Abstract

Dynamics features of high repetition rate continuously pumped solid-state regenerative amplifiers were studied numerically. A space independent rate equations and discrete-time dynamical system approach were used for system state evolution analysis. Regular single-energy operation, quasi-periodic pulsing and chaotic behavior regions are distinguished in space of control parameters. Diagrams of dynamical regimes comprehensively exhibiting operation features of the system are presented. Seed energy is shown to be an important parameter determining the stability space. Conditions of stable operation are described quantitatively.

©2007 Optical Society of America

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References

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  1. W. Koechner, Solid-State Laser Engineering (Springer, 1996), Chap. 9.4.2.
  2. S. Forget, F. Balembois, P. Georges, and P. Devilder, “A new 3D multipass amplifier based on Nd:YAG or Nd:YVO4 crystals,” Appl. Phys. B 75, 481 (2002).
    [Crossref]
  3. V. Kolev, M. Lederer, B. Luther-Davies, and A. Rode, “Passive mode locking of a Nd:YVO4 laser with an extra-long optical resonator,” Opt. Lett. 28, 1275 (2003).
    [Crossref] [PubMed]
  4. D. Nickel, C. Stolzenburg, A. Bevertt, A. Geisen, J. Haüssermann, F. Butze, and M. Leitner, “200 kHz electro-optic switch for ultrafast laser systems,” Rev. Sci. Instrum. 76, 033111 (2005).
    [Crossref]
  5. G. Raciukaitis, M. Grishin, R. Danielius, J. Pocius, and L. Giniūnas, “High repetition rate ps- and fs- DPSS lasers for micromachining”, ICALEO 2006 Proceedings on CD-ROM, (Laser Institute of America, 2006),  99. http://www.laserinstitute.org/store/CONF/599
  6. S. Valling, T. Fordell, and A. M. Lindberg, “Experimental and numerical intensity time series of an optically injected solid state laser,” Opt. Commun. 254, 282 (2005).
    [Crossref]
  7. J. Dörring, A. Killi, U. Morgner, A. Lang, M. Lederer, and D. Kopf, “Period doubling and deterministic chaos in continuously pumped regenerative amplifiers,” Opt. Express 12, 1759 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-8-1759
    [Crossref] [PubMed]
  8. Orazio Svelto, Principles of Lasers (Plenum Press, 1998), Chap. 7.2.
  9. Kathleen T. Alligood, Tim D. Sauer, and James A. Yorke, Chaos. An Introduction to Dynamical Systems (Springer, 1996), Chap. 1.

2006 (1)

G. Raciukaitis, M. Grishin, R. Danielius, J. Pocius, and L. Giniūnas, “High repetition rate ps- and fs- DPSS lasers for micromachining”, ICALEO 2006 Proceedings on CD-ROM, (Laser Institute of America, 2006),  99. http://www.laserinstitute.org/store/CONF/599

2005 (2)

S. Valling, T. Fordell, and A. M. Lindberg, “Experimental and numerical intensity time series of an optically injected solid state laser,” Opt. Commun. 254, 282 (2005).
[Crossref]

D. Nickel, C. Stolzenburg, A. Bevertt, A. Geisen, J. Haüssermann, F. Butze, and M. Leitner, “200 kHz electro-optic switch for ultrafast laser systems,” Rev. Sci. Instrum. 76, 033111 (2005).
[Crossref]

2004 (1)

2003 (1)

2002 (1)

S. Forget, F. Balembois, P. Georges, and P. Devilder, “A new 3D multipass amplifier based on Nd:YAG or Nd:YVO4 crystals,” Appl. Phys. B 75, 481 (2002).
[Crossref]

Alligood, Kathleen T.

Kathleen T. Alligood, Tim D. Sauer, and James A. Yorke, Chaos. An Introduction to Dynamical Systems (Springer, 1996), Chap. 1.

Balembois, F.

S. Forget, F. Balembois, P. Georges, and P. Devilder, “A new 3D multipass amplifier based on Nd:YAG or Nd:YVO4 crystals,” Appl. Phys. B 75, 481 (2002).
[Crossref]

Bevertt, A.

D. Nickel, C. Stolzenburg, A. Bevertt, A. Geisen, J. Haüssermann, F. Butze, and M. Leitner, “200 kHz electro-optic switch for ultrafast laser systems,” Rev. Sci. Instrum. 76, 033111 (2005).
[Crossref]

Butze, F.

D. Nickel, C. Stolzenburg, A. Bevertt, A. Geisen, J. Haüssermann, F. Butze, and M. Leitner, “200 kHz electro-optic switch for ultrafast laser systems,” Rev. Sci. Instrum. 76, 033111 (2005).
[Crossref]

Danielius, R.

