Abstract

We present a general formula fitted for computing the amplification and laser output power in a Yb-doped material under various quasi-end-pumping configurations. These configurations include single pass pumping, backreflection pumping in which the pump is reflected by a mirror set on the rear face of the amplifier medium, contrapropagation pumping where two pump beams are launched on both sides of the amplifier and, for every configuration, regenerative pumping in which the transmitted or reflected pump beam is recycled using the proper apparatus. We show that, with regenerative pumping, the efficiency is drastically improved and the optimum amplifier length leading to the maximum laser output power is shorter compared with the one obtained with conventional pumping. In this model, we do not take temperature effect into account.

© 2006 Optical Society of America

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References

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  1. G. L. Bourdet, "Theoretical investigations of quasi-three level longitudinally pumped cw laser," Appl. Opt. 39, 966-971 (2000).
    [CrossRef]
  2. W. W. Rigrod, "Gain saturation and output power of optical masers," J. Appl. Phys. 34, 2602-2609 (1963).
    [CrossRef]
  3. U. Brauch, A. Giesen, M. Karszewski, C. Stewen, and A. Voss, "Multiwatt diode-pumped Yb:YAG thin disk laser continuously tunable between 1018 and 1053 nm," Opt. Lett. 20, 713-715 (1995).
    [CrossRef] [PubMed]
  4. K. Contag, M. Karszewsky, C. Stewen, A. Giesen, and H. Hügel, "Theoretical modelling and experimental investigations of the diode-pumped thin-disc Yb:YAG laser," Quantum Electron. 29, 697-703 (1999).
    [CrossRef]
  5. C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hügel, "A 1-kW CW thin disc laser," IEEE J. Sel. Top. Quantum Electron. 6, 650-657 (2000).
    [CrossRef]
  6. S. Forget, F. Balembois, P. Georges, and P.-J. Devilder, "A new 3D multipass amplifier based on Nd:YAG or Nd:YVO4 crystals," Appl. Phys. B 75, 481-485 (2002).
    [CrossRef]
  7. A. Starodoumov, "Optical coupling arrangement," U.S. patent 2004/0196537 Al (7 October 2004).

2002

S. Forget, F. Balembois, P. Georges, and P.-J. Devilder, "A new 3D multipass amplifier based on Nd:YAG or Nd:YVO4 crystals," Appl. Phys. B 75, 481-485 (2002).
[CrossRef]

2000

C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hügel, "A 1-kW CW thin disc laser," IEEE J. Sel. Top. Quantum Electron. 6, 650-657 (2000).
[CrossRef]

G. L. Bourdet, "Theoretical investigations of quasi-three level longitudinally pumped cw laser," Appl. Opt. 39, 966-971 (2000).
[CrossRef]

1999

K. Contag, M. Karszewsky, C. Stewen, A. Giesen, and H. Hügel, "Theoretical modelling and experimental investigations of the diode-pumped thin-disc Yb:YAG laser," Quantum Electron. 29, 697-703 (1999).
[CrossRef]

1995

1963

W. W. Rigrod, "Gain saturation and output power of optical masers," J. Appl. Phys. 34, 2602-2609 (1963).
[CrossRef]

Balembois, F.

S. Forget, F. Balembois, P. Georges, and P.-J. Devilder, "A new 3D multipass amplifier based on Nd:YAG or Nd:YVO4 crystals," Appl. Phys. B 75, 481-485 (2002).
[CrossRef]

Bourdet, G. L.

Brauch, U.

Contag, K.

C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hügel, "A 1-kW CW thin disc laser," IEEE J. Sel. Top. Quantum Electron. 6, 650-657 (2000).
[CrossRef]

K. Contag, M. Karszewsky, C. Stewen, A. Giesen, and H. Hügel, "Theoretical modelling and experimental investigations of the diode-pumped thin-disc Yb:YAG laser," Quantum Electron. 29, 697-703 (1999).
[CrossRef]

Devilder, P.-J.

S. Forget, F. Balembois, P. Georges, and P.-J. Devilder, "A new 3D multipass amplifier based on Nd:YAG or Nd:YVO4 crystals," Appl. Phys. B 75, 481-485 (2002).
[CrossRef]

Forget, S.

