Abstract

We present a theoretical and experimental study of the dynamics of the diode-pumped Kerr-lens mode-locked Nd:YAG laser. The theoretical approach, which is based on a two-variable Poincaré map, allows the calculation of the pulse parameters with satisfactory accuracy. It is concluded (both theoretically and experimentally) that this laser does not present instabilities, which is an interesting feature for short-pulse laser engineering. We also find a robust two pulses per round trip mode of operation that appears to be a simple way for doubling the repetition rate.

© 2001 Optical Society of America

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References

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  1. C. Wang, W. Zhang, K. Lee, and K. Yoo, “Pulse splitting in a self-mode-locked Ti:sapphire laser,” Opt. Commun. 137, 89–92 (1997).
    [CrossRef]
  2. S. Bolton, R. Jonks, C. Elkinton, and G. Sucha, “Pulse resolved measurements of subharmonic oscillations in a Kerr-lens mode-locked Ti:sapphire laser,” J. Opt. Soc. Am. B 16, 339–344 (1999).
    [CrossRef]
  3. M. Kovalsky, A. Hnilo, and C. González Inchauspe, “Hidden instabilities in the Ti:sapphire Kerr lens mode-locked laser,” Opt. Lett. 24, 1638–1940 (1999).
    [CrossRef]
  4. J. Jasapara, W. Rudolph, V. Kalashnikov, D. Krimer, J. Poloyko, and M. Lenzner, “Automodulations in Kerr-lens mode-locked solid-state lasers,” J. Opt. Soc. Am. B 17, 319–326 (2000).
    [CrossRef]
  5. M. Larotonda, A. Hnilo, and F. Diodati, “Diode-pumped self-starting Kerr-lens mode locking Nd:YAG laser,” Opt. Commun. 183, 485–491 (2000).
    [CrossRef]
  6. M. Kovalsky and A. Hnilo, “Stability and bifurcations in Kerr-lens mode-locked Ti:sapphire lasers,” Opt. Commun. 186, 155–166 (2000).
    [CrossRef]
  7. K. Liu, C. Flood, D. Walker, and H. van Driel, “Kerr lens mode locking of a diode pumped Nd:YAG laser,” Opt. Lett. 17, 1361–1363 (1992).
    [CrossRef]
  8. A. Hnilo, “Self-mode-locking Ti:sapphire laser description with an iterative map,” J. Opt. Soc. Am. B 12, 718–725 (1995).
    [CrossRef]
  9. G. Cerullo, S. De Silvestri, V. Magni, and L. Pallaro, “Resonators for Kerr-lens mode-locking femtosecond Ti:sapphire lasers,” Opt. Lett. 19, 807–809 (1994).
    [CrossRef] [PubMed]
  10. See, e.g., A. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 27.
  11. M. Lai, J. Nicholson, and W. Rudolph, “Multiple pulse operation of a femtosecond Ti:sapphire laser,” Opt. Commun. 142, 45–49 (1997).
    [CrossRef]

2000

J. Jasapara, W. Rudolph, V. Kalashnikov, D. Krimer, J. Poloyko, and M. Lenzner, “Automodulations in Kerr-lens mode-locked solid-state lasers,” J. Opt. Soc. Am. B 17, 319–326 (2000).
[CrossRef]

M. Larotonda, A. Hnilo, and F. Diodati, “Diode-pumped self-starting Kerr-lens mode locking Nd:YAG laser,” Opt. Commun. 183, 485–491 (2000).
[CrossRef]

M. Kovalsky and A. Hnilo, “Stability and bifurcations in Kerr-lens mode-locked Ti:sapphire lasers,” Opt. Commun. 186, 155–166 (2000).
[CrossRef]

1999

1997

C. Wang, W. Zhang, K. Lee, and K. Yoo, “Pulse splitting in a self-mode-locked Ti:sapphire laser,” Opt. Commun. 137, 89–92 (1997).
[CrossRef]

M. Lai, J. Nicholson, and W. Rudolph, “Multiple pulse operation of a femtosecond Ti:sapphire laser,” Opt. Commun. 142, 45–49 (1997).
[CrossRef]

1995

1994

1992

Bolton, S.

Cerullo, G.

De Silvestri, S.

Diodati, F.

M. Larotonda, A. Hnilo, and F. Diodati, “Diode-pumped self-starting Kerr-lens mode locking Nd:YAG laser,” Opt. Commun. 183, 485–491 (2000).
[CrossRef]

Elkinton, C.

Flood, C.

Hnilo, A.

M. Kovalsky and A. Hnilo, “Stability and bifurcations in Kerr-lens mode-locked Ti:sapphire lasers,” Opt. Commun. 186, 155–166 (2000).
[CrossRef]

M. Larotonda, A. Hnilo, and F. Diodati, “Diode-pumped self-starting Kerr-lens mode locking Nd:YAG laser,” Opt. Commun. 183, 485–491 (2000).
[CrossRef]

M. Kovalsky, A. Hnilo, and C. González Inchauspe, “Hidden instabilities in the Ti:sapphire Kerr lens mode-locked laser,” Opt. Lett. 24, 1638–1940 (1999).
[CrossRef]

A. Hnilo, “Self-mode-locking Ti:sapphire laser description with an iterative map,” J. Opt. Soc. Am. B 12, 718–725 (1995).
[CrossRef]

Inchauspe, C. González

Jasapara, J.

Jonks, R.

Kalashnikov, V.

Kovalsky, M.

