## Computational model for operation of 2 µm co-doped Tm,Ho solid state lasers

Optics Express, Vol. 15, Issue 19, pp. 11903-11912 (2007)

http://dx.doi.org/10.1364/OE.15.011903

Acrobat PDF (205 KB)

### Abstract

A computational model for operation of co-doped Tm,Ho solid-state lasers is developed coupling (i) 8-level rate equations with (ii) TEM00 laser beam distribution, and (iii) complex heat dissipation model. Simulations done for Q-switched ≈0.1 J giant pulse generation by Tm,Ho:YLF laser show that ≈43 % of the 785 nm light diode side-pumped energy is directly transformed into the heat inside the crystal, whereas ≈45 % is the spontaneously emitted radiation from ^{3}F_{4}, ^{5}I_{7}, ^{3}H_{4} and ^{3}H_{5} levels. In water-cooled operation this radiation is absorbed inside the thermal boundary layer where the heat transfer is dominated by heat conduction. In high-power operation the resulting temperature increase is shown to lead to (i) significant decrease in giant pulse energy and (ii) thermal lensing.

© 2007 Optical Society of America

## 1. Introduction

## 2. Optics model

^{5}I

_{7}):

^{5}I

_{8}):

*n*

*(*

_{i}*t*,

**r**) are the level concentrations,

*p*

*are the probabilities of the optical transitions,*

_{ij}*τ*

*are the level lifetimes,*

_{i}*R*

*(*

_{p}*t*) is the pumping source,

*ϕ*(

*t*,

**r**) is the local laser photon density, σ

_{se}is the stimulated emission cross-section,

*f*

*(*

_{i}*t*,

**r**) are the Boltzmann level population factors and

*η*is the refractive index of the crystal.

17. B.M. Walsh, N.P. Barnes, M. Petros, J. Yu, and U.N. Singh, “Spectroscopy and modeling of solid state lanthanide lasers: Application to trivalent Tm^{3+} and Ho^{3+} in YLiF_{4} and LuLiF_{4},” J. Appl. Phys . **95**, 3255–3271 (2004). [CrossRef]

17. B.M. Walsh, N.P. Barnes, M. Petros, J. Yu, and U.N. Singh, “Spectroscopy and modeling of solid state lanthanide lasers: Application to trivalent Tm^{3+} and Ho^{3+} in YLiF_{4} and LuLiF_{4},” J. Appl. Phys . **95**, 3255–3271 (2004). [CrossRef]

6. J. Yu, U.N. Singh, N.P. Barnes, and M. Petros “125-mJ diode-pumped injection-seeded Ho:Tm:YLF laser,” Opt. Lett . **23**, 780–782 (1998). [CrossRef]

*ϕ*(

*t*,

**r**) is represented by the product of (i) the total number of photons inside the oscillator cavity, Φ

_{0}(

*t*), depending on

*t*and (ii) the normalized space distribution function,

*ϕ*

_{0}(

**r**). The resulting equation for Φ

_{0}(

*t*) is given by a differential equation including integration of the stimulated and spontaneous radiation over the crystal volume [17

17. B.M. Walsh, N.P. Barnes, M. Petros, J. Yu, and U.N. Singh, “Spectroscopy and modeling of solid state lanthanide lasers: Application to trivalent Tm^{3+} and Ho^{3+} in YLiF_{4} and LuLiF_{4},” J. Appl. Phys . **95**, 3255–3271 (2004). [CrossRef]

23. P. Černý and D. Burns, “Modeling and experimental investigation of a diode-pumped Tm:YAlO_{3} laser with *a*- and *b*-cut crystal orientations,” IEEE J. of selected topics in quantum electron . **11**, 674–681 (2005). [CrossRef]

*V*

*is the crystal volume, and*

_{cr}*ε*≈10

^{-7}-10

^{-8}is a factor taking into account the proportion of photons spontaneously emitted within the solid angle of the mirrors, and

*τ*

*is the cavity lifetime given by:*

_{c}*L*

_{opt}=

*L*

*+(*

_{cav}*η*-1)

*L*

*is the characteristic optical length,*

_{cr}*L*

*is the cavity length and*

_{cav}*L*

*is the crystal length;*

_{cr}*R*

*is the back mirror reflectance,*

_{l}*T*

*is the output mirror transmittance and*

_{out}*β*is the parameter used in our simulations for the optical loss associated with the active Q-switching:

*β*=0 for the open resonator and

*β*≫-ln

*R*

_{1}(1-

*T*

*) for the closed resonator. For the acousto-optic Q-switch, if the fraction of the main beam diffracted out of the resonator is 0.9,*

_{out}*β*=-ln(1-0.9)=2.3. We neglect here additional reflectance and scattering loss on crystal and Q-switch. However, these factors can also be included into the round trip optical loss in Eq. (10).

