Abstract

Pump-saturation effects in end-pumped solid-state lasers are considered. In particular we investigate the influence of the pump beam width on both the laser threshold and the laser efficiency in four-level laser material. We demonstrate that, in contrast with the results obtained when pump saturation is neglected, a pure on-axis pumping does not ensure the lowest threshold and the highest laser efficiency. Pump-saturation effects lead to an optimum pump beam width for a fixed laser beam radius.

© 1998 Optical Society of America

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References

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  1. G. Harkness and W. J. Firth, “Transverse modes of microchip solid-state lasers,” J. Mod. Opt. 39, 2023 (1992).
    [CrossRef]
  2. T. Y. Fan and R. L. Byer, “Diode laser-pumped solid-state lasers,” IEEE J. Quantum Electron. 24, 895–912 (1988).
    [CrossRef]
  3. S. Taccheo, P. Laporta, S. Longhi, and C. Svelto, “Experimental analysis and theoretical modeling of a diode-pumped Er:Yb:glass microchip laser,” Opt. Lett. 20, 889–891 (1995).
    [CrossRef] [PubMed]
  4. T. Y. Fan, “Aperture guiding in quasi-three-level lasers,” Opt. Lett. 19, 554–556 (1994).
    [CrossRef] [PubMed]
  5. P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Analysis and modeling of the erbium–ytterbium glass laser,” Opt. Commun. 100, 311–321 (1993).
    [CrossRef]
  6. D. G. Hall, R. G. Smith, and R. R. Rice, “Pump size effects in Nd:YAG lasers,” Appl. Opt. 19, 3041–3043 (1980).
    [CrossRef] [PubMed]
  7. D. G. Hall, “Optimum mode criterion for low-gain lasers,” Appl. Opt. 20, 1579–1583 (1981).
    [CrossRef] [PubMed]
  8. 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]
  9. F. Sanchez and A. Chardon, “Pump size optimization in microchip lasers,” Opt. Commun. 136, 405–409 (1997).
    [CrossRef]
  10. W. F. Krupke and L. L. Chase, “Ground-state depleted solid-state lasers: principles, characteristics and scaling,” Opt. Quantum Electron. 22, S1–S22 (1990).
    [CrossRef]
  11. T. Y. Fan, “Optimizing the efficiency and stored energy in quasi-three-level lasers,” IEEE J. Quantum Electron. 28, 2692–2697 (1992).
    [CrossRef]
  12. P. Peterson, A. Gavrielides, and P. M. Sharma, “CW theory of a laser diode-pumped two-manifold solid-state laser,” Opt. Commun. 109, 282–287 (1994).
    [CrossRef]
  13. Z. Cai, A. Chardon, F. Sanchez, and G. Stephan, “Investigation of absorption saturation in diode end-pumped microchip lasers,” Proc. SPIE 2889, 70–78 (1996).
    [CrossRef]
  14. C. Paré, “Optimum laser beam profile for maximum energy extraction from a saturable amplifier,” Opt. Commun. 123, 762–776 (1996).
    [CrossRef]
  15. W. P. Risk, “Modeling of longitudinally pumped solid-state lasers exhibiting reabsorption losses,” J. Opt. Soc. Am. B 5, 1412–1423 (1988).
    [CrossRef]
  16. A. Chardon, Ph.D. dissertation (Université de Rennes 1, France, 1996).

1997 (1)

F. Sanchez and A. Chardon, “Pump size optimization in microchip lasers,” Opt. Commun. 136, 405–409 (1997).
[CrossRef]

1996 (2)

Z. Cai, A. Chardon, F. Sanchez, and G. Stephan, “Investigation of absorption saturation in diode end-pumped microchip lasers,” Proc. SPIE 2889, 70–78 (1996).
[CrossRef]

C. Paré, “Optimum laser beam profile for maximum energy extraction from a saturable amplifier,” Opt. Commun. 123, 762–776 (1996).
[CrossRef]

1995 (1)

1994 (2)

P. Peterson, A. Gavrielides, and P. M. Sharma, “CW theory of a laser diode-pumped two-manifold solid-state laser,” Opt. Commun. 109, 282–287 (1994).
[CrossRef]

T. Y. Fan, “Aperture guiding in quasi-three-level lasers,” Opt. Lett. 19, 554–556 (1994).
[CrossRef] [PubMed]

1993 (1)

P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Analysis and modeling of the erbium–ytterbium glass laser,” Opt. Commun. 100, 311–321 (1993).
[CrossRef]

1992 (2)

G. Harkness and W. J. Firth, “Transverse modes of microchip solid-state lasers,” J. Mod. Opt. 39, 2023 (1992).
[CrossRef]

T. Y. Fan, “Optimizing the efficiency and stored energy in quasi-three-level lasers,” IEEE J. Quantum Electron. 28, 2692–2697 (1992).
[CrossRef]

1991 (1)

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]

1990 (1)

W. F. Krupke and L. L. Chase, “Ground-state depleted solid-state lasers: principles, characteristics and scaling,” Opt. Quantum Electron. 22, S1–S22 (1990).
[CrossRef]

1988 (2)

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

W. P. Risk, “Modeling of longitudinally pumped solid-state lasers exhibiting reabsorption losses,” J. Opt. Soc. Am. B 5, 1412–1423 (1988).
[CrossRef]

1981 (1)

1980 (1)

Brussard, M.