S. Forget, F. Balembois, P. Georges, and P.-J. Devilder, "A new 3D multipass amplifier based on Nd:YAG or Nd:YVO4 crystals," Appl. Phys. B 75, 481-485 (2002).
[CrossRef]

Georges, P.

S. Forget, F. Balembois, P. Georges, and P.-J. Devilder, "A new 3D multipass amplifier based on Nd:YAG or Nd:YVO4 crystals," Appl. Phys. B 75, 481-485 (2002).
[CrossRef]

Giesen, A.

C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hügel, "A 1-kW CW thin disc laser," IEEE J. Sel. Top. Quantum Electron. 6, 650-657 (2000).
[CrossRef]

K. Contag, M. Karszewsky, C. Stewen, A. Giesen, and H. Hügel, "Theoretical modelling and experimental investigations of the diode-pumped thin-disc Yb:YAG laser," Quantum Electron. 29, 697-703 (1999).
[CrossRef]

U. Brauch, A. Giesen, M. Karszewski, C. Stewen, and A. Voss, "Multiwatt diode-pumped Yb:YAG thin disk laser continuously tunable between 1018 and 1053 nm," Opt. Lett. 20, 713-715 (1995).
[CrossRef] [PubMed]

Hügel, H.

C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hügel, "A 1-kW CW thin disc laser," IEEE J. Sel. Top. Quantum Electron. 6, 650-657 (2000).
[CrossRef]

K. Contag, M. Karszewsky, C. Stewen, A. Giesen, and H. Hügel, "Theoretical modelling and experimental investigations of the diode-pumped thin-disc Yb:YAG laser," Quantum Electron. 29, 697-703 (1999).
[CrossRef]

Karszewski, M.

Karszewsky, M.

K. Contag, M. Karszewsky, C. Stewen, A. Giesen, and H. Hügel, "Theoretical modelling and experimental investigations of the diode-pumped thin-disc Yb:YAG laser," Quantum Electron. 29, 697-703 (1999).
[CrossRef]

Larionov, M.

C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hügel, "A 1-kW CW thin disc laser," IEEE J. Sel. Top. Quantum Electron. 6, 650-657 (2000).
[CrossRef]

Rigrod, W. W.

W. W. Rigrod, "Gain saturation and output power of optical masers," J. Appl. Phys. 34, 2602-2609 (1963).
[CrossRef]

Starodoumov, A.

A. Starodoumov, "Optical coupling arrangement," U.S. patent 2004/0196537 Al (7 October 2004).

Stewen, C.

C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hügel, "A 1-kW CW thin disc laser," IEEE J. Sel. Top. Quantum Electron. 6, 650-657 (2000).
[CrossRef]

K. Contag, M. Karszewsky, C. Stewen, A. Giesen, and H. Hügel, "Theoretical modelling and experimental investigations of the diode-pumped thin-disc Yb:YAG laser," Quantum Electron. 29, 697-703 (1999).
[CrossRef]

U. Brauch, A. Giesen, M. Karszewski, C. Stewen, and A. Voss, "Multiwatt diode-pumped Yb:YAG thin disk laser continuously tunable between 1018 and 1053 nm," Opt. Lett. 20, 713-715 (1995).
[CrossRef] [PubMed]

Voss, A.

Appl. Opt.

Appl. Phys. B

S. Forget, F. Balembois, P. Georges, and P.-J. Devilder, "A new 3D multipass amplifier based on Nd:YAG or Nd:YVO4 crystals," Appl. Phys. B 75, 481-485 (2002).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hügel, "A 1-kW CW thin disc laser," IEEE J. Sel. Top. Quantum Electron. 6, 650-657 (2000).
[CrossRef]

J. Appl. Phys.

W. W. Rigrod, "Gain saturation and output power of optical masers," J. Appl. Phys. 34, 2602-2609 (1963).
[CrossRef]

Opt. Lett.

Quantum Electron.