G. Raciukaitis, M. Grishin, R. Danielius, J. Pocius, and L. Giniūnas, “High repetition rate ps- and fs- DPSS lasers for micromachining”, ICALEO 2006 Proceedings on CD-ROM, (Laser Institute of America, 2006),  99. http://www.laserinstitute.org/store/CONF/599

Devilder, P.

S. Forget, F. Balembois, P. Georges, and P. Devilder, “A new 3D multipass amplifier based on Nd:YAG or Nd:YVO4 crystals,” Appl. Phys. B 75, 481 (2002).
[Crossref]

Dörring, J.

Fordell, T.

S. Valling, T. Fordell, and A. M. Lindberg, “Experimental and numerical intensity time series of an optically injected solid state laser,” Opt. Commun. 254, 282 (2005).
[Crossref]

Forget, S.

S. Forget, F. Balembois, P. Georges, and P. Devilder, “A new 3D multipass amplifier based on Nd:YAG or Nd:YVO4 crystals,” Appl. Phys. B 75, 481 (2002).
[Crossref]

Geisen, A.

D. Nickel, C. Stolzenburg, A. Bevertt, A. Geisen, J. Haüssermann, F. Butze, and M. Leitner, “200 kHz electro-optic switch for ultrafast laser systems,” Rev. Sci. Instrum. 76, 033111 (2005).
[Crossref]

Georges, P.

S. Forget, F. Balembois, P. Georges, and P. Devilder, “A new 3D multipass amplifier based on Nd:YAG or Nd:YVO4 crystals,” Appl. Phys. B 75, 481 (2002).
[Crossref]

Giniunas, L.

G. Raciukaitis, M. Grishin, R. Danielius, J. Pocius, and L. Giniūnas, “High repetition rate ps- and fs- DPSS lasers for micromachining”, ICALEO 2006 Proceedings on CD-ROM, (Laser Institute of America, 2006),  99. http://www.laserinstitute.org/store/CONF/599

Grishin, M.

G. Raciukaitis, M. Grishin, R. Danielius, J. Pocius, and L. Giniūnas, “High repetition rate ps- and fs- DPSS lasers for micromachining”, ICALEO 2006 Proceedings on CD-ROM, (Laser Institute of America, 2006),  99. http://www.laserinstitute.org/store/CONF/599

Haüssermann, J.

D. Nickel, C. Stolzenburg, A. Bevertt, A. Geisen, J. Haüssermann, F. Butze, and M. Leitner, “200 kHz electro-optic switch for ultrafast laser systems,” Rev. Sci. Instrum. 76, 033111 (2005).
[Crossref]

Killi, A.

Koechner, W.

W. Koechner, Solid-State Laser Engineering (Springer, 1996), Chap. 9.4.2.

Kolev, V.

Kopf, D.

Lang, A.

Lederer, M.

Leitner, M.

D. Nickel, C. Stolzenburg, A. Bevertt, A. Geisen, J. Haüssermann, F. Butze, and M. Leitner, “200 kHz electro-optic switch for ultrafast laser systems,” Rev. Sci. Instrum. 76, 033111 (2005).
[Crossref]

Lindberg, A. M.

S. Valling, T. Fordell, and A. M. Lindberg, “Experimental and numerical intensity time series of an optically injected solid state laser,” Opt. Commun. 254, 282 (2005).
[Crossref]

Luther-Davies, B.

Morgner, U.

Nickel, D.

D. Nickel, C. Stolzenburg, A. Bevertt, A. Geisen, J. Haüssermann, F. Butze, and M. Leitner, “200 kHz electro-optic switch for ultrafast laser systems,” Rev. Sci. Instrum. 76, 033111 (2005).
[Crossref]

Pocius, J.

G. Raciukaitis, M. Grishin, R. Danielius, J. Pocius, and L. Giniūnas, “High repetition rate ps- and fs- DPSS lasers for micromachining”, ICALEO 2006 Proceedings on CD-ROM, (Laser Institute of America, 2006),  99. http://www.laserinstitute.org/store/CONF/599

Raciukaitis, G.

G. Raciukaitis, M. Grishin, R. Danielius, J. Pocius, and L. Giniūnas, “High repetition rate ps- and fs- DPSS lasers for micromachining”, ICALEO 2006 Proceedings on CD-ROM, (Laser Institute of America, 2006),  99. http://www.laserinstitute.org/store/CONF/599

Rode, A.

Sauer, Tim D.

Kathleen T. Alligood, Tim D. Sauer, and James A. Yorke, Chaos. An Introduction to Dynamical Systems (Springer, 1996), Chap. 1.

Stolzenburg, C.