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]

Byer, R. L.

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

Cai, Z.

Z. Cai, A. Chardon, F. Sanchez, and G. Stephan, “Investigation of absorption saturation in diode end-pumped microchip lasers,” Proc. SPIE 2889, 70–78 (1996).
[CrossRef]

Chardon, A.

F. Sanchez and A. Chardon, “Pump size optimization in microchip lasers,” Opt. Commun. 136, 405–409 (1997).
[CrossRef]

Z. Cai, A. Chardon, F. Sanchez, and G. Stephan, “Investigation of absorption saturation in diode end-pumped microchip lasers,” Proc. SPIE 2889, 70–78 (1996).
[CrossRef]

Chase, L. L.

W. F. Krupke and L. L. Chase, “Ground-state depleted solid-state lasers: principles, characteristics and scaling,” Opt. Quantum Electron. 22, S1–S22 (1990).
[CrossRef]

Fan, T. Y.

T. Y. Fan, “Aperture guiding in quasi-three-level lasers,” Opt. Lett. 19, 554–556 (1994).
[CrossRef] [PubMed]

T. Y. Fan, “Optimizing the efficiency and stored energy in quasi-three-level lasers,” IEEE J. Quantum Electron. 28, 2692–2697 (1992).
[CrossRef]

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

Firth, W. J.

G. Harkness and W. J. Firth, “Transverse modes of microchip solid-state lasers,” J. Mod. Opt. 39, 2023 (1992).
[CrossRef]

Gavrielides, A.

P. Peterson, A. Gavrielides, and P. M. Sharma, “CW theory of a laser diode-pumped two-manifold solid-state laser,” Opt. Commun. 109, 282–287 (1994).
[CrossRef]

Hall, D. G.

Harkness, G.

G. Harkness and W. J. Firth, “Transverse modes of microchip solid-state lasers,” J. Mod. Opt. 39, 2023 (1992).
[CrossRef]

Krupke, W. F.

W. F. Krupke and L. L. Chase, “Ground-state depleted solid-state lasers: principles, characteristics and scaling,” Opt. Quantum Electron. 22, S1–S22 (1990).
[CrossRef]

Laporta, P.

S. Taccheo, P. Laporta, S. Longhi, and C. Svelto, “Experimental analysis and theoretical modeling of a diode-pumped Er:Yb:glass microchip laser,” Opt. Lett. 20, 889–891 (1995).
[CrossRef] [PubMed]

P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Analysis and modeling of the erbium–ytterbium glass laser,” Opt. Commun. 100, 311–321 (1993).
[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]

Longhi, S.

S. Taccheo, P. Laporta, S. Longhi, and C. Svelto, “Experimental analysis and theoretical modeling of a diode-pumped Er:Yb:glass microchip laser,” Opt. Lett. 20, 889–891 (1995).
[CrossRef] [PubMed]

P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Analysis and modeling of the erbium–ytterbium glass laser,” Opt. Commun. 100, 311–321 (1993).
[CrossRef]

Paré, C.

C. Paré, “Optimum laser beam profile for maximum energy extraction from a saturable amplifier,” Opt. Commun. 123, 762–776 (1996).
[CrossRef]

Peterson, P.

P. Peterson, A. Gavrielides, and P. M. Sharma, “CW theory of a laser diode-pumped two-manifold solid-state laser,” Opt. Commun. 109, 282–287 (1994).
[CrossRef]

Rice, R. R.

Risk, W. P.

Sanchez, F.

F. Sanchez and A. Chardon, “Pump size optimization in microchip lasers,” Opt. Commun. 136, 405–409 (1997).
[CrossRef]

Z. Cai, A. Chardon, F. Sanchez, and G. Stephan, “Investigation of absorption saturation in diode end-pumped microchip lasers,” Proc. SPIE 2889, 70–78 (1996).
[CrossRef]

Sharma, P. M.

P. Peterson, A. Gavrielides, and P. M. Sharma, “CW theory of a laser diode-pumped two-manifold solid-state laser,” Opt. Commun. 109, 282–287 (1994).
[CrossRef]

Smith, R. G.

Stephan, G.

Z. Cai, A. Chardon, F. Sanchez, and G. Stephan, “Investigation of absorption saturation in diode end-pumped microchip lasers,” Proc. SPIE 2889, 70–78 (1996).
[CrossRef]

Svelto, C.

Svelto, O.

P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Analysis and modeling of the erbium–ytterbium glass laser,” Opt. Commun. 100, 311–321 (1993).
[CrossRef]

Taccheo, S.

