Abstract

We model the behavior of short and ultrashort laser pulses in high-finesse Fabry-Perot resonators, examining, in particular, the influence of cavity mirror reflectance and dispersion. The total coupling, peak power enhancement and temporal broadening of circulating pulses are characterized a function of the duration of the incident pulses.We show that there is an optimal input pulse duration which maximizes peak power for a given set of mirror characteristics.

© 2003 Optical Society of America

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References

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  1. R.W.P. Drever, J.L. Hall, F.V. Kowalski, J. Hough, G.M. Ford, A.J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97 (1983).
    [Crossref]
  2. R.J. Jones and J.-C. Diels, “Stabilization of femtosecond lasers for optical frequency metrology and direct optical to radio frequency synthesis,” Phys. Rev. Lett. 86, 3288 (2001).
    [Crossref] [PubMed]
  3. S. Link, H.A. Dürr, and W. Eberhardt, “Femtosecond spectroscopy,” J. Phys.: Condens. Matter 137873–7884 (2001).
    [Crossref]
  4. J.C. Petersen and A.N. Luiten, “Resonant Polarization Interferometry with Ultrashort Laser Pulses,” Phys. Rev. A (in preparation).
  5. R.J. Jones and J. Ye, “Femtosecond pulse amplification by coherent addition in a passive optical cavity,” Opt. Lett. 27, 1848 (2002).
    [Crossref]
  6. T. Udem, J. Reichert, R. Holzwarth, M. Niering, M. Weitz, and T.W. Hänsch, “Measuring the Frequency of Light with Mode-Locked Lasers,” in A.N. Luiten (Ed.), Frequency Measurement and Control, Topics Appl. Phys.79275 (Springer-Verlag, Berlin, 2001).
    [Crossref]
  7. A.E. Siegman, Lasers (University Science Books, Sausalito, 1986).
  8. CVI Laser Corporation (www.cvilaser.com).
  9. F. Brunneret al, “240-fs pulses with 22-W average power from a mode-locked thin-disk Yb:KY(WO4)2 laser,” Opt. Lett. 27, 1162–1164 (2002).
    [Crossref]
  10. T. Beddardet al, “High-average-power, 1-MW peak-power self-mode-locked Ti:sapphire oscillator,” Opt. Lett. 24, 163–165 (1999).
    [Crossref]

2002 (2)

2001 (2)

R.J. Jones and J.-C. Diels, “Stabilization of femtosecond lasers for optical frequency metrology and direct optical to radio frequency synthesis,” Phys. Rev. Lett. 86, 3288 (2001).
[Crossref] [PubMed]

S. Link, H.A. Dürr, and W. Eberhardt, “Femtosecond spectroscopy,” J. Phys.: Condens. Matter 137873–7884 (2001).
[Crossref]

1999 (1)

1983 (1)

R.W.P. Drever, J.L. Hall, F.V. Kowalski, J. Hough, G.M. Ford, A.J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97 (1983).
[Crossref]

Beddard, T.

Brunner, F.

Diels, J.-C.

R.J. Jones and J.-C. Diels, “Stabilization of femtosecond lasers for optical frequency metrology and direct optical to radio frequency synthesis,” Phys. Rev. Lett. 86, 3288 (2001).
[Crossref] [PubMed]

Drever, R.W.P.

R.W.P. Drever, J.L. Hall, F.V. Kowalski, J. Hough, G.M. Ford, A.J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97 (1983).
[Crossref]

Dürr, H.A.

S. Link, H.A. Dürr, and W. Eberhardt, “Femtosecond spectroscopy,” J. Phys.: Condens. Matter 137873–7884 (2001).
[Crossref]

Eberhardt, W.

S. Link, H.A. Dürr, and W. Eberhardt, “Femtosecond spectroscopy,” J. Phys.: Condens. Matter 137873–7884 (2001).
[Crossref]

Ford, G.M.

R.W.P. Drever, J.L. Hall, F.V. Kowalski, J. Hough, G.M. Ford, A.J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97 (1983).
[Crossref]

Hall, J.L.

