Abstract

An iterative model based on the LambertW function was developed for estimating the fundamental mode parameters of resonators with saturable gain guiding. The process of pulse buildup in passively Q-switched, end-pumped lasers was analyzed. The effective ABCD cavity matrix for consecutive round-trips was calculated, taking into account spatially variable saturated gain in an active medium and absorption bleaching in a saturable absorber. The twofold decrease in beam width, as compared with the fundamental mode of the bare cavity, was demonstrated. The application of such a model for resonators with other nonlinear elements is feasible.

© 2002 Optical Society of America

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References

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  1. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  2. T. Y. Fan and R. L. Byer, ??Diode laser-pumped solid state lasers,?? IEEE J. Quantum Electron. 24, 895-912 (1988).
    [CrossRef]
  3. P. Laporta and M. Brussard, ??Design criteria for mode size optimization in diode-pumped solid-state lasers,?? IEEE J. Quantum Electron. 27, 2319-2326 (1991).
    [CrossRef]
  4. R. Kapoor, P. K. Mukhopadhyay, and J. George, ??A new approach to compute overlap efficiency in axially pumped solid state lasers,?? Opt. Express 5, 125-133 (1999), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-5-6-125">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-5-6-125</a>.
    [CrossRef] [PubMed]
  5. J. J. Zayhowski. ??Thermal guiding in microchips,?? in OSA Proceedings on Advanced Solid State Lasers, G. Dube and H. P. Jensen, eds. (Optical Society of America, Washington, D.C., 1990), pp. 9-13.
  6. M. E. Innocenzi, H. T. Yura, C. L. Fincher, and R. A. Fields, ??Thermal modeling of continuous-wave-endpumped solid-state lasers,?? Appl. Phys. Lett. 56, 1831-1833 (1990).
    [CrossRef]
  7. X. Zhang, S. Zhao, Q. Wang, B. Ozygus, and H. Weber, ??Modeling of passively Q-switched lasers,?? J. Opt. Soc. Am B 17, 1166-1175 (2000).
    [CrossRef]
  8. F. Salin and J. Squier, ??Gain guiding in solid state lasers,?? Opt. Lett. 17, 2319-2326 (1992).
    [CrossRef]
  9. V. Magni, G. Cerullo, and S. De Silvestri, "Closed form gaussian beam analysis of resonators containing a Kerr medium for femtosecond lasers,?? Opt. Commun. 101, 365-370 (1993).
    [CrossRef]
  10. A. J. Kemp, R. S. Conroy, G. J. Friel, and B. Sinclair, ??Guiding effects in Nd:YVO4 microchip lasers operating well above threshold,?? IEEE J. Quantum Electron. 35, 675-681 (1999).
    [CrossRef]
  11. C. Serrat, M. P. van Exter, N. J. van Druten, and J. P. Woerdman, ??Transverse mode formation in microlasers by combined gain- and index-guiding,?? IEEE J. Quantum Electron. 35, 1341-1320 (1999).
    [CrossRef]
  12. O. Denchev, S. Kurtev, and P. Petrov, ??Modes of unstable resonators with a saturable gain guide,?? Appl. Opt. 40, 921-929 (2001).
    [CrossRef]
  13. E. J. Grace, G. H. New, and P. M. W. French, ??Simple ABCD matrix treatment for transversely varying saturable gain,?? Opt. Lett. 26, 1776-1778 (2001).
    [CrossRef]
  14. D. A. Barry, J. Y. Parlange, L. Li, H. Prommer, C. J. Cunningham, and F. Stagnitti, ??Analytical approximations for real values of the LambertW-function,?? Math Comput. Simulations 53, 95-103 (2000).
    [CrossRef]
  15. A. E. Siegman, ??New developments in laser resonators,?? in Optical Resonators, Proc. SPIE 1224, 4-14 (1990).
  16. J. K. Jabczynski, J. Kwiatkowski, and W. Zendzian, ??Laser beam propagation in gain media,?? Appl. Opt. (to be published).
  17. J. J. Degnan, ??Optimization of passively Q-switched lasers,?? IEEE J. Quantum Electron. 31, 1890-1901 (1995).
    [CrossRef]

Advanced Solid State Lasers (1)

J. J. Zayhowski. ??Thermal guiding in microchips,?? in OSA Proceedings on Advanced Solid State Lasers, G. Dube and H. P. Jensen, eds. (Optical Society of America, Washington, D.C., 1990), pp. 9-13.

Appl. Opt. (2)

O. Denchev, S. Kurtev, and P. Petrov, ??Modes of unstable resonators with a saturable gain guide,?? Appl. Opt. 40, 921-929 (2001).
[CrossRef]

J. K. Jabczynski, J. Kwiatkowski, and W. Zendzian, ??Laser beam propagation in gain media,?? Appl. Opt. (to be published).