*L*

*≫*

_{cav}*L*

*and the spatial photon distribution inside the operating crystal can be described by TEM*

_{cr}_{00}fundamental mode as:

*w*

_{0}is the beam waist radius of TEM

_{00}mode defined by the resonator parameters.

^{2}) at the output mirror as:

*w**

_{0}is the modified beam radius outside the resonator (for instance, for the case of a TEM

_{00}Gaussian beam inside the confocal spherical resonator one has

*w**

_{0}=√2

*w*

_{0}at the output mirror).

*η*

*=(1-*

_{a}*ρ*)[1-exp(-2

*αd*)] is the absorption efficiency of pumping,

*ρ*is the reflection factor of the pumping radiation into laser material,

*Q*

*is the pumping pulse energy, Δ*

_{p}*t*

*is the pumping pulse duration and*

_{p}*η*

*is quantum efficiency.*

_{p}*T*

*=0.05 and*

_{out}*R*

*=0.98) with a 0.85 mm radius waist in the TEM*

_{l}_{00}laser beam distribution. The Q-switch is open after a 0.5 ms pumping period with a delay of 0.7 ms to ensure that the G-pulse generation starts after achieving the maximal possible gain. This delay is associated with the delay of excitation transfer from

^{3}H

_{4}to

^{3}F

_{4}, and finally towards the lasing

^{5}I

_{7}level [22

22. O.A. Louchev, Y. Urata, and S. Wada, “Numerical simulation and optimization of Q-switched 2 µm Tm,Ho:YLF laser,” Opt. Express **15**, 3940–3947 (2007). [CrossRef] [PubMed]

## 3. Thermal model

*k*

*is the Boltzmann constant,*

_{B}*g*

*is the degeneracy of the*

_{i}*i*-level, and

*T*(

*t*,

**r**) is the local temperature.

*E*

*is the energy difference between the*

_{i}*i*-manifold and the next lower manifold into which the electron makes the transition (Fig. 1) and

*τ*

*are the non-radiative times inversely proportional to the non-radiative transition probabilities.*

_{inr}12. D. Bruneau, S. Delmonte, and J. Pelon, “Modeling of Tm,Ho:YAG and Tm,Ho:YLF 2-µm lasers and calculation of extractable energies,” Appl. Opt . **37**, 8406–8419 (1998). [CrossRef]

^{3+}and Ho

^{3+}ions as:

*E*

*we introduce the energy difference between the*

_{i}*i*-manifold and the ground state Δ

*E**

*(Fig. 1), and then*

_{i}*τ*

*are the corresponding radiative times [17*

_{ir}^{3+} and Ho^{3+} in YLiF_{4} and LuLiF_{4},” J. Appl. Phys . **95**, 3255–3271 (2004). [CrossRef]

^{3}F

_{4}and

^{5}I

_{7}[12

12. D. Bruneau, S. Delmonte, and J. Pelon, “Modeling of Tm,Ho:YAG and Tm,Ho:YLF 2-µm lasers and calculation of extractable energies,” Appl. Opt . **37**, 8406–8419 (1998). [CrossRef]

^{3}H

_{5},

^{3}H

_{4},

^{5}I

_{5}and

^{5}I

_{6}, are implicitly included into the heat released inside the crystal [12

12. D. Bruneau, S. Delmonte, and J. Pelon, “Modeling of Tm,Ho:YAG and Tm,Ho:YLF 2-µm lasers and calculation of extractable energies,” Appl. Opt . **37**, 8406–8419 (1998). [CrossRef]

^{5}I

_{5}and

^{5}I

_{6}levels into the spontaneous emission loss is negligibly small, whereas the contribution of

^{3}H

_{4}and

^{3}H

_{5}appears to be quite significant, ≈0.1 and ≈0.4 J, respectively (see Fig. 3(b)). Adding these values to the heat release of ≈0.75 J gives ≈70 %, similar to the result from the 2-level model [12