S. Taccheo, P. Laporta, S. Longhi, and C. Svelto, “Experimental analysis and theoretical modeling of a diode-pumped Er:Yb:glass microchip laser,” Opt. Lett. 20, 889–891 (1995).
[CrossRef] [PubMed]

P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Analysis and modeling of the erbium–ytterbium glass laser,” Opt. Commun. 100, 311–321 (1993).
[CrossRef]

Appl. Opt. (2)

IEEE J. Quantum Electron. (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]

T. Y. Fan, “Optimizing the efficiency and stored energy in quasi-three-level lasers,” IEEE J. Quantum Electron. 28, 2692–2697 (1992).
[CrossRef]

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

J. Mod. Opt. (1)

G. Harkness and W. J. Firth, “Transverse modes of microchip solid-state lasers,” J. Mod. Opt. 39, 2023 (1992).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (4)

C. Paré, “Optimum laser beam profile for maximum energy extraction from a saturable amplifier,” Opt. Commun. 123, 762–776 (1996).
[CrossRef]

P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Analysis and modeling of the erbium–ytterbium glass laser,” Opt. Commun. 100, 311–321 (1993).
[CrossRef]

P. Peterson, A. Gavrielides, and P. M. Sharma, “CW theory of a laser diode-pumped two-manifold solid-state laser,” Opt. Commun. 109, 282–287 (1994).
[CrossRef]

F. Sanchez and A. Chardon, “Pump size optimization in microchip lasers,” Opt. Commun. 136, 405–409 (1997).
[CrossRef]

Opt. Lett. (2)

Opt. Quantum Electron. (1)

W. F. Krupke and L. L. Chase, “Ground-state depleted solid-state lasers: principles, characteristics and scaling,” Opt. Quantum Electron. 22, S1–S22 (1990).
[CrossRef]

Proc. SPIE (1)

Z. Cai, A. Chardon, F. Sanchez, and G. Stephan, “Investigation of absorption saturation in diode end-pumped microchip lasers,” Proc. SPIE 2889, 70–78 (1996).
[CrossRef]

Other (1)

A. Chardon, Ph.D. dissertation (Université de Rennes 1, France, 1996).

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Figures (5)

Fig. 1
Fig. 1

Evolution of the absorbed pump power versus I p sat / I p 0 .

Fig. 2
Fig. 2

Evolution of the normalized threshold versus the ratio of the pump to the laser beam widths: solid curve, with pump saturation; dashed curve, without pump saturation.

Fig. 3
Fig. 3

Evolution of the normalized laser efficiency as a function of the pump to the laser radius ratio: solid curve, with pump saturation; dashed curve, without pump saturation.

Fig. 4
Fig. 4

Evolution of the optimum value of ρ for maximum output power as a function of the normalized incident pump power.

Fig. 5
Fig. 5

Evolution of the normalized output power and of the normalized transmitted pump power versus z / z R : (a) ρ 0 = 0.1 and (b) ρ 0 = 0.25 . The other parameters are P ¯ 0 = 0.5 and XY = 0.05 .

Equations (22)

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E p z - i 2 k   2 E p = - 1 2   α p E p 1 + | E p | 2 / I p sat ,
d P p d z = -   α p | E p | 2 1 + | E p | 2 / I p sat   d S ,
P abs = l α p | E p ( r ) | 2 1 + | E p ( r ) | 2 / I p sat   d S .
P abs = α 0 I p ( r ) 1 + I p ( r ) / I p sat   d S .
I p ( r ) = I p 0   exp - r 2 w p 2 ,
P abs = α 0 P 0   I p sat I p 0   Ln 1 + I p 0 I p sat .
g 0 ( r ) = κ   I abs ( r ) I l sat ,
I abs ( r ) = P abs   1 π w p 2   exp - r 2 w p 2 = P abs f ( r ) .
I l ( r ) = I 0   exp - r 2 w l 2 = I 0 h ( r ) ,
g 0 ( r ) I l ( r ) 1 + 2 I l ( r ) / I l sat   d S = γ I l ( r ) d S ,
P th = π w l 2 I p sat ρ 2 exp XY 1 + 1 ρ 2 - 1 ,
X = γ κ α 0 , Y = I l sat I p sat , ρ = w p w l .
P th = π w l 2 I p sat XY ( 1 + ρ 2 ) .
η = d P out d P 0 .
P out = T I l ( r ) d S ,
η = T   d I 0 d P 0   h ( r ) d S .
η = T 2   d P abs d P 0 th   I l sat P abs th   f ( r ) h ( r ) d S h ( r ) d S f ( r ) h 2 ( r ) d S .
η = η max   exp - XY 1 + 1 ρ 2   1 + 2 ρ 2 ( 1 + ρ 2 ) 2 ,
η = η max   1 + 2 ρ 2 ( 1 + ρ 2 ) 2 .
P out = η ( P 0 - P 0 th ) .
P ¯ out = exp - XY 1 + 1 ρ 2   1 + 2 ρ 2 ( 1 + ρ 2 ) 2 × P ¯ 0 - ρ 2 exp XY 1 + 1 ρ 2 - 1 ,
w p = w p 0 1 + ( z / z R ) 2 ,

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