## Optimization of end-pumped, actively Q-switched quasi-III-level lasers |

Optics Express, Vol. 19, Issue 17, pp. 15652-15668 (2011)

http://dx.doi.org/10.1364/OE.19.015652

Acrobat PDF (1186 KB)

### Abstract

The new model of end-pumped quasi-III-level laser considering transient pumping processes, ground-state-depletion and up-conversion effects was developed. The model consists of two parts: pumping stage and Q-switched part, which can be separated in a case of active Q-switching regime. For pumping stage the semi-analytical model was developed, enabling the calculations for final occupation of upper laser level for given pump power and duration, spatial profile of pump beam, length and dopant level of gain medium. For quasi-stationary inversion, the optimization procedure of Q-switching regime based on Lagrange multiplier technique was developed. The new approach for optimization of CW regime of quasi-three-level lasers was developed to optimize the Q-switched lasers operating with high repetition rates. Both methods of optimizations enable calculation of optimal absorbance of gain medium and output losses for given pump rate.

© 2011 OSA

## 1. Introduction

11. M. Eichhorn, “Quasi-three-level solid-state lasers in the near and mid infrared based on trivalent rare earth ions,” Appl. Phys. B **93**(2-3), 269–316 (2008). [CrossRef]

2. W. P. Risk, “Modeling of longitudinally pumped solid-state lasers exhibiting reabsorption losses,” J. Opt. Soc. Am. B **5**(7), 1412–1423 (1988). [CrossRef]

3. T. Y. Fan, “Optimizing the efficiency and stored energy in quasi-three-level lasers,” IEEE J. Quantum Electron. **28**(12), 2692–2697 (1992). [CrossRef]

3. T. Y. Fan, “Optimizing the efficiency and stored energy in quasi-three-level lasers,” IEEE J. Quantum Electron. **28**(12), 2692–2697 (1992). [CrossRef]

11. M. Eichhorn, “Quasi-three-level solid-state lasers in the near and mid infrared based on trivalent rare earth ions,” Appl. Phys. B **93**(2-3), 269–316 (2008). [CrossRef]

11. M. Eichhorn, “Quasi-three-level solid-state lasers in the near and mid infrared based on trivalent rare earth ions,” Appl. Phys. B **93**(2-3), 269–316 (2008). [CrossRef]

12. I. Kudryashov, D. Garbuzov, and M. Dubinskii, “Latest developments in resonantly diode-pumped Er:YAG lasers,” in *Laser Source Technology for Defence and Security* III, Proc. SPIE **6552**, 65520K (2007). [CrossRef]

13. B. M. Walsh, “Review of Tm and Ho Materials; Spectroscopy and Lasers,” Laser Phys. **19**(4), 855–866 (2009). [CrossRef]

15. J. Kwiatkowski, J. K. Jabczynski, Ł. Gorajek, W. Zendzian, H. Jelínková, J. Sulc, M. Nemec, and P. Koranda, “Resonantly pumped tunable Ho:YAG laser,” Laser Phys. Lett. **6**(7), 531–534 (2009). [CrossRef]

16. N. P. Barnes, K. E. Murray, and M. G. Jani, “Flash-lamp-pumped Ho:Tm:Cr:YAG and Ho:Tm:Er:YLF lasers: modeling of a single, long pulse length comparison,” Appl. Opt. **36**(15), 3363–3374 (1997). [CrossRef] [PubMed]

17. E. C. Honea, R. J. Beach, S. B. Sutton, J. A. Speth, S. C. Mitchell, J. A. Skidmore, M. A. Emanuel, and S. A. Payne, “115-W Tm:YAG diode-pumped solid-state laser,” IEEE J. Quantum Electron. **33**(9), 1592–1600 (1997). [CrossRef]

26. S. D. Jackson, “The spectroscopic and energy transfer characteristics of the rare earth ions used for silicate glass fibre lasers operating in the shortwave infrared,” Laser & Photon. Rev. **3**(5), 466–482 (2009). [CrossRef]

32. G. Rustad and K. Stenersen, “Modeling of laser-pumped Tm and Ho lasers accounting for up conversion and ground-state depletion,” IEEE J. Quantum Electron. **32**(9), 1645–1656 (1996). [CrossRef]

3. T. Y. Fan, “Optimizing the efficiency and stored energy in quasi-three-level lasers,” IEEE J. Quantum Electron. **28**(12), 2692–2697 (1992). [CrossRef]

4. C. D. Nabors, “Q-switched operation of quasi-three-level lasers,” IEEE J. Quantum Electron. **30**(12), 2896–2901(1994). [CrossRef]

29. J. M. Sousa, J. R. Salcedo, and V. V. Kuzmin, “Simulation of laser dynamics and active Q-switching in Tm,Ho:YAG and Tm:YAG lasers,” Appl. Phys. B **64**(1), 25–36 (1996). [CrossRef]

31. O. A. Louchev, Y. Urata, and S. Wada, “Numerical simulation and optimization of Q-switched 2 mum Tm,Ho:YLF laser,” Opt. Express **15**(7), 3940–3947 (2007). [CrossRef] [PubMed]

32. G. Rustad and K. Stenersen, “