Abstract

We explore mode locked operation of a Ti:Sapphire laser with enhanced Kerr nonlinearity, where the threshold for pulsed operation can be continuously tuned down to the threshold for continuous-wave (CW) operation, and even below it. At the point of equality, even though a CW solution does not exist, pulsed oscillation can be realized directly from zero CW oscillation. We experimentally investigate the evolution of the mode locking mechanism towards this point and beyond it, and provide a qualitative theoretical model to explain the results.

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    [CrossRef]
  2. T. Brabec, P. F. Curley, C. Spielmann, E. Wintner, and A. J. Schmidt, “Hard-aperture kerr-lens mode locking,” J. Opt. Soc. Am. B10, 1029–1034 (1993).
    [CrossRef]
  3. H. Haken and H. Ohno, “Onset of ultrashort laser pulses: First or second order phase transition?” Opt. Commun.26, 117–118 (1978).
    [CrossRef]
  4. A. Gordon and B. Fischer, “Phase transition theory of pulse formation in passively mode-locked lasers with dispersion and kerr nonlinearity,” Opt. Commun.223, 151–156 (2003).
    [CrossRef]
  5. A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, and B. Fischer, “Experimental observation of critical phenomena in a laser light system,” Phys. Rev. Lett.105, 013905 (2010).
    [CrossRef] [PubMed]
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    [CrossRef]
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  12. X. Han and H. Zeng, “Kerr-lens mode-locked ti:sapphire laser with an additional intracavity nonlinear medium,” Opt. Express16, 18875–18880 (2008).
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    [CrossRef]
  14. L. Chen, M. Y. Sander, and F. X. Kartner, “Kerr-lens mode locking with minimum nonlinearity using gain-matched output couplers,” Opt. Le35, 2916–2918 (2010).
    [CrossRef]
  15. M. Muller, J. Herrmann, and S. Gatz, “Kerr-lens mode locking at pump rates below continuous wave threshold,” Opt. Commun.148, 281–284 (1998).
    [CrossRef]
  16. G. Fibich and A. L. Gaeta, “Critical power for self-focusing in bulk media and in hollow waveguides,” Opt. Lett.25, 335–337 (2000).
    [CrossRef]
  17. V. Magni, G. Cerullo, and S. D. Silvestri, “Closed form gaussian beam analysis of resonators containing a kerr medium for femtosecond lasers,” Opt. Commun.101, 365–370 (1993).
    [CrossRef]
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    [CrossRef]
  20. C. G. Durfee, T. Storz, J. Garlick, S. Hill, J. A. Squier, M. Kirchner, G. Taft, K. Shea, H. Kapteyn, M. Murnane, and S. Backus, “Direct diode-pumped kerr-lens mode-locked ti:sapphire laser,” Opt. Express20, 13677–13683 (2012).
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2012 (1)

2010 (2)

A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, and B. Fischer, “Experimental observation of critical phenomena in a laser light system,” Phys. Rev. Lett.105, 013905 (2010).
[CrossRef] [PubMed]

L. Chen, M. Y. Sander, and F. X. Kartner, “Kerr-lens mode locking with minimum nonlinearity using gain-matched output couplers,” Opt. Le35, 2916–2918 (2010).
[CrossRef]

2008 (1)

2003 (1)

A. Gordon and B. Fischer, “Phase transition theory of pulse formation in passively mode-locked lasers with dispersion and kerr nonlinearity,” Opt. Commun.223, 151–156 (2003).
[CrossRef]

2001 (1)

2000 (3)

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

G. Fibich and A. L. Gaeta, “Critical power for self-focusing in bulk media and in hollow waveguides,” Opt. Lett.25, 335–337 (2000).
[CrossRef]

H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron.6, 1173–1185 (2000).
[CrossRef]

1998 (1)

M. Muller, J. Herrmann, and S. Gatz, “Kerr-lens mode locking at pump rates below continuous wave threshold,” Opt. Commun.148, 281–284 (1998).
[CrossRef]

1995 (1)

1993 (3)

