 35, 441-444 (1980).
[CrossRef]

Hänsch, T. W.

Ch. Gohle, Th. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz and T. W. Hänsch, "A frequency comb in the extreme ultraviolet," Nature (London) 436, 234-237 (2005).
[CrossRef]

Herrmann, M.

Ch. Gohle, Th. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz and T. W. Hänsch, "A frequency comb in the extreme ultraviolet," Nature (London) 436, 234-237 (2005).
[CrossRef]

Hoffnagle, J.

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]

Holzwarth, R.

Ch. Gohle, Th. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz and T. W. Hänsch, "A frequency comb in the extreme ultraviolet," Nature (London) 436, 234-237 (2005).
[CrossRef]

Hood, C. J.

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]

Jones, R. J.

M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi and J. Ye, "Broadband Cavity Ringdown Spectroscopy for Sensitive and Rapid Molecular Detection," Science 311, 1595-1599 (2006).
[CrossRef] [PubMed]

R. J. Jones, K. D. Moll, M. J. Thorpe and J. Ye, "Phase-Coherent Frequency Combs in the Vacuum Ultraviolet via High-Harmonic Generation inside a Femtosecond Enhancement Cavity," Phys. Rev. Lett. 94, 193201 (2005).
[CrossRef] [PubMed]

M. J. Thorpe, R. J. Jones, K. D. Moll, J. Ye, and R. Lalezari, "Precise measurements of optical cavity dispersion and mirror coating properties via femtosecond combs," Opt. Express 13, 882-888 (2005).
[CrossRef] [PubMed]

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]

Jungmann, K.

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]

Kimble, H. J.

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]

Kleineberg,

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U.Kleineberg, U. Heinzmann, M. Drescher, F. Krausz, "Direct measurement of light waves," Science 305, 1267-1269 (2004).
[CrossRef] [PubMed]

Krausz, F.

Ch. Gohle, Th. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz and T. W. Hänsch, "A frequency comb in the extreme ultraviolet," Nature (London) 436, 234-237 (2005).
[CrossRef]

Lalezari, R.

Li, Z. H.

Moll, K. D.

M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi and J. Ye, "Broadband Cavity Ringdown Spectroscopy for Sensitive and Rapid Molecular Detection," Science 311, 1595-1599 (2006).
[CrossRef] [PubMed]

R. J. Jones, K. D. Moll, M. J. Thorpe and J. Ye, "Phase-Coherent Frequency Combs in the Vacuum Ultraviolet via High-Harmonic Generation inside a Femtosecond Enhancement Cavity," Phys. Rev. Lett. 94, 193201 (2005).
[CrossRef] [PubMed]

M. J. Thorpe, R. J. Jones, K. D. Moll, J. Ye, and R. Lalezari, "Precise measurements of optical cavity dispersion and mirror coating properties via femtosecond combs," Opt. Express 13, 882-888 (2005).
[CrossRef] [PubMed]

Rauschenberger, J.

Ch. Gohle, Th. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz and T. W. Hänsch, "A frequency comb in the extreme ultraviolet," Nature (London) 436, 234-237 (2005).
[CrossRef]

Rothman, L. S.

L. S. Rothman et al., "The HITRAN 2004 molecular spectroscopic database," J. Quant. Spect. Rad. Trans. 96, 139-204, (2005).
[CrossRef]

Safdi, B.

M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi and J. Ye, "Broadband Cavity Ringdown Spectroscopy for Sensitive and Rapid Molecular Detection," Science 311, 1595-1599 (2006).
[CrossRef] [PubMed]

Schuessler, H. A.

Ch. Gohle, Th. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz and T. W. Hänsch, "A frequency comb in the extreme ultraviolet," Nature (London) 436, 234-237 (2005).
[CrossRef]

Thorpe, M. J.

M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi and J. Ye, "Broadband Cavity Ringdown Spectroscopy for Sensitive and Rapid Molecular Detection," Science 311, 1595-1599 (2006).
[CrossRef] [PubMed]

R. J. Jones, K. D. Moll, M. J. Thorpe and J. Ye, "Phase-Coherent Frequency Combs in the Vacuum Ultraviolet via High-Harmonic Generation inside a Femtosecond Enhancement Cavity," Phys. Rev. Lett. 94, 193201 (2005).
[CrossRef] [PubMed]

M. J. Thorpe, R. J. Jones, K. D. Moll, J. Ye, and R. Lalezari, "Precise measurements of optical cavity dispersion and mirror coating properties via femtosecond combs," Opt. Express 13, 882-888 (2005).
[CrossRef] [PubMed]

Udem, Th.

Ch. Gohle, Th. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz and T. W. Hänsch, "A frequency comb in the extreme ultraviolet," Nature (London) 436, 234-237 (2005).
[CrossRef]

Wang, L. J.

Ye, J.

M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi and J. Ye, "Broadband Cavity Ringdown Spectroscopy for Sensitive and Rapid Molecular Detection," Science 311, 1595-1599 (2006).
[CrossRef] [PubMed]

R. J. Jones, K. D. Moll, M. J. Thorpe and J. Ye, "Phase-Coherent Frequency Combs in the Vacuum Ultraviolet via High-Harmonic Generation inside a Femtosecond Enhancement Cavity," Phys. Rev. Lett. 94, 193201 (2005).
[CrossRef] [PubMed]

M. J. Thorpe, R. J. Jones, K. D. Moll, J. Ye, and R. Lalezari, "Precise measurements of optical cavity dispersion and mirror coating properties via femtosecond combs," Opt. Express 13, 882-888 (2005).
[CrossRef] [PubMed]

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]

S. T. Cundiff and J. Ye, "Colloquium: Femtosecond optical frequency combs," Rev. Mod. Phys. 75, 325-342, (2003).
[CrossRef]

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]

Zhang, J.

