Abstract

We present a technique that enhances the intensity of a nanosecond laser pulse by confining it in an enhancement cavity. The point of the technique is that a weak continuous-wave laser radiation, locked to the enhancement cavity, is injected into a nanosecond injection-locked pulsed laser as a seed. This leads to a stable confinement of the nanosecond pulse in the enhancement cavity. It is demonstrated that the pulsed intensity is enhanced by a factor of 120 for a 40-ns pulse, consistent with the theoretical prediction.

© 2008 Optical Society of America

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References

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  1. A. Yariv, Quantum Electronics 3rd Edition (John Wiley & Sons Inc, 1989).
  2. C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, and T. W. Hänsch, "A frequency comb in the extreme ultraviolet," Nature 436, 234-237 (2005).
    [CrossRef] [PubMed]
  3. 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, 193201-193204 (2005).
    [CrossRef] [PubMed]
  4. 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: Lasers Opt. 31, 97-105 (1983).
    [CrossRef]
  5. C. E. Hamilton, "Single-frequency, injection-seeded Ti:sapphire ring laser with high temporal precision," Opt. Lett. 17, 728 - 730 (1992).
    [CrossRef] [PubMed]
  6. M. Katsuragawa and T. Onose, "Dual-Wavelength Injection-Locked Pulsed Laser," Opt. Lett. 30, 2421 - 2423 (2005).
    [CrossRef] [PubMed]
  7. A. Ogino, M. Katsuragawa, and K. Hakuta, "Single-Frequency Injection seeded Pulsed Ti: Al2O3 Ring Laser," Jpn. J. Appl. Phys. 36, 5112-5115 (1997).
    [CrossRef]
  8. We assume a typical specification of 7 mJ, 10 kHz at 532 nm for a high-repetition-rate, LD-pump, nanosecond pulsed laser. When we generate a tunable nanosecond single-frequency pulse with a specification of 2.5 mJ at 30 ns by employing such a nanosecond pulsed laser as a pump and then confine such pulses in an enhancement cavity with a finesse of 250, we can achieve a radiation intensity of 50 GW/cm2 and a Rayleigh length of 10 cm (beam waist diameter: ?200 ?m) at a repetition rate of 10 kHz.
  9. T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, "Trapping and delaying photons for one nanosecond in an ultra-small high-Q photonic-crystal nanocavity," Nature Photon. 1, 49-52 (2007).
    [CrossRef]
  10. In Figure 4, the peak of the transmitted pulse was delayed by 18.6 ns against that of the incident pulse. This delay is equivalent to the slowing of the light velocity by a factor of 1/74 against the speed of light in vacuum, since the cavity length was 7.5 cm.

2007 (1)

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, "Trapping and delaying photons for one nanosecond in an ultra-small high-Q photonic-crystal nanocavity," Nature Photon. 1, 49-52 (2007).
[CrossRef]

2005 (3)

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, and T. W. Hänsch, "A frequency comb in the extreme ultraviolet," Nature 436, 234-237 (2005).
[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, 193201-193204 (2005).
[CrossRef] [PubMed]

M. Katsuragawa and T. Onose, "Dual-Wavelength Injection-Locked Pulsed Laser," Opt. Lett. 30, 2421 - 2423 (2005).
[CrossRef] [PubMed]

1997 (1)

A. Ogino, M. Katsuragawa, and K. Hakuta, "Single-Frequency Injection seeded Pulsed Ti: Al2O3 Ring Laser," Jpn. J. Appl. Phys. 36, 5112-5115 (1997).
[CrossRef]

1992 (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: Lasers Opt. 31, 97-105 (1983).
[CrossRef]

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: Lasers Opt. 31, 97-105 (1983).
[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: Lasers Opt. 31, 97-105 (1983).
[CrossRef]

Gohle, C.

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

Hakuta, K.

A. Ogino, M. Katsuragawa, and K. Hakuta, "Single-Frequency Injection seeded Pulsed Ti: Al2O3 Ring Laser," Jpn. J. Appl. Phys. 36, 5112-5115 (1997).
[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: Lasers Opt. 31, 97-105 (1983).
[CrossRef]

Hamilton, C. E.

Hänsch, T. W.

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

Herrmann, M.

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

Holzwarth, R.

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

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: Lasers Opt. 31, 97-105 (1983).
[CrossRef]

Jones, R. J.

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, 193201-193204 (2005).
[CrossRef] [PubMed]

Katsuragawa, M.

M. Katsuragawa and T. Onose, "Dual-Wavelength Injection-Locked Pulsed Laser," Opt. Lett. 30, 2421 - 2423 (2005).
[CrossRef] [PubMed]

A. Ogino, M. Katsuragawa, and K. Hakuta, "Single-Frequency Injection seeded Pulsed Ti: Al2O3 Ring Laser," Jpn. J. Appl. Phys. 36, 5112-5115 (1997).
[CrossRef]

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: Lasers Opt. 31, 97-105 (1983).
[CrossRef]

Kuramochi, E.

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, "Trapping and delaying photons for one nanosecond in an ultra-small high-Q photonic-crystal nanocavity," Nature Photon. 1, 49-52 (2007).
[CrossRef]

Moll, K. D.

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, 193201-193204 (2005).
[CrossRef] [PubMed]

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: Lasers Opt. 31, 97-105 (1983).
[CrossRef]

Notomi, M.

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, "Trapping and delaying photons for one nanosecond in an ultra-small high-Q photonic-crystal nanocavity," Nature Photon. 1, 49-52 (2007).
[CrossRef]

Ogino, A.

A. Ogino, M. Katsuragawa, and K. Hakuta, "Single-Frequency Injection seeded Pulsed Ti: Al2O3 Ring Laser," Jpn. J. Appl. Phys. 36, 5112-5115 (1997).
[CrossRef]

Onose, T.