M. Kovalsky and A. Hnilo, “Stability and bifurcations in Kerr-lens mode-locked Ti:sapphire lasers,” Opt. Commun. 186, 155–166 (2000).
[CrossRef]

M. Kovalsky, A. Hnilo, and C. González Inchauspe, “Hidden instabilities in the Ti:sapphire Kerr lens mode-locked laser,” Opt. Lett. 24, 1638–1940 (1999).
[CrossRef]

Krimer, D.

Lai, M.

M. Lai, J. Nicholson, and W. Rudolph, “Multiple pulse operation of a femtosecond Ti:sapphire laser,” Opt. Commun. 142, 45–49 (1997).
[CrossRef]

Larotonda, M.

M. Larotonda, A. Hnilo, and F. Diodati, “Diode-pumped self-starting Kerr-lens mode locking Nd:YAG laser,” Opt. Commun. 183, 485–491 (2000).
[CrossRef]

Lee, K.

C. Wang, W. Zhang, K. Lee, and K. Yoo, “Pulse splitting in a self-mode-locked Ti:sapphire laser,” Opt. Commun. 137, 89–92 (1997).
[CrossRef]

Lenzner, M.

Liu, K.

Magni, V.

Nicholson, J.

M. Lai, J. Nicholson, and W. Rudolph, “Multiple pulse operation of a femtosecond Ti:sapphire laser,” Opt. Commun. 142, 45–49 (1997).
[CrossRef]

Pallaro, L.

Poloyko, J.

Rudolph, W.

Sucha, G.

van Driel, H.

Walker, D.

Wang, C.

C. Wang, W. Zhang, K. Lee, and K. Yoo, “Pulse splitting in a self-mode-locked Ti:sapphire laser,” Opt. Commun. 137, 89–92 (1997).
[CrossRef]

Yoo, K.

C. Wang, W. Zhang, K. Lee, and K. Yoo, “Pulse splitting in a self-mode-locked Ti:sapphire laser,” Opt. Commun. 137, 89–92 (1997).
[CrossRef]

Zhang, W.

C. Wang, W. Zhang, K. Lee, and K. Yoo, “Pulse splitting in a self-mode-locked Ti:sapphire laser,” Opt. Commun. 137, 89–92 (1997).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

M. Larotonda, A. Hnilo, and F. Diodati, “Diode-pumped self-starting Kerr-lens mode locking Nd:YAG laser,” Opt. Commun. 183, 485–491 (2000).
[CrossRef]

M. Kovalsky and A. Hnilo, “Stability and bifurcations in Kerr-lens mode-locked Ti:sapphire lasers,” Opt. Commun. 186, 155–166 (2000).
[CrossRef]

C. Wang, W. Zhang, K. Lee, and K. Yoo, “Pulse splitting in a self-mode-locked Ti:sapphire laser,” Opt. Commun. 137, 89–92 (1997).
[CrossRef]

M. Lai, J. Nicholson, and W. Rudolph, “Multiple pulse operation of a femtosecond Ti:sapphire laser,” Opt. Commun. 142, 45–49 (1997).
[CrossRef]

Opt. Lett.

Other

See, e.g., A. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 27.

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Figures (3)

Fig. 1
Fig. 1

Scheme of the laser cavity (from Ref. 5). The output coupler is wedged and has a transmission of 6%. The dimensions are a=343 mm, b=104 mm, c=1006 mm, and x=56 mm.

Fig. 2
Fig. 2

Values of the fixed points as functions of the control parameters. The variable r is proportional to the pulse’s peak power, and α-1/2 is proportional to the pulse duration. The dotted curves indicate that the fixed point is unstable in that region. (a) The gain parameter g varies for k=0.95 and μ=1. (b) The beam-aperture overlap parameter μ varies for g=8 and k=0.95. (c) The field feedback factor k varies for μ=1 and g=8.

Fig. 3
Fig. 3

Trace of the two pulses per round trip mode of operation (here named P2), obtained with a fast photodiode (<0.3-ns rise time) and a 2-GSa/s sampling oscilloscope. The pulses have a duration (Gaussian fit) of 6.2 ps (not measurable with this method of observation). The small peaks between pulses are electrical echoes.

Equations (18)

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δ-(1/w)dw/dP|P=0,
E(t)=E0 exp(-at2+iω0t),
Tap(t)exp-[w(t)/wap]2,
Tap(t)=exp{-(wcw/wap)2 exp[-2δP(t)]}.
E(t)=E0 exp{-[1+r exp(-r/μ)]at2+iω0t-μ exp(-r/μ)},
1/(4aout)=1/(4ain)+4G/Δω2,
Eout=Ein exp(G),
αn+1=αn[1+rn exp(-rn/μ)]1+16Gαn[1+rn exp(-rn/μ)],
rn+1=rn exp{2[G-μ exp(-rn/μ)+ln(k)]},
GgssIsat/I=gssIsatπw2τrt/U=gssIsatπwcw2 exp(-r/μ)τrt/U,
G=g(α1/2/r)exp(-r/μ),
αn+1=αn[1+rn exp(-rn/μ)]1+16gαn3/2 exp(-rn/μ)rn[1+rn exp(-rn/μ)],
rn+1=rn exp{2[g(αn1/2/rn)exp(-rn/μ)-μ exp(-rn/μ)+ln(k)]}.
α=r216g[1+r exp(-r/μ)]2/3,
g216r[1+r exp(-r/μ)]1/3-μexp(-r/μ)+ln(k)=0.
δ(P2)=δ(P1)(z++z-)/2,
z+=KU(P2)/w(P2)4τ(P2)KU(P1)/w(P1)4τ(P1)=τ(P1)2τ(P2),
δ(P2)=δ(P1)(5/4)(τ(P1)/τ(P2)).

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