R.W.P. Drever, J.L. Hall, F.V. Kowalski, J. Hough, G.M. Ford, A.J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97 (1983).
[Crossref]

Hänsch, T.W.

T. Udem, J. Reichert, R. Holzwarth, M. Niering, M. Weitz, and T.W. Hänsch, “Measuring the Frequency of Light with Mode-Locked Lasers,” in A.N. Luiten (Ed.), Frequency Measurement and Control, Topics Appl. Phys.79275 (Springer-Verlag, Berlin, 2001).
[Crossref]

Holzwarth, R.

T. Udem, J. Reichert, R. Holzwarth, M. Niering, M. Weitz, and T.W. Hänsch, “Measuring the Frequency of Light with Mode-Locked Lasers,” in A.N. Luiten (Ed.), Frequency Measurement and Control, Topics Appl. Phys.79275 (Springer-Verlag, Berlin, 2001).
[Crossref]

Hough, J.

R.W.P. Drever, J.L. Hall, F.V. Kowalski, J. Hough, G.M. Ford, A.J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97 (1983).
[Crossref]

Jones, R.J.

R.J. Jones and J. Ye, “Femtosecond pulse amplification by coherent addition in a passive optical cavity,” Opt. Lett. 27, 1848 (2002).
[Crossref]

R.J. Jones and J.-C. Diels, “Stabilization of femtosecond lasers for optical frequency metrology and direct optical to radio frequency synthesis,” Phys. Rev. Lett. 86, 3288 (2001).
[Crossref] [PubMed]

Kowalski, F.V.

R.W.P. Drever, J.L. Hall, F.V. Kowalski, J. Hough, G.M. Ford, A.J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97 (1983).
[Crossref]

Link, S.

S. Link, H.A. Dürr, and W. Eberhardt, “Femtosecond spectroscopy,” J. Phys.: Condens. Matter 137873–7884 (2001).
[Crossref]

Luiten, A.N.

J.C. Petersen and A.N. Luiten, “Resonant Polarization Interferometry with Ultrashort Laser Pulses,” Phys. Rev. A (in preparation).

Munley, A.J.

R.W.P. Drever, J.L. Hall, F.V. Kowalski, J. Hough, G.M. Ford, A.J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97 (1983).
[Crossref]

Niering, M.

T. Udem, J. Reichert, R. Holzwarth, M. Niering, M. Weitz, and T.W. Hänsch, “Measuring the Frequency of Light with Mode-Locked Lasers,” in A.N. Luiten (Ed.), Frequency Measurement and Control, Topics Appl. Phys.79275 (Springer-Verlag, Berlin, 2001).
[Crossref]

Petersen, J.C.

J.C. Petersen and A.N. Luiten, “Resonant Polarization Interferometry with Ultrashort Laser Pulses,” Phys. Rev. A (in preparation).

Reichert, J.

T. Udem, J. Reichert, R. Holzwarth, M. Niering, M. Weitz, and T.W. Hänsch, “Measuring the Frequency of Light with Mode-Locked Lasers,” in A.N. Luiten (Ed.), Frequency Measurement and Control, Topics Appl. Phys.79275 (Springer-Verlag, Berlin, 2001).
[Crossref]

Siegman, A.E.

A.E. Siegman, Lasers (University Science Books, Sausalito, 1986).

Udem, T.

T. Udem, J. Reichert, R. Holzwarth, M. Niering, M. Weitz, and T.W. Hänsch, “Measuring the Frequency of Light with Mode-Locked Lasers,” in A.N. Luiten (Ed.), Frequency Measurement and Control, Topics Appl. Phys.79275 (Springer-Verlag, Berlin, 2001).
[Crossref]

Ward, H.

R.W.P. Drever, J.L. Hall, F.V. Kowalski, J. Hough, G.M. Ford, A.J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97 (1983).
[Crossref]

Weitz, M.