J. Quant. Spect. Rad. Trans. (1)

L. S. Rothman et al., "The HITRAN 2004 molecular spectroscopic database," J. Quant. Spect. Rad. Trans. 96, 139-204, (2005).
[CrossRef]

Nature (London) (1)

Ch. Gohle, Th. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz and T. W. Hänsch, "A frequency comb in the extreme ultraviolet," Nature (London) 436, 234-237 (2005).
[CrossRef]

Opt. Commun. (1)

T. W. Hansch and B. Couillaud, "Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity," Opt. Commun. 35, 441-444 (1980).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (2)

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]

Phys. Rev. Lett. (1)

R. J. Jones, K. D. Moll, M. J. Thorpe and J. Ye, "Phase-Coherent Frequency Combs in the Vacuum Ultraviolet via High-Harmonic Generation inside a Femtosecond Enhancement Cavity," Phys. Rev. Lett. 94, 193201 (2005).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

S. T. Cundiff and J. Ye, "Colloquium: Femtosecond optical frequency combs," Rev. Mod. Phys. 75, 325-342, (2003).
[CrossRef]

Science (2)

M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi and J. Ye, "Broadband Cavity Ringdown Spectroscopy for Sensitive and Rapid Molecular Detection," Science 311, 1595-1599 (2006).
[CrossRef] [PubMed]

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U.Kleineberg, U. Heinzmann, M. Drescher, F. Krausz, "Direct measurement of light waves," Science 305, 1267-1269 (2004).
[CrossRef] [PubMed]

Other (4)

Th. Udem, R. Holzwarth, and T. W. Hänsch, "Optical frequency metrology," Nature (London) 416, 233-237 (2002).
[CrossRef]

A. P. Kovács, K. Osvay, Z. Bor and R. Szipöcs, "Group-delay measurement on laser mirrors by spectrally resolved white-light interferometry," Opt. Lett. 20, 788-90, (1995).
[CrossRef] [PubMed]

For example A. E. Siegmann, "Lasers," Chapter 11, 416 (1986).

M. J. Weber, "CRC Handbook of Laser Science and Technology, Volume IV Optical Materials: Part 2," CRC Press (1986).

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Figures (5)

Fig. 1.
Fig. 1.

Experimental setup. The Ti:Sapphire and the passive cavity (schematically represented by input coupler IC, and mirrors S, M, and OC) are locked to resonance at a frequency ω lock selected by a grating G. The resonant spectrum |E c(ω,ϕ CE)|2, and the comb parameters ω r and ω CE are simultaneously recorded with a computer.

Fig. 2.
Fig. 2.

Raw data obtained using the described method. A: The cavity transmission (color coded) as a function of carrier envelope phase slippage ϕ CE and optical wavelength. The lock frequency ω lock of the cavity is close to 800 nm. B: section of the shown data at a fixed ϕ CE. It can be used to determine the lock point ω lock. C: section at a fixed wavelength (green) and a fit to it (black) using the square modulus of (2) with phase (4) as the model. Excellent agreement between data and model is observed.

Fig. 3.
Fig. 3.

GDD and round-trip loss factor data of an 8-mirror passive cavity, obtained from three measurements with lock frequencies 780.5 (red) and 801.0nm (green and black), respectively. The dashed vertical lines mark the locked points. The GDD data have been smoothed with a 0.6THz BW filter. The modified cavity studied in this work (in contrast to ref. [4]) has not been dispersion engineered and thus displays significant GDD over the entire 150nm measurement bandwidth. The strong resonances around 760 and 822 nm will be discussed in section 5.

Fig. 4.
Fig. 4.

Comparison between measured and expected change of resonator dispersion. The measured GDD of a 0.525 mm sapphire window at Brewster’s angle vs. Sellmeir formula [13] and a quarter wave stack dielectric mirror vs. coating design data both show agreement with deviations on the order of 2.5 fs2 rms (resolution bandwidth 2 THz). The mirror data is systematically shifted by -1 fs2 compared to the design indicating a wavelength shift of the actual stack due to production tolerances.

Fig. 5.
Fig. 5.

The oxygen A-band, as observed in the power loss factor (squared amplitude loss factor r2, upper panel, red) and the GDD (lower panel). The absorption of molecular oxygen, as calculated from HITRAN [15] data (blue spikes, right ordinates), can explain the increased losses very well. The expected reduction in the round-trip power loss factor for our experimental conditions is indicated with a dotted blue line (left ordinate).

Equations (6)

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φ ( ω ) = ϕ CE + ( L c + τ ) ω + ψ ( ω ) .
E c ( ω n ) = t ( ω n ) E i ( ω n ) 1 r ( ω n ) e i φ ( ω n ) ,
Δ φ ( ω , ϕ CE ) ϕ CE + ϕ CE + ω ( T T ) + ψ ( ω ) .
Δ φ ( ω , ϕ CE ) = ( 1 ω ω lock ) ( ϕ CE ϕ CE ) + ω ω lock ( 2 π l ψ ( ω lock ) ) + ψ ( ω ) .
Δ φ ( ω , ϕ CE ) = ( 1 ω ω lock ) ( ϕ CE ϕ CE res ( ω ) )
( ω ω lock 1 ) ϕ CE res ( ω ) ( ω ω lock 1 ) ϕ CE + ω ω lock ( 2 π l ψ ( ω lock ) ) + ψ ( ω ) .

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