C. Radzewicz, G. W. Pearson, and J. S. Krasinski, “Use of zns as an additional highly nonlinear intracavity selffocusing element in a ti:sapphire self-modelocked laser,” Opt. Commun.102, 464–468 (1993).
[CrossRef]

T. Brabec, P. F. Curley, C. Spielmann, E. Wintner, and A. J. Schmidt, “Hard-aperture kerr-lens mode locking,” J. Opt. Soc. Am. B10, 1029–1034 (1993).
[CrossRef]

V. Magni, G. Cerullo, and S. D. Silvestri, “Closed form gaussian beam analysis of resonators containing a kerr medium for femtosecond lasers,” Opt. Commun.101, 365–370 (1993).
[CrossRef]

1992 (2)

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and kerr lens mode locking,” IEEE J. Quantum Electron.28, 2086–2096 (1992).
[CrossRef]

G. W. Pearson, C. Radzewicz, and J. S. Krasinski, “Analysis of self-focusing mode-locked lasers with additional highly nonlinear self-focusing elements,” Opt. Commun.94, 221–226 (1992).
[CrossRef]

1991 (2)

1978 (1)

H. Haken and H. Ohno, “Onset of ultrashort laser pulses: First or second order phase transition?” Opt. Commun.26, 117–118 (1978).
[CrossRef]

1966 (1)

Angelow, G.

Backus, S.

Bekker, A.

A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, and B. Fischer, “Experimental observation of critical phenomena in a laser light system,” Phys. Rev. Lett.105, 013905 (2010).
[CrossRef] [PubMed]

Boiko, A.

Brabec, T.

Cerullo, G.

V. Magni, G. Cerullo, S. D. Silvestri, and A. Monguzzi, “Astigmatism in gaussian-beam self-focusing and in resonators for kerr-lens mode locking,” J. Opt. Soc. Am. B12, 476–485 (1995).
[CrossRef]

V. Magni, G. Cerullo, and S. D. Silvestri, “Closed form gaussian beam analysis of resonators containing a kerr medium for femtosecond lasers,” Opt. Commun.101, 365–370 (1993).
[CrossRef]

Chen, L.

L. Chen, M. Y. Sander, and F. X. Kartner, “Kerr-lens mode locking with minimum nonlinearity using gain-matched output couplers,” Opt. Le35, 2916–2918 (2010).
[CrossRef]

Curley, P. F.

Diodati, F. P.

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

Durfee, C. G.

Ell, R.

Ferguson, A. I.

Fibich, G.

Fischer, B.

A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, and B. Fischer, “Experimental observation of critical phenomena in a laser light system,” Phys. Rev. Lett.105, 013905 (2010).
[CrossRef] [PubMed]

A. Gordon and B. Fischer, “Phase transition theory of pulse formation in passively mode-locked lasers with dispersion and kerr nonlinearity,” Opt. Commun.223, 151–156 (2003).
[CrossRef]

Fujimoto, J. G.

Gabetta, G.

Gaeta, A. L.

Garlick, J.

Gatz, S.

M. Muller, J. Herrmann, and S. Gatz, “Kerr-lens mode locking at pump rates below continuous wave threshold,” Opt. Commun.148, 281–284 (1998).
[CrossRef]

Gordon, A.

A. Gordon and B. Fischer, “Phase transition theory of pulse formation in passively mode-locked lasers with dispersion and kerr nonlinearity,” Opt. Commun.223, 151–156 (2003).
[CrossRef]

Haken, H.

H. Haken and H. Ohno, “Onset of ultrashort laser pulses: First or second order phase transition?” Opt. Commun.26, 117–118 (1978).
[CrossRef]

Han, X.

Haus, H. A.

H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron.6, 1173–1185 (2000).
[CrossRef]

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and kerr lens mode locking,” IEEE J. Quantum Electron.28, 2086–2096 (1992).
[CrossRef]

Herrmann, J.

M. Muller, J. Herrmann, and S. Gatz, “Kerr-lens mode locking at pump rates below continuous wave threshold,” Opt. Commun.148, 281–284 (1998).
[CrossRef]

Hill, S.