Rauschenberger, J.

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

Schuessler, H. A.

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

Shinya, A.

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, "Trapping and delaying photons for one nanosecond in an ultra-small high-Q photonic-crystal nanocavity," Nature Photon. 1, 49-52 (2007).
[CrossRef]

Tanabe, T.

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, "Trapping and delaying photons for one nanosecond in an ultra-small high-Q photonic-crystal nanocavity," Nature Photon. 1, 49-52 (2007).
[CrossRef]

Taniyama, H.

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, "Trapping and delaying photons for one nanosecond in an ultra-small high-Q photonic-crystal nanocavity," Nature Photon. 1, 49-52 (2007).
[CrossRef]

Thorpe, M. J.

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, 193201-193204 (2005).
[CrossRef] [PubMed]

Udem, T.

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

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: Lasers Opt. 31, 97-105 (1983).
[CrossRef]

Ye, J.

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, 193201-193204 (2005).
[CrossRef] [PubMed]

Appl. Phys. B: Lasers Opt. (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: Lasers Opt. 31, 97-105 (1983).
[CrossRef]

Jpn. J. Appl. Phys. (1)

A. Ogino, M. Katsuragawa, and K. Hakuta, "Single-Frequency Injection seeded Pulsed Ti: Al2O3 Ring Laser," Jpn. J. Appl. Phys. 36, 5112-5115 (1997).
[CrossRef]

Nature (1)

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

Nature Photon. (1)

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, "Trapping and delaying photons for one nanosecond in an ultra-small high-Q photonic-crystal nanocavity," Nature Photon. 1, 49-52 (2007).
[CrossRef]

Opt. Lett. (2)

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, 193201-193204 (2005).
[CrossRef] [PubMed]

Other (3)

We assume a typical specification of 7 mJ, 10 kHz at 532 nm for a high-repetition-rate, LD-pump, nanosecond pulsed laser. When we generate a tunable nanosecond single-frequency pulse with a specification of 2.5 mJ at 30 ns by employing such a nanosecond pulsed laser as a pump and then confine such pulses in an enhancement cavity with a finesse of 250, we can achieve a radiation intensity of 50 GW/cm2 and a Rayleigh length of 10 cm (beam waist diameter: ?200 ?m) at a repetition rate of 10 kHz.

In Figure 4, the peak of the transmitted pulse was delayed by 18.6 ns against that of the incident pulse. This delay is equivalent to the slowing of the light velocity by a factor of 1/74 against the speed of light in vacuum, since the cavity length was 7.5 cm.

A. Yariv, Quantum Electronics 3rd Edition (John Wiley & Sons Inc, 1989).

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Figures (5)

Fig.1
Fig.1

schematic illustrating carrier-frequency stabilization and intensity-enhancement of a nanosecond pulse.

Fig. 2.
Fig. 2.

Calculated electric field intensity waveforms of a nanosecond single-frequency pulse introduced into an enhancement cavity. a: incident (black dotted curve), reflected (red solid curve), and transmitted (green solid curve) waveforms; b: intracavity waveform (black solid curve) and transmitted waveform with a multiplication factor of 4 T (green bold curve, T=0.0125 is the transmission of the cavity mirror). The temporal duration of the incident Gaussian pulse is 28.3 ns. The FSR and finesse of the enhancement cavity are 2.00 GHz (cavity length: 75.0 mm) and 250, respectively.

Fig. 3.
Fig. 3.

System for carrier-frequency stabilization and intensity enhancement of nanosecond laser pulses. Blue shading: system for locking the oscillation frequency, ω 0, of the external-cavity controlled laser diode (ECLD) to the enhancement cavity. Yellow shading: system for confining the nanosecond laser pulse in the enhancement cavity. EOM: electro-optic modulator, FG: function generator, PD: photo diode, DBM: double balanced mixer, PZT: PZT actuator.

Fig. 4.
Fig. 4.

Intensity waveforms of the incident (gray dotted), reflected (red soild), and transmitted (green solid) radiations. The waveforms are normalized by the peak intensity of the incident laser pulse. The temporal duration of the incident laser pulse was set to be 28.3 ns at FWHM. The FSR and the finesse of the enhancement cavity employed were 2.0 GHz (cavity length of 76 mm) and 250, respectively. The peak intensity of the transmitted waveform was 0.26. The inset shows a 10 shot superposed transmitted waveform (the incident laser pulse duration was 20.7 ns for this data).

Fig. 5.
Fig. 5.

Enhancement factor of a nanosecond laser pulse in the cavity as a function of the pulse duration of the nanosecond pulse. The solid curve shows calculated enhancement factor. The red circles denote the observed enhancement factors. The dotted curve is the enhancement factor obtained with the boundary condition in which the incident pulsed energy is kept constant.

Equations (6)

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E r = ( R E ( t ) + T n = 1 ( R ) 2 n 1 exp ( in δ ) E ( t n 2 L c ) ) exp ( i ( ω t + k z ) ) .
E t = T n = 0 ( R ) 2 n exp ( in δ ) E ( t ( n + 1 ) 2 L c ) exp ( i ( ω t + k z ) ) .
E i = T n = 0 ( R ) 2 n exp ( i ( ω ( t z c n 2 L c ) k z n δ ) ) E ( t z c n 2 L c ) +
T n = 0 ( R ) 2 n + 1 exp ( i ( ω ( t 2 L z c n 2 L c ) k z n δ ) ) E ( t 2 L z c z c ) .
n = 0 T ( R ) 2 n E ( t z c 2 L c n )
( R { exp ( i ( ω 0 t k z ) ) exp ( i ( ω 0 t + k z ) ) } + ( 1 R ) exp ( i ( ω 0 t k z ) ) ) .

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