Abstract

A four-level, plane wave model is proposed for a resonantly pumped 1.6μm Er3+ laser, including the effect of upconversion. A mean population approximation leads to analytical expressions for the threshold and slope efficiency that are highly accurate compared to the numerical solution. Using the beam area as an adjustable parameter, the threshold and slope efficiency agree well with data obtained using a 1% Er:YAG crystal, pumped at 1470nm, lasing at 1617nm, in the range 0100°C. According to the model for this laser, the slope efficiency versus absorbed pump power is unaffected by upconversion, but the threshold is increased by a factor of 2–3. The results are important for choosing the optimum doping level and fiber or rod length.

© 2007 Optical Society of America

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References

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  1. K. Spariosu, V. Leyva, R. A. Reeder, and M. J. Klotz, "Efficient Er:YAG laser operating at 1645 and 1617 nm," IEEE J. Quantum Electron. 42, 182-186 (2006).
    [CrossRef]
  2. D. Y. Shen, J. K. Sahu, and W. A. Clarkson, "Highly efficient in-band pumped Er:YAG laser with 60 W of ouput at 1645 nm," Opt. Lett. 31, 754-756 (2006).
    [CrossRef] [PubMed]
  3. K. Spariosu, M. Birnbaum, and B. Viana, "Er3+:Y3Al5O12 laser dynamics: effects of upconversion," J. Opt. Soc. Am. B 11, 894-900 (1994).
    [CrossRef]
  4. T. Y. Fan, "Optimizing the efficiency and stored energy in quasi-three-level lasers," IEEE J. Quantum Electron. 28, 2692-2697 (1992).
    [CrossRef]
  5. R. J. Beach, "CW theory of quasi-three level end-pumped laser oscillators," Opt. Commun. 123, 385-393 (1996).
    [CrossRef]
  6. D. K. Sardar, W. M. Bradley, J. J. Perez, J. B. Gruber, B. Zandi, J. A. Hutchinson, C. W. Trussell, and M. R. Kokta, "Judd-Ofelt analysis of the Er3+(4f11) absorption intensities in Er3+-doped garnets," J. Appl. Phys. 93, 2602-2607 (2003).
    [CrossRef]
  7. D. K. Sardar, C. C. Russell III, J. B. Gruber, and T. H. Allik, "Absorption intensities and emission cross sections of principal intermanifold and inter-Stark transitions of Er3+(4f11) in polycrystalline ceramic garnet Y3Al5O12," J. Appl. Phys. 97, 123501 (2005).
    [CrossRef]
  8. S. Georgescu, V. Lupei, A. Lupei, V. I. Zhekov, T. M. Murina, and M. I. Studenikin, "Concentration effects on the up-conversion from the I13/24 level of Er3+ in YAG," Opt. Commun. 81, 186-192 (1991).
    [CrossRef]
  9. M. O. Iskandarov, A. A. Nikitichev, and A. I. Stepanov, "Quasi-two-level Er3+:Y3Al5O12 laser for the 1.6 μm range," J. Opt. Technol. 68, 885-888 (2001).
    [CrossRef]
  10. D. Garbuzov, I. Kudryashov, and M. Dubinskii, "Resonantly diode laser pumped 1.6-μm-erbium-doped yttrium aluminum garnet solid-state laser," Appl. Phys. Lett. 86, 131115 (2005).
    [CrossRef]
  11. D. Garbuzov, I. Kudryashov, and M. Dubinskii, "110 W(0.9 J) pulsed power from resonantly diode-laser-pumped 1.6-μm Er:YAG laser," Appl. Phys. Lett. 87, 121101 (2005).
    [CrossRef]

2006

K. Spariosu, V. Leyva, R. A. Reeder, and M. J. Klotz, "Efficient Er:YAG laser operating at 1645 and 1617 nm," IEEE J. Quantum Electron. 42, 182-186 (2006).
[CrossRef]