Hnilo, A. A.

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

Huang, D.

Ippen, E. P.

Jacobson, J.

Kapteyn, H.

Kartner, F. X.

Kirchner, M.

Kogelnik, H.

Krasinski, J. S.

C. Radzewicz, G. W. Pearson, and J. S. Krasinski, “Use of zns as an additional highly nonlinear intracavity selffocusing element in a ti:sapphire self-modelocked laser,” Opt. Commun.102, 464–468 (1993).
[CrossRef]

G. W. Pearson, C. Radzewicz, and J. S. Krasinski, “Analysis of self-focusing mode-locked lasers with additional highly nonlinear self-focusing elements,” Opt. Commun.94, 221–226 (1992).
[CrossRef]

Larotonda, M. A.

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

Lederer, M. J.

Levit, B.

A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, and B. Fischer, “Experimental observation of critical phenomena in a laser light system,” Phys. Rev. Lett.105, 013905 (2010).
[CrossRef] [PubMed]

Li, T.

Luther-Davies, B.

Magni, V.

V. Magni, G. Cerullo, S. D. Silvestri, and A. Monguzzi, “Astigmatism in gaussian-beam self-focusing and in resonators for kerr-lens mode locking,” J. Opt. Soc. Am. B12, 476–485 (1995).
[CrossRef]

V. Magni, G. Cerullo, and S. D. Silvestri, “Closed form gaussian beam analysis of resonators containing a kerr medium for femtosecond lasers,” Opt. Commun.101, 365–370 (1993).
[CrossRef]

Malcolm, G. P. A.

Monguzzi, A.

Morgner, U.

Muller, M.

M. Muller, J. Herrmann, and S. Gatz, “Kerr-lens mode locking at pump rates below continuous wave threshold,” Opt. Commun.148, 281–284 (1998).
[CrossRef]

Murnane, M.

Ohno, H.

H. Haken and H. Ohno, “Onset of ultrashort laser pulses: First or second order phase transition?” Opt. Commun.26, 117–118 (1978).
[CrossRef]

Pearson, G. W.

C. Radzewicz, G. W. Pearson, and J. S. Krasinski, “Use of zns as an additional highly nonlinear intracavity selffocusing element in a ti:sapphire self-modelocked laser,” Opt. Commun.102, 464–468 (1993).
[CrossRef]

G. W. Pearson, C. Radzewicz, and J. S. Krasinski, “Analysis of self-focusing mode-locked lasers with additional highly nonlinear self-focusing elements,” Opt. Commun.94, 221–226 (1992).
[CrossRef]

Radzewicz, C.

C. Radzewicz, G. W. Pearson, and J. S. Krasinski, “Use of zns as an additional highly nonlinear intracavity selffocusing element in a ti:sapphire self-modelocked laser,” Opt. Commun.102, 464–468 (1993).
[CrossRef]

G. W. Pearson, C. Radzewicz, and J. S. Krasinski, “Analysis of self-focusing mode-locked lasers with additional highly nonlinear self-focusing elements,” Opt. Commun.94, 221–226 (1992).
[CrossRef]

Ramaswamy, M.

Rosen, A.

A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, and B. Fischer, “Experimental observation of critical phenomena in a laser light system,” Phys. Rev. Lett.105, 013905 (2010).
[CrossRef] [PubMed]

Sander, M. Y.

L. Chen, M. Y. Sander, and F. X. Kartner, “Kerr-lens mode locking with minimum nonlinearity using gain-matched output couplers,” Opt. Le35, 2916–2918 (2010).
[CrossRef]

Scheuer, V.

Schmidt, A. J.

Shea, K.

Silvestri, S. D.

V. Magni, G. Cerullo, S. D. Silvestri, and A. Monguzzi, “Astigmatism in gaussian-beam self-focusing and in resonators for kerr-lens mode locking,” J. Opt. Soc. Am. B12, 476–485 (1995).
[CrossRef]

V. Magni, G. Cerullo, and S. D. Silvestri, “Closed form gaussian beam analysis of resonators containing a kerr medium for femtosecond lasers,” Opt. Commun.101, 365–370 (1993).
[CrossRef]

Smulakovsky, V.