T. Udem, J. Reichert, R. Holzwarth, M. Niering, M. Weitz, and T.W. Hänsch, “Measuring the Frequency of Light with Mode-Locked Lasers,” in A.N. Luiten (Ed.), Frequency Measurement and Control, Topics Appl. Phys.79275 (Springer-Verlag, Berlin, 2001).
[Crossref]

Ye, J.

Appl. Phys. B (1)

R.W.P. Drever, J.L. Hall, F.V. Kowalski, J. Hough, G.M. Ford, A.J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97 (1983).
[Crossref]

J. Phys.: Condens. Matter (1)

S. Link, H.A. Dürr, and W. Eberhardt, “Femtosecond spectroscopy,” J. Phys.: Condens. Matter 137873–7884 (2001).
[Crossref]

Opt. Lett. (3)

Phys. Rev. Lett. (1)

R.J. Jones and J.-C. Diels, “Stabilization of femtosecond lasers for optical frequency metrology and direct optical to radio frequency synthesis,” Phys. Rev. Lett. 86, 3288 (2001).
[Crossref] [PubMed]

Other (4)

J.C. Petersen and A.N. Luiten, “Resonant Polarization Interferometry with Ultrashort Laser Pulses,” Phys. Rev. A (in preparation).

T. Udem, J. Reichert, R. Holzwarth, M. Niering, M. Weitz, and T.W. Hänsch, “Measuring the Frequency of Light with Mode-Locked Lasers,” in A.N. Luiten (Ed.), Frequency Measurement and Control, Topics Appl. Phys.79275 (Springer-Verlag, Berlin, 2001).
[Crossref]

A.E. Siegman, Lasers (University Science Books, Sausalito, 1986).

CVI Laser Corporation (www.cvilaser.com).

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Figures (3)

Fig. 1.
Fig. 1.

(a) Dispersive phase shift δϕ(Ω) on reflection from CVI LGVD ultrafast mirrors. (b) Calculated circulating phase ϕcirc (Ω). (c) Calculated power coupling efficiency β(Ω).

Fig. 2.
Fig. 2.

(a) Calculated power Pcirc (t) of the circulating pulse due to 20 fs Gaussian incident pulses. R=99.8%. A 37 fs Gaussian pulse (dashed) is shown for comparison. (b) Calculated circulating phase ϕcirc (t).

Fig. 3.
Fig. 3.

(a) Total power coupling efficiency βnet and relative pulse broadening τcircinc . (b) Peak circulating power Pmax (per µJ of energy per incident pulse).

Equations (15)

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( t ) = 2 τ log 2 π exp ( 2 log 2 t 2 τ 2 ) .
˜ ( Ω ) = τ 2 π log 2 exp ( Ω 2 τ 2 8 log 2 ) .
ν n = n c 2 L opt .
n λ = 2 ( L + Δ ϕ ( ω ) λ 2 π ) .
ν n = ( n δ ϕ ( ω ) π ϕ 0 π ) c 2 ( L + c ϕ 0 ) .
β ( Ω ) = P circ ( Ω ) F π P inc ( Ω ) .
h ( Ω ) = R exp ( i δ ϕ ( Ω ) )
˜ circ ( Ω ) = 1 R ˜ inc ( Ω ) ( 1 + h ( Ω ) 2 + h ( Ω ) 4 + )
= 1 R 1 h ( Ω ) 2 ˜ inc ( Ω )
= 1 R 1 R exp ( 2 i δ ϕ ( Ω ) ) ˜ inc ( Ω ) .
ϕ circ ( Ω ) = arg ( 1 1 R exp ( 2 i δ ϕ ( Ω ) ) ) ;
β ( Ω ) = ˜ circ ( Ω ) 2 F π ˜ inc ( Ω ) 2 = 1 R 1 R exp ( 2 i δ ϕ ( Ω ) ) 2 .
P circ ( t ) = circ ( t ) 2
ϕ circ ( t ) = arg ( circ ( t ) )
β net = β ( Ω ) P inc ( Ω ) d Ω = P circ ( Ω ) d Ω F π ,

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