D. Y. Shen, J. K. Sahu, and W. A. Clarkson, "Highly efficient in-band pumped Er:YAG laser with 60 W of ouput at 1645 nm," Opt. Lett. 31, 754-756 (2006).
[CrossRef] [PubMed]

2005

D. K. Sardar, C. C. Russell III, J. B. Gruber, and T. H. Allik, "Absorption intensities and emission cross sections of principal intermanifold and inter-Stark transitions of Er3+(4f11) in polycrystalline ceramic garnet Y3Al5O12," J. Appl. Phys. 97, 123501 (2005).
[CrossRef]

D. Garbuzov, I. Kudryashov, and M. Dubinskii, "Resonantly diode laser pumped 1.6-μm-erbium-doped yttrium aluminum garnet solid-state laser," Appl. Phys. Lett. 86, 131115 (2005).
[CrossRef]

D. Garbuzov, I. Kudryashov, and M. Dubinskii, "110 W(0.9 J) pulsed power from resonantly diode-laser-pumped 1.6-μm Er:YAG laser," Appl. Phys. Lett. 87, 121101 (2005).
[CrossRef]

2003

D. K. Sardar, W. M. Bradley, J. J. Perez, J. B. Gruber, B. Zandi, J. A. Hutchinson, C. W. Trussell, and M. R. Kokta, "Judd-Ofelt analysis of the Er3+(4f11) absorption intensities in Er3+-doped garnets," J. Appl. Phys. 93, 2602-2607 (2003).
[CrossRef]

2001

1996

R. J. Beach, "CW theory of quasi-three level end-pumped laser oscillators," Opt. Commun. 123, 385-393 (1996).
[CrossRef]

1994

1992

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

1991

S. Georgescu, V. Lupei, A. Lupei, V. I. Zhekov, T. M. Murina, and M. I. Studenikin, "Concentration effects on the up-conversion from the I13/24 level of Er3+ in YAG," Opt. Commun. 81, 186-192 (1991).
[CrossRef]

Appl. Phys. Lett.

D. Garbuzov, I. Kudryashov, and M. Dubinskii, "Resonantly diode laser pumped 1.6-μm-erbium-doped yttrium aluminum garnet solid-state laser," Appl. Phys. Lett. 86, 131115 (2005).
[CrossRef]

D. Garbuzov, I. Kudryashov, and M. Dubinskii, "110 W(0.9 J) pulsed power from resonantly diode-laser-pumped 1.6-μm Er:YAG laser," Appl. Phys. Lett. 87, 121101 (2005).
[CrossRef]

IEEE J. Quantum Electron.

K. Spariosu, V. Leyva, R. A. Reeder, and M. J. Klotz, "Efficient Er:YAG laser operating at 1645 and 1617 nm," IEEE J. Quantum Electron. 42, 182-186 (2006).
[CrossRef]

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

J. Appl. Phys.

D. K. Sardar, W. M. Bradley, J. J. Perez, J. B. Gruber, B. Zandi, J. A. Hutchinson, C. W. Trussell, and M. R. Kokta, "Judd-Ofelt analysis of the Er3+(4f11) absorption intensities in Er3+-doped garnets," J. Appl. Phys. 93, 2602-2607 (2003).
[CrossRef]

D. K. Sardar, C. C. Russell III, J. B. Gruber, and T. H. Allik, "Absorption intensities and emission cross sections of principal intermanifold and inter-Stark transitions of Er3+(4f11) in polycrystalline ceramic garnet Y3Al5O12," J. Appl. Phys. 97, 123501 (2005).
[CrossRef]

J. Opt. Soc. Am. B

J. Opt. Technol.

Opt. Commun.

S. Georgescu, V. Lupei, A. Lupei, V. I. Zhekov, T. M. Murina, and M. I. Studenikin, "Concentration effects on the up-conversion from the I13/24 level of Er3+ in YAG," Opt. Commun. 81, 186-192 (1991).
[CrossRef]

R. J. Beach, "CW theory of quasi-three level end-pumped laser oscillators," Opt. Commun. 123, 385-393 (1996).
[CrossRef]

Opt. Lett.