A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, and B. Fischer, “Experimental observation of critical phenomena in a laser light system,” Phys. Rev. Lett.105, 013905 (2010).
[CrossRef] [PubMed]

Spielmann, C.

Squier, J. A.

Storz, T.

Taft, G.

Tschudi, T.

Weill, R.

A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, and B. Fischer, “Experimental observation of critical phenomena in a laser light system,” Phys. Rev. Lett.105, 013905 (2010).
[CrossRef] [PubMed]

Wintner, E.

Zeng, H.

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and kerr lens mode locking,” IEEE J. Quantum Electron.28, 2086–2096 (1992).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron.6, 1173–1185 (2000).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Commun. (7)

G. W. Pearson, C. Radzewicz, and J. S. Krasinski, “Analysis of self-focusing mode-locked lasers with additional highly nonlinear self-focusing elements,” Opt. Commun.94, 221–226 (1992).
[CrossRef]

C. Radzewicz, G. W. Pearson, and J. S. Krasinski, “Use of zns as an additional highly nonlinear intracavity selffocusing element in a ti:sapphire self-modelocked laser,” Opt. Commun.102, 464–468 (1993).
[CrossRef]

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

H. Haken and H. Ohno, “Onset of ultrashort laser pulses: First or second order phase transition?” Opt. Commun.26, 117–118 (1978).
[CrossRef]

A. Gordon and B. Fischer, “Phase transition theory of pulse formation in passively mode-locked lasers with dispersion and kerr nonlinearity,” Opt. Commun.223, 151–156 (2003).
[CrossRef]

M. Muller, J. Herrmann, and S. Gatz, “Kerr-lens mode locking at pump rates below continuous wave threshold,” Opt. Commun.148, 281–284 (1998).
[CrossRef]

V. Magni, G. Cerullo, and S. D. Silvestri, “Closed form gaussian beam analysis of resonators containing a kerr medium for femtosecond lasers,” Opt. Commun.101, 365–370 (1993).
[CrossRef]

Opt. Express (2)

Opt. Le (1)

L. Chen, M. Y. Sander, and F. X. Kartner, “Kerr-lens mode locking with minimum nonlinearity using gain-matched output couplers,” Opt. Le35, 2916–2918 (2010).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. Lett. (1)

A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, and B. Fischer, “Experimental observation of critical phenomena in a laser light system,” Phys. Rev. Lett.105, 013905 (2010).
[CrossRef] [PubMed]

Supplementary Material (3)

» Media 1: AVI (117371 KB)     
» Media 2: AVI (117371 KB)     
» Media 3: MOV (98304 KB)     

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Figures (4)

Fig. 1
Fig. 1

Cavity configuration. The gain medium is a 3mm long Brewster-cut TiS crystal with 0.25 wt% doping. The curved mirrors (M1, M2) radius of curvature is R=15cm, with high reflector (HR) and a 95% output coupler (OC) as end mirrors. An additional planar-cut BK7 window is inserted near the image point of the TiS crystal, created by the two-lens telescope of focal length f = 10cm. The short cavity arm is 42cm long and the long arm (90cm) contains a prism-pair of BK7 glass (60cm). Each cavity mirror except the OC provides group velocity dispersion of GVD ≈ −55 fs2. The oscillator is running in the regime of anomalous dispersion.

Fig. 2
Fig. 2

ML (red) and CW (blue) operation parameters as a function of Z = δδ2 for two 3mm long BK7 window positions: off-focus (a)+(b) and in-focus (c)+(d). Mode locking at the critical point Zc where the ML threshold equals the CW threshold is demonstrated in the attached media file ( Media 1).

Fig. 3
Fig. 3

(a)–(d) Experimental definition of the Kerr strength as a function of Z for BK7 window with different lengths, (e) measured spectrum for 2mm BK7 window at Zss.

Fig. 4
Fig. 4

Theoretical definition of the Kerr strength as a function of P for TiS crystal with added window.

Equations (1)

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γ s P c ω d ω d P ,

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