Appl. Phys. Lett. (1)

M. E. Innocenzi, H. T. Yura, C. L. Fincher, and R. A. Fields, ??Thermal modeling of continuous-wave-endpumped solid-state lasers,?? Appl. Phys. Lett. 56, 1831-1833 (1990).
[CrossRef]

IEEE J. Quantum Electron. (5)

T. Y. Fan and R. L. Byer, ??Diode laser-pumped solid state lasers,?? IEEE J. Quantum Electron. 24, 895-912 (1988).
[CrossRef]

P. Laporta and M. Brussard, ??Design criteria for mode size optimization in diode-pumped solid-state lasers,?? IEEE J. Quantum Electron. 27, 2319-2326 (1991).
[CrossRef]

J. J. Degnan, ??Optimization of passively Q-switched lasers,?? IEEE J. Quantum Electron. 31, 1890-1901 (1995).
[CrossRef]

A. J. Kemp, R. S. Conroy, G. J. Friel, and B. Sinclair, ??Guiding effects in Nd:YVO4 microchip lasers operating well above threshold,?? IEEE J. Quantum Electron. 35, 675-681 (1999).
[CrossRef]

C. Serrat, M. P. van Exter, N. J. van Druten, and J. P. Woerdman, ??Transverse mode formation in microlasers by combined gain- and index-guiding,?? IEEE J. Quantum Electron. 35, 1341-1320 (1999).
[CrossRef]

J. Opt. Soc. Am B (1)

X. Zhang, S. Zhao, Q. Wang, B. Ozygus, and H. Weber, ??Modeling of passively Q-switched lasers,?? J. Opt. Soc. Am B 17, 1166-1175 (2000).
[CrossRef]

Math Comput. Simulations (1)

D. A. Barry, J. Y. Parlange, L. Li, H. Prommer, C. J. Cunningham, and F. Stagnitti, ??Analytical approximations for real values of the LambertW-function,?? Math Comput. Simulations 53, 95-103 (2000).
[CrossRef]

Opt. Commun. (1)

V. Magni, G. Cerullo, and S. De Silvestri, "Closed form gaussian beam analysis of resonators containing a Kerr medium for femtosecond lasers,?? Opt. Commun. 101, 365-370 (1993).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Proc. SPIE (1)

A. E. Siegman, ??New developments in laser resonators,?? in Optical Resonators, Proc. SPIE 1224, 4-14 (1990).

Other (1)

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

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Figures (7)

Fig. 1.
Fig. 1.

Scheme of an iterative procedure for a cavity including saturable gain medium.

Fig. 2.
Fig. 2.

Relative mode radius W act/W 00 with dependence on round-trip number, fundamental mode radius W 00=0.384 mm, gain profile radius wg =0.1 mm, stationary value of effective mode radius w last=0.359 mm, reabsorption loss L reab=0.15, transmission of output coupler T oc=0.15, small-signal gain g 0 l=10.

Fig. 3.
Fig. 3.

Variations of internal intensity with dependence on round-trip number.

Fig. 4.
Fig. 4.

Scheme of the iterative procedure for a cavity including a saturable gain medium and a saturable absorber.

Fig. 5.
Fig. 5.

Instantaneous intensity (continuous curve), relative radius of pulse (dotted curve), and width of passive Q-switch diaphragm (dashed curve) with dependence on round-trip number for a passively Q-switched laser with initial Q-switch transmission T ini=0.5, passive losses L pas=0.1, radius of the fundamental mode of the bare cavity W 00=0.546 mm, ratio of absorption to gain cross sections α=σ a e =5, and transmission of output coupler T oc=0.5.

Fig. 6.
Fig. 6.

Two-dimensional maps of instantaneous intensity during pulse formation for two passively Q-switched lasers having the same bare cavity matrix and different initial saturable losses: upper plot for passive Q switch of 10% initial transmission, lower plot for 50% initial transmission.

Fig. 7.
Fig. 7.

Dependence of fundamental mode width of the bare cavity (continuous curve), ratio of effective pulse beam radius Wm /W 00 to fundamental mode W 00 (dashed curve), and ratio of waist areas (W 00/Wm )2 of bare cavity and pulsed beam (dotted curve) on the trace of the ABCD round-trip matrix. Parameter values: ratio of absorption to gain cross sections α=σ a e =5, passive losses L pas=0.1, output coupler transmission T oc=0.25, initial transmission of Q switch T ini=0.5.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

1 I r d I r dz = g 1 + I r I r exp ( I r ) = G ( z ) = exp ( g z ) ,
W ( z ) exp [ W ( z ) ] = z .
I r , 1 exp ( I r , 1 ) = I r , 0 exp ( g l + I r , 0 ) .
I r , 1 = W [ I r , 0 exp ( I r , 0 ) G ( l ) ] .
M SG = [ 1 0 C SG 1 ] ; C SG = i λ π w SG 2 ,
w SG 2 = w out , sg 2 w inp 2 ,
w out , sg 2 = 2 0 x 3 I r , out ( x ) d x 0 x I r , out ( x ) d x .

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