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Figures (8)

Fig. 1
Fig. 1

Stark-split manifolds, in Er 3 + : YAG , which are involved in 1.6 μ m emission and upconversion.

Fig. 2
Fig. 2

Cavity geometry used in the model.

Fig. 3
Fig. 3

Threshold absorbed pump intensity and slope efficiency (with respect to absorbed pump) as a function of R 1 L at 0 ° C , for the parameters given in the text. (∘) are the experimental results. The MPA results are shown with lines for (⋯) C up = 0 , (—) 0.5 × 10 17 , and (---) 1.0 × 10 17 cm 3 s . (∎●▴) are the corresponding exact results. The model results for η abs are almost independent of C up , therefore the three lines and three sets of solid symbols overlap.

Fig. 4
Fig. 4

An attempt to fit the data with C up = 0 . (∘) are the experimental results. The MPA results are shown for (---) Λ = 0.07 and (—) Λ = 0.35 . (∎●) are the corresponding exact results.

Fig. 5
Fig. 5

Threshold and slope efficiency (with respect to incident pump) as a function of temperature, for R 1 L = 0.967 . Lines and symbols are the same as in Fig. 3.

Fig. 6
Fig. 6

Comparison of the exact solution and the MPA, for a laser operating at 4 × threshold, for the same parameters as in Fig. 3, with R 1 L = 0.9 and C up = 0.5 × 10 17 cm 3 s . For the top graphs, the lines indicate MPA results for light propagating in (—) + z and (---) z . The solid symbols (●) indicate the exact solution. For the bottom graphs, (엯) indicates the MPA values, (+) indicates the exact values, averaged over z.

Fig. 7
Fig. 7

Comparison of the exact solution and the MPA, for a laser operating at 4 × threshold, with the same parameters as Fig. 6, except l = 4 cm , or 8 α p . Lines and symbols are the same as in Fig. 6.

Fig. 8
Fig. 8

Threshold absorbed pump power and slope efficiency with respect to absorbed pump, as a function of Er atomic fraction, keeping the product of [Er] and length constant. The MPA results are shown with lines for (⋯) D up = 0 , (—) 5 × 10 16 , and (---) 1.0 × 10 15 cm 3 s . In the MPA, the slope efficiencies are nearly independent of D up , so the lines overlap. The exact results are shown by (∎●▴).

Tables (4)

Tables Icon

Table 1 Definition of Symbols

Tables Icon

Table 2 Radiative Decay Rates for Er:YAG at Room Temperature [6, 7]

Tables Icon

Table 3 Cross Sections for Er:YAG

Tables Icon

Table 4 Experimental Parameters Based on [10]

Equations (31)