K. Contag, M. Karszewsky, C. Stewen, A. Giesen, and H. Hügel, "Theoretical modelling and experimental investigations of the diode-pumped thin-disc Yb:YAG laser," Quantum Electron. 29, 697-703 (1999).
[CrossRef]

Other

A. Starodoumov, "Optical coupling arrangement," U.S. patent 2004/0196537 Al (7 October 2004).

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Figures (15)

Fig. 1
Fig. 1

Pumping schemes: (a) Single pass pumping, (b) contrapropagating pumping, and (c) backreflection pumping.

Fig. 2
Fig. 2

Amplifier and relevant notations.

Fig. 3
Fig. 3

Laser scheme and relevant notations.

Fig. 4
Fig. 4

(a) SPRP, (b) BRRP.

Fig. 5
Fig. 5

Output intensity normalized to the saturation intensity versus coupling mirror reflectivity for the four pumping schemes investigated ( I p0 = 10 kW / cm 2 , γ = 85 % ).

Fig. 6
Fig. 6

Optimal crystal length.

Fig. 7
Fig. 7

Efficiency.

Fig. 8
Fig. 8

Fraction of pump energy stored in the amplifier versus the transmission of the amplifier for a recycling loop of 85%.

Fig. 9
Fig. 9

Fraction of pump energy stored in the amplifier versus recycling loop transmission for the 10 kW∕cm2 pump intensity.

Fig. 10
Fig. 10

Optimal length versus recycling loop transmission for the 10 kW / cm 2 pump intensity.

Fig. 11
Fig. 11

Efficiency versus recycling loop transmission for the 10 kW / cm 2 pump intensity.

Fig. 12
Fig. 12

Fraction of pump energy stored in the amplifier versus pump intensity for γ = 85 % .

Fig. 13
Fig. 13

Efficiency and optimum length versus pump intensity for γ = 85 % .

Fig. 14
Fig. 14

Ratio of the efficiencies for the BRRP and BRP configurations versus the injected pump intensity ( γ = 85 % ) .

Fig. 15
Fig. 15

Optimal length for the BRRP and BRP configurations versus the injected pump intensity ( γ = 85 % ) .

Tables (4)

Tables Icon

Table 1 Amplifier Formula

Tables Icon

Table 3 Optimum Length

Tables Icon

Table 4 Amplifier and Cavity Parameters

Equations (41)