**37**, 8406–8419 (1998). [CrossRef]

_{2}=1.93 µm,

*λ*

_{3}=4.32 µm,

*λ*

_{4}=2.46 µm and

*λ*

_{7}=2.07 µm. These wavelengths are within the transparency range of the crystal and are therefore able to leave the crystal. Fig. 3(b) shows the values of the total optical loss,

*E*

_{i}*n*

*/*

_{i}*τ*

*integrated over the crystal volume. These radiation fluxes leaving the crystal are absorbed by the water flow typically used for crystal cooling. The water absorption coefficients for these wavelengths are [26*

_{ir}26. D. M. Wieliczka, S. Weng, and M. R. Querry, “Wedge shaped cell for highly absorbent liquids: infrared optical constants of water,” Appl. Opt . **28**, 1714–1719 (1989). [CrossRef] [PubMed]

*α*

_{2}=124 cm

^{-1},

*α*

_{3}=300 cm

^{-1},

*α*

_{4}=63.5 cm

^{-1}and

*α*

_{7}=31 cm

^{-1}. That is, the spontaneously emitted fluxes leaving the crystal are absorbed within lengths of ≈

*α*

^{-1}

*, i.e. within 80, 33, 157 and 320 µm from the surface, respectively. The absorption of these fluxes in the vicinity of the crystal surface can significantly inhibit heat dissipation from the crystal. The heat transfer to the water flow depends on the Reynolds number,*

_{i}*Re*, defining the level of the flow turbulency dependent on the water flow rate through the channel inside which the operating crystal is set up. Numerical estimates show that for the typical coaxial crystal in a tube water channel geometry and typical flow rates, the value of the heat transfer coefficient is

*h*=10

^{3}-10

^{5}W/m

^{2}K [27]. The main thermal resistance to the heat flow from the crystal surface is due to the thermal boundary layer,

*δ*

*, within which the heat conductance dominates over the convective transport. The estimate of*

_{T}*δ*

*follows from the equivalency of -*

_{T}*k*

*∂*

_{cr}*T*

*/∂*

_{cr}*r*|

*=-*

_{sur}*k*

*∂*

_{w}*T*

*/∂*

_{w}*r*|

*=*

_{sur}*h*(

*T*

*|*

_{cr}*-*

_{sur}*T*

*), where*

_{w∞}*k*

_{cr}≈6 and

*k*

_{w}≈0.6 W/m K are the thermal conductivity of crystal and water, respectively. That is, using ∂

*T*

_{w}/∂

*r*|

*≈-(*

_{sur}*T*

*|*

_{cr}*-*

_{sur}*T*

*)/*

_{w∞}*δ*

*one finally obtains for*

_{T}*h*=10

^{3}-10

^{5}W/m

^{2}K:

*T*

*(*

_{cr}*t*,

**r**), and the thermal boundary layer in water,

*T*

*(*

_{w}*t*,

**r**), are defined by:

*i*=

*cr*) and water (

*i*=

*w*) with the boundary condition

*T*

*=*

_{w}*T*

*at*

_{w∞}*r*=

*R*

_{0}+

*δ*

*, where*

_{T}*δ*

*=*

_{T}*R*

_{0}[exp(

*k*

*/*

_{w}*R*

_{0}

*h*)-1] takes into account the radial curvature.

*J*

_{0i}(

*t*) are the IR flux densities isotropically leaving the crystal given by:

*h*>10

^{5}W/m

^{2}K and

*δ*

*<6 µm, when*

_{T}*δ*

*≪*

_{T}*α*

^{-1}

*. However, for*

_{i}*h*≈10

^{4}W/m

^{2}K (

*δ*

*≈60 µm) this effect is very significant, and can lead to the onset of an inverted temperature distribution inside the crystal when the temperature inside the boundary layer is higher than that inside the crystal. This effect is shown to take place in a coupled thermo-optical simulation performed using a conservative 50x100 conservative finite-difference approximation. The main results of this simulation given in Fig. 4 at three times show that a significant temperature increase has occured (≈2 K) by the start of G-pulse generation (1.2 ms), which leads to a pulse energy decrease due to the decrease in*

_{T}*f*

_{7}

*n*

_{7}-

*f*

_{8}

*n*

_{8}over the crystal volume. This figure also shows that an inverted temperature distribution inside the crystal is present at period of time of ≈10 ms.