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d N 1 d t = + I p σ p h ν p ( f e p N 2 f a p N 1 ) + I L σ L h ν L ( f e L N 2 f a L N 1 ) + N 2 W 21 + N 3 W 31 + N 4 W 41 + C up N 2 2 ,
d N 2 d t = I p σ p h ν p ( f e p N 2 f a p N 1 ) I L σ L h ν L ( f e L N 2 f a L N 1 ) N 2 W 21 + N 3 W 32 + N 4 W 42 2 C up N 2 2 ,
d N 3 d t = N 4 W 43 N 3 ( W 32 + W 31 ) ,
d N 4 d t = C up N 2 2 N 4 ( W 43 + W 42 + W 41 ) .
N Er = N 1 + N 2 + N 3 + N 4 .
d I L + d z = I L + σ L ( f e L N 2 f a L N 1 ) = α L I L + ,
d I L d z = I L σ L ( f e L N 2 f a L N 1 ) = α L I L ,
d I p + d z = I p + σ p ( f e p N 2 f a p N 1 ) = α p I p + ,
d I p d z = I p σ p ( f e p N 2 f a p N 1 ) = α p I p .
I L + ( 0 ) = R 2 L I L ( 0 ) and I L ( l ) = R 1 L I L + ( l ) ,
I p + ( 0 ) = ( 1 R 2 p ) I p , inc and I p ( l ) = R 1 p I p + ( l ) .
I p + ( l ) = I p + ( 0 ) γ p , where γ p = exp ( α p l ) , and α p = σ p ( f a p N ̂ 1 f e p N ̂ 2 ) ,
I L + ( l ) = I L + ( 0 ) γ L , where γ L = exp ( α L l ) , and α L = σ L ( f a L N ̂ 1 f e L N ̂ 2 ) .
0 = I p + ( 0 ) + I p ( l ) h ν p 1 γ p l I L + ( 0 ) + I L ( l ) h ν L 1 γ L l + N ̂ 2 W 21 + N ̂ 3 W 31 + N ̂ 4 W 41 + C up N ̂ 2 2 .
0 = I p + ( 0 ) + I p ( l ) h ν p 1 γ p l + I L + ( 0 ) + I L ( l ) h ν L 1 γ L l N ̂ 2 W 21 + N ̂ 3 W 32 + N ̂ 4 W 42 2 C up N ̂ 2 2 ,
0 = N ̂ 4 W 43 N ̂ 3 ( W 32 + W 31 ) ,
0 = C up N ̂ 2 2 N ̂ 4 ( W 43 + W 42 + W 41 ) ,
N Er = N ̂ 1 + N ̂ 2 + N ̂ 3 + N ̂ 4 .
( σ e L N ̂ 2 σ a L N ̂ 1 ) 2 l + ln ( R 1 L R 2 L ) = 0 .
N ̂ 2 2 ( σ a L C up ( W 3 + W 43 ) W 3 W 4 ) + N ̂ 2 ( σ e L + σ a L ) + ( ln R 1 L R 2 L ) 2 l σ a L N Er = 0 ,
N ̂ 3 = ( C up W 43 W 3 W 4 ) N ̂ 2 2 ,
N ̂ 4 = ( C up W 4 ) N ̂ 2 2 ,
N ̂ 1 = N Er N ̂ 2 N ̂ 2 2 C up ( W 3 + W 43 ) W 3 W 4 .
0 = I p + ( 0 ) h ν p 1 γ p l ( 1 + R 1 p γ p ) I L + ( 0 ) h ν L 1 γ L l ( 1 + R 1 L γ L ) + N ̂ 2 W 21 + N ̂ 3 W 31 + N ̂ 4 W 41 + C up N ̂ 2 2 ,
0 = I p + ( 0 ) h ν p 1 γ p l ( 1 + R 1 p γ p ) + I L + ( 0 ) h ν L 1 γ L l ( 1 + R 1 L γ L ) N ̂ 2 W 21 + N ̂ 3 W 32 + N ̂ 4 W 42 2 C up N ̂ 2 2 .
η int = d I L + ( 0 ) d I p + ( 0 ) = ν L ν p 1 γ p 1 γ L 1 + R 1 p γ p 1 + R 1 L γ L .
η abs = d I L , out d I p , abs = η int γ L ( 1 R 1 L ) ( 1 γ p ) ( 1 + R 1 p γ p ) = ν L ν p γ L 1 γ L 1 R 1 L 1 + R 1 L γ L .
η inc = d I L , out d I p , inc = η abs ( 1 γ p ) ( 1 + R 1 p γ p ) ( 1 R 2 p ) .
I p , abs th = h ν p l ( + N ̂ 2 W 21 + N ̂ 3 W 31 + N ̂ 4 W 41 + C up N ̂ 2 2 )
I p , abs th = h ν p l ( N ̂ 2 W 21 + N ̂ 3 W 32 + N ̂ 4 W 42 2 C up N ̂ 2 2 ) .
I p , inc th = I p , abs th ( 1 γ p ) ( 1 + R 1 p γ p ) ( 1 R 2 p ) .

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