D. Nickel, C. Stolzenburg, A. Bevertt, A. Geisen, J. Haüssermann, F. Butze, and M. Leitner, “200 kHz electro-optic switch for ultrafast laser systems,” Rev. Sci. Instrum. 76, 033111 (2005).
[Crossref]

Svelto, Orazio

Orazio Svelto, Principles of Lasers (Plenum Press, 1998), Chap. 7.2.

Valling, S.

S. Valling, T. Fordell, and A. M. Lindberg, “Experimental and numerical intensity time series of an optically injected solid state laser,” Opt. Commun. 254, 282 (2005).
[Crossref]

Yorke, James A.

Kathleen T. Alligood, Tim D. Sauer, and James A. Yorke, Chaos. An Introduction to Dynamical Systems (Springer, 1996), Chap. 1.

Appl. Phys. B (1)

S. Forget, F. Balembois, P. Georges, and P. Devilder, “A new 3D multipass amplifier based on Nd:YAG or Nd:YVO4 crystals,” Appl. Phys. B 75, 481 (2002).
[Crossref]

Opt. Commun. (1)

S. Valling, T. Fordell, and A. M. Lindberg, “Experimental and numerical intensity time series of an optically injected solid state laser,” Opt. Commun. 254, 282 (2005).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Rev. Sci. Instrum. (1)

D. Nickel, C. Stolzenburg, A. Bevertt, A. Geisen, J. Haüssermann, F. Butze, and M. Leitner, “200 kHz electro-optic switch for ultrafast laser systems,” Rev. Sci. Instrum. 76, 033111 (2005).
[Crossref]

Other (4)

G. Raciukaitis, M. Grishin, R. Danielius, J. Pocius, and L. Giniūnas, “High repetition rate ps- and fs- DPSS lasers for micromachining”, ICALEO 2006 Proceedings on CD-ROM, (Laser Institute of America, 2006),  99. http://www.laserinstitute.org/store/CONF/599

Orazio Svelto, Principles of Lasers (Plenum Press, 1998), Chap. 7.2.

Kathleen T. Alligood, Tim D. Sauer, and James A. Yorke, Chaos. An Introduction to Dynamical Systems (Springer, 1996), Chap. 1.

W. Koechner, Solid-State Laser Engineering (Springer, 1996), Chap. 9.4.2.

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Figures (4)

Fig. 1.
Fig. 1.

Optical layout of the solid-state diode pumped regenerative amplifier.

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Fig. 2.
Fig. 2.

Graphical presentation of the orbits in state space. Blue and red curves are right and left hand parts of Eq. (13), respectively. Transition to the stable (attracting) fixed point (a) at εs =3×10-7; τ=18.0; T1/T=3.0. Period-4T orbit (b) at εs =10-10; τ=42.0; T1/T=2.56.

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Fig. 3.
Fig. 3.

Diagrams of RA dynamical regimes in parameter space for different seed energy: εs =10-10 (a); εs =2.5×10-7 (b); εs =3×10-7 (c); εs =1.3×10-4 (d). Green, red, and black lines correspond to stored energy extraction efficiency of 50 %, 70 %, and 90 %, respectively.

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Fig. 4.
Fig. 4.

Stability diagrams in system parameters space (normalized repetition rate - effective round trip number) for different seed energies.

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Tables (2)

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Table 1. Legend of System State Evolution in Discrete Time Scale

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Table 2. Dynamic Regimes Realizable for Corresponding Seed Energy Range

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Equations (12)

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d N dt = R p − σ c V ϕ N − N T 1
d ϕ dt = ( σ c L a A a V N − 1 T c ) ϕ ,
dg ( τ ) d τ = − ε ( τ ) g ( τ ) + 1 − g ( τ ) τ 1
dε ( τ ) d τ = ε ( τ ) g ( τ ) − ε ( τ ) τ c .
dg ( τ ) d τ = 1 − g ( τ ) τ 1 .
g p = 1 − ( 1 − g 1 ) exp ( − T T 1 ) .
dg ( τ ) d τ = − ε ( τ ) g ( τ )
d ε ( τ ) d τ = ε ( τ ) g ( τ ) .
g a = g 0 + ε s 1 + ε s g 0 exp ( g 0 τ )
ε = g 0 + ε s 1 + g 0 ε s exp ( − g 0 τ ) .
g Σ ( g 0 ) = 1 − [ 1 − g 0 + ε s 1 + ε s g 0 exp ( g 0 τ ) ] exp ( − T T 1 ) .
1 − ( 1 − g 0 ) exp ( T T 1 ) = g 1 = g 0 + ε s 1 + ε s g 0 exp ( g 0 τ ) .

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