## 4. Summary

^{3+}ions from LD pumped Tm

^{3+}ions integrated together with the equation for the total number of stimulated photons inside the cavity. This model is also coupled with a two-dimensional time dependent heat transfer model including absorption, heat release and heat transfer inside the operating crystal as well as the absorption and the thermal effect of infrared radiation fluxes spontaneously emitted by the operating crystal. In the case of water cooled laser operation the thermal effect is shown to be split into two simultaneously occurring processes: (i) direct heat release inside the crystal and (ii) infrared spontaneously emitted radiation fully absorbed in water over a distance of several hundreds of microns, which corresponds to a typical value of boundary layer thickness. In particular, the simulations show that only ≈43 % of the pumped energy is transformed into heat directly inside the crystal, whereas ≈45 % is IR radiation spontaneously emitted by

^{3}H

_{4},

^{3}H

_{5},

^{3}F

_{4}and

^{5}I

_{7}levels and absorbed in the vicinity of the crystal surface. The absorption taking place within the boundary layer provides an additional strong thermal effect, inhibiting the dissipation of the heat from the crystal and significantly increasing crystal temperature. The resulting temperature increase is shown to reduce significantly G-pulse energy.

## Acknowledgments

## References and links

1. | J.K. Tyminski, D.M. Franich, and M. Kokta “Gain dynamics of Tm,Ho:YAG pumped in near infrared,” J. Appl. Phys . |

2. | V.A. French, R.R. Petrin, R.C. Powell, and M. Kokta, “Energy-transfer processes in Y |

3. | R.R. Petrin, M.G. Jani, R.C. Powell, and M. Kokta, “Spectral dynamics of laser-pumped Y |

4. | M.G. Jani, R J. Reeves, R.C. Powell, G.J. Quarles, and L. Esterovitz, “Alexandrite-laser excitation of a Tm:Ho:Y |

5. | M. G. Jani, F. L. Naranjo, N. P. Barnes, K.E. Murray, and G.E. Lockard, “Diode-pumped long-pulse-length Ho:Tm:YLiF4 laser at 10 Hz,” Opt. Lett . |

6. | J. Yu, U.N. Singh, N.P. Barnes, and M. Petros “125-mJ diode-pumped injection-seeded Ho:Tm:YLF laser,” Opt. Lett . |

7. | A.N. Alpat’ev, V.A. Smirnov, and I.A. Shcherbakov, “Relaxation oscillations of the radiation from a 2-µm holmium laser with a Cr,Tm,Ho:YSGG crystal,” Quantum Electron . |

8. | I.F. Elder and M.J.P. Payne, “Lasing in diode-pumped Tm:YAP, Tm,Ho:YAP and Tm,Ho,YLF,” Opt. Commun . |

9. | N. P. Barnes, E. D. Filer, C. A. Morrison, and C. J. Lee, “Ho:Tm Lasers I: Theoretical,” IEEE J. Quantum Electron . |

10. | C. J. Lee, G. Han, and N.P. Barnes, “Ho:Tm Lasers II: Experiments,” IEEE J. Quantum Electron . |

11. | G. Rustad and K. Stenersen, “Modeling of laser-pumped Tm and Ho lasers accounting for upconversion and ground-state depletion,” IEEE J. Quantum Electron . |

12. | D. Bruneau, S. Delmonte, and J. Pelon, “Modeling of Tm,Ho:YAG and Tm,Ho:YLF 2-µm lasers and calculation of extractable energies,” Appl. Opt . |

13. | G. L. Bourdet and G. Lescroart, “Theoretical modeling and design of a Tm,Ho:YLiF |

14. | S. D. Jackson and T.A. King, “CW operation of a 1.064-µm pumped Tm-Ho-Doped silica fiber laser,” IEEE J. of Quantum Electron . |

15. | V. Sudesh and K. Asai, “Spectroscopic and diode-pumped-laser properties of Tm,Ho:YLF; Tm,Ho:LuLF; and Tm,Ho:LuAG crystals: a comparative study,” J. Opt. Soc. Am . |

16. | A. Sato, K. Asai, and K. Mizutani, “Lasing characteristics and optimizations of diode-side-pumped Tm,Ho:GdVO |

17. | B.M. Walsh, N.P. Barnes, M. Petros, J. Yu, and U.N. Singh, “Spectroscopy and modeling of solid state lanthanide lasers: Application to trivalent Tm |