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α 0 = σ p N Yb ( f l 1 + f u j ) ,
g 0 = σ l N Yb ( f l k + f u 1 ) ,
f p = f l 1 f l 1 + f u j , f l = f l k f l k + f u 1 ,
d I l ε I l ε = ε g 0 { X u f l } d z ,
d I p ε I p ε = ε α 0 { f p X u } d z ,
I sat p = h ν p ( f l 1 + f u j ) τ u σ p , I sat l = h ν l ( f l k + f u 1 ) τ u σ l ,
I p + ( z ) I p ( z ) = C p , I l + ( z ) I l ( z ) = C l .
C p = I p + ( 0 ) I p ( 0 ) = I p + ( L ) I p ( L ) ,
C l = I l + ( 0 ) I l ( 0 ) = I l + ( L ) I l ( L ) .
ε g 0 d I l ε I l ε = ε α 0 d I p ε I p ε + ( f p f l ) d z ,
I l ε ( z ) = C ε ε { I p ε ( z ) } ε ε ( g 0 / α 0 ) exp { ε g 0 ( f p f l ) z } .
Γ = I p ( 0 ) I p ( L ) = I p + ( L ) I p + ( 0 ) , G = I l ( 0 ) I l ( L ) = I l + ( L ) I l + ( 0 ) ,
Γ = G α 0 / g 0 exp ( α 0 ( f p f l ) L ) .
I p ( f p X u ) X u I l ( X u f l ) = 0.
I i = I i + + I i , i = p , l .
X u = f p I p + f l I l 1 + I p + I l .
X u = f l , I p min = f l f p f l .
d I p ε I p ε = ε α 0 f p + I l ( f p f l ) 1 + I p + I l  d z ,
d I l ε I l ε = ε g 0 I p ( f p f l ) f l 1 + I p + I l  d z .
1 ε g 0 d I l ε I l ε ( f p + ( I l + + I l ) ( f p f l ) ) = 1 ε α 0 d I p ε I p ε ( ( I p + + I p ) × ( f p f l ) f l ) .
1 g 0 ( ε f p l n I l ε + ( I l ε C l I l ε ) ( f p f l ) ) = 1 α 0 ( ε f l l n I p ε ( I p ε C p I p ε ) × ( f p f l ) ) + C l .
I l ( 0 ) = g 0 { I p + ( 0 ) ( 1 Γ ) α 0 f l L } l n G G 1 .
I l ( L ) = g 0 { I p + ( 0 ) ( 1 Γ ) α 0 f l L } l n G ( G 1 ) ( 1 + R m l G ) .
I l ( L ) = g 0 { I p + ( 0 ) ( 1 Γ ) ( 1 + R m p Γ ) α 0 f l L } l n G ( G 1 ) ( 1 + R m l G ) .
I l ( L ) = g 0 { 2 I p + ( 0 ) ( 1 Γ ) α 0 f l L } l n G ( G 1 ) ( 1 + R m l G ) .
I l ( L ) = g 0 { I p + ( 0 ) B ( Γ ) α 0 f l L } l n G ( G 1 ) ( 1 + R m l G ) ,
G 2 R m l R s l = 1 , Γ = exp { α 0 [ l n ( R m l R s l ) 2 g 0 + ( f p f l ) L ] } .
I las = ( 1 R s ) R m g 0 ( I p + ( 0 ) ( 1 Γ ) α 0 f l L ) + l n R m R s ( 1 R m R s ) ( R m + R s ) .
I las = ( 1 R s l ) R m l × g 0 ( I p + ( 0 ) ( 1 Γ ) ( 1 + R m p Γ ) α 0 f l L ) + l n R m l R s l ( 1 R m l R s l ) ( R m l + R s l ) .
I las = ( 1 R s l ) R m l × g 0 ( 2 I p + ( 0 ) ( 1 Γ ) α 0 f l L ) + l n R m l R s l ( 1 R m l R s l ) ( R m l + R s l ) .
I las = A [ g 0 ( I p + ( 0 ) B α 0 f l L ) + l n R m l R s l ] .
β = I p min I p + ( 0 ) , I p min = f l f p f l .
d I las d L = 0 , d d L ( B ( Γ ) I p ( 0 ) α 0 f l L ) = I p ( 0 ) α 0 d B ( Γ ) d Γ d Γ d L f l = 0,
d Γ d L = α 0 ( f p f l ) Γ , Γ d B ( Γ ) d Γ = f l f p f l 1 I p + = I p min I p + ( 0 ) = β .
Γ opt = exp ( α 0 [ l n ( R m l R s l ) 2 g 0 + ( f p f l ) ] L opt ) ,
L opt = l n [ R m l R s l 1 / g 0 Γ opt 1 / α 0 ] f p f l .
Δ = ( 1 R m p ) 2 + 8 R m p f l I p + ( 0 ) ( f p f l ) = ( 1 R m p ) 2 + 8 R m p β .
I p ( 0 ) = I p ( 0 ) { 1 + γ Γ + ( γ Γ ) 2 + ( γ Γ ) 3 + } = I p ( 0 ) 1 γ Γ ,
B SPRP ( Γ ) = 1 Γ 1 γ Γ , B BRRP ( Γ ) = ( 1 Γ ) ( 1 + R m p Γ ) 1 γ R m p Γ 2 .
γ 2 Γ opt 2 ( 2 γ + 1 γ β ) Γ opt + 1 = 0, Γ opt = 1 + 2 γ β 1 γ 1 + 4 γ β 1 γ 2 γ 2 β 1 γ .
( 1 γ R m p Γ opt 2 ) R m p ( 1 Γ opt ) ( 1 + R m p Γ opt ) + 2 γ R m p Γ opt ( 1 Γ opt ) ( 1 + R m p Γ opt ) ( 1 γ R m p Γ opt 2 ) 2 Γ o p t = β .

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