18. | G. Galzerano, E. Sani, A. Toncelli, G. Della Valle, S. Taccheo, M. Tonelli, and P. Laporta, “Widely tunable continuous-wave diode-pumped 2-µm Tm-Ho:KYF |

19. | J. Izawa, H. Nakajima, H. Hara, and Y. Arimoto, “Comparison of lasing performance of Tm,Ho:YLF lasers by use of single and double cavities,” Appl. Opt . |

20. | J. Yu, B. C. Trieu, E. A. Modlin, U.N. Singh, M. J. Kavaya, S. Chen, Y. Bai, P. J. Petzar, and M. Petros, “1 J/pulse Q-switched 2 µm solid-state laser,” Opt. Lett . |

21. | X. Zhang, Y. Ju, and Y. Wang, “Theoretical and experimental investigation of actively Q-switched Tm,Ho:YLF lasers,” Opt. Express |

22. | O.A. Louchev, Y. Urata, and S. Wada, “Numerical simulation and optimization of Q-switched 2 µm Tm,Ho:YLF laser,” Opt. Express |

23. | P. Černý and D. Burns, “Modeling and experimental investigation of a diode-pumped Tm:YAlO |

24. | V.P. Risk, “Modeling of longitudinally pumped solid-state lasers exhibiting reabsorption losses,” J. Opt. Soc. Am . |

25. | D. Golla, M. Bode, S. Knoke, W. Schöne, and A. Tünnermann, “62-W cw TEM |

26. | D. M. Wieliczka, S. Weng, and M. R. Querry, “Wedge shaped cell for highly absorbent liquids: infrared optical constants of water,” Appl. Opt . |

27. | W. Koechner, |

**OCIS Codes**

(140.3480) Lasers and laser optics : Lasers, diode-pumped

(140.3540) Lasers and laser optics : Lasers, Q-switched

(140.3580) Lasers and laser optics : Lasers, solid-state

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: May 2, 2007

Revised Manuscript: July 26, 2007

Manuscript Accepted: July 26, 2007

Published: September 5, 2007

**Citation**

Oleg A. Louchev, Yoshiharu Urata, Norihito Saito, and Satoshi Wada, "Computational model for operation of 2 μm co-doped Tm,Ho solid state lasers," Opt. Express **15**, 11903-11912 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-19-11903

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### References

- J.K. Tyminski, D.M. Franich and M. Kokta, "Gain dynamics of Tm,Ho:YAG pumped in near infrared," J. Appl. Phys. 65, 3181-3188 (1989). [CrossRef]
- V.A. French, R.R. Petrin, R.C. Powell, and M. Kokta, "Energy-transfer processes in Y3Al5O12:Tm,Ho," Phys. Rev. B 46, 8018-8026 (1992).
- R.R. Petrin, M.G. Jani, R.C. Powell and M. Kokta, "Spectral dynamics of laser-pumped Y3Al5O12:Tm,Ho lasers," Opt. Mater. 1,111-124 (1992). [CrossRef]
- M.G. Jani, R J. Reeves, R.C. Powell, G.J. Quarles and L. Esterovitz, "Alexandrite-laser excitation of a Tm:Ho:Y3Al5O12 laser." J. Opt. Soc. Am. B 8, 741-746 (1991).
- M. G. Jani, F. L. Naranjo, N. P. Barnes, K.E. Murray, and G.E. Lockard, "Diode-pumped long-pulse-length Ho:Tm:YLiF4 laser at 10 Hz," Opt. Lett. 20, 872-874 (1995) [CrossRef] [PubMed]
- J. Yu, U.N. Singh, N.P. Barnes and M. Petros "125-mJ diode-pumped injection-seeded Ho:Tm:YLF laser," Opt. Lett. 23, 780-782 (1998). [CrossRef]
- A.N. Alpat'ev, V.A. Smirnov, I.A. Shcherbakov, "Relaxation oscillations of the radiation from a 2-μm holmium laser with a Cr,Tm,Ho:YSGG crystal," Quantum Electron. 28, 143-146 (1998). [CrossRef]
- I.F. Elder and M.J.P. Payne, "Lasing in diode-pumped Tm:YAP, Tm,Ho:YAP and Tm,Ho,YLF," Opt. Commun. 145, 329-339 (1995). [CrossRef]
- N. P. Barnes, E. D. Filer, C. A. Morrison and C. J. Lee, "Ho:Tm Lasers I: Theoretical," IEEE J. Quantum Electron. 32, 92-103 (1996). [CrossRef]
- C. J. Lee, G. Han and N.P. Barnes, "Ho:Tm Lasers II: Experiments," IEEE J. Quantum Electron. 32, 104-111 (1996). [CrossRef]
- G. Rustad and K. Stenersen, "Modeling of laser-pumped Tm and Ho lasers accounting for upconversion and ground-state depletion," IEEE J. Quantum Electron. 32, 1645 -1656 (1996). [CrossRef]
- D. Bruneau, S. Delmonte and J. Pelon, "Modeling of Tm,Ho:YAG and Tm,Ho:YLF 2-μm lasers and calculation of extractable energies," Appl. Opt. 37, 8406-8419 (1998). [CrossRef]
- G. L. Bourdet and G. Lescroart, "Theoretical modeling and design of a Tm,Ho:YLiF4 microchip laser," Appl. Opt. 38, 3275-3281 (1999). [CrossRef]
- S. D. Jackson and T.A. King, "CW operation of a 1.064-μm pumped Tm-Ho-Doped silica fiber laser," IEEE J. of Quantum Electron. 34,1578-1587 (1998). [CrossRef]
- V. Sudesh and K. Asai, "Spectroscopic and diode-pumped-laser properties of Tm,Ho:YLF; Tm,Ho:LuLF; and Tm,Ho:LuAG crystals: a comparative study," J. Opt. Soc. Am. B 20, 1829-1837 (2003).
- A. Sato, K. Asai and K. Mizutani, "Lasing characteristics and optimizations of diode-side-pumped Tm,Ho:GdVO4 laser," Opt. Lett. 29, 836 -838 (2004). [CrossRef] [PubMed]
- B.M. Walsh, N.P. Barnes, M. Petros, J. Yu and U.N. Singh, "Spectroscopy and modeling of solid state lanthanide lasers: Application to trivalent Tm3+ and Ho3+ in YLiF4 and LuLiF4," J. Appl. Phys. 95, 3255-3271 (2004). [CrossRef]
- G. Galzerano, E. Sani, A. Toncelli, G. Della Valle, S. Taccheo, M. Tonelli, P. Laporta, "Widely tunable continuous-wave diode-pumped 2-µm Tm-Ho:KYF4 laser," Opt. Lett. 29, 715-717 (2004). [CrossRef] [PubMed]
- J. Izawa, H. Nakajima, H. Hara, and Y. Arimoto, "Comparison of lasing performance of Tm,Ho:YLF lasers by use of single and double cavities," Appl. Opt. 39, 2418-2421 (2000). [CrossRef]
- J. Yu, B. C. Trieu, E. A. Modlin, U.N. Singh, M. J. Kavaya, S. Chen, Y. Bai, P. J. Petzar, and M. Petros, "1 J/pulse Q-switched 2 μm solid-state laser," Opt. Lett. 31, 462-464 (2006). [CrossRef] [PubMed]
- X. Zhang, Y. Ju and Y. Wang, "Theoretical and experimental investigation of actively Q-switched Tm,Ho:YLF lasers," Opt. Express 14, 7745-7750 (2006). [CrossRef] [PubMed]
- O.A. Louchev, Y. Urata, and S. Wada, "Numerical simulation and optimization of Q-switched 2 μm Tm,Ho:YLF laser," Opt. Express 15, 3940-3947 (2007). [CrossRef] [PubMed]
- P. Černý and D. Burns, "Modeling and experimental investigation of a diode-pumped Tm:YAlO3 laser with a- and b-cut crystal orientations," IEEE J. of selected topics in quantum electron. 11, 674-681 (2005). [CrossRef]
- V.P. Risk, "Modeling of longitudinally pumped solid-state lasers exhibiting reabsorption losses," J. Opt. Soc. Am. B 5, 1412-1423 (1988).
- D. Golla, M. Bode, S. Knoke, W. Schöne, and A. Tünnermann, "62-W cw TEM00 Nd:YAG laser side-pumped by fiber-coupled diode lasers," Opt. Lett. 21, 210-212 (1996). [CrossRef] [PubMed]
- D. M. Wieliczka, S. Weng, and M. R. Querry, "Wedge shaped cell for highly absorbent liquids: infrared optical constants of water," Appl. Opt. 28, 1714-1719 (1989). [CrossRef] [PubMed]
- W. Koechner, Solid -State Laser Engineering, 6th Edition (New-York, Springer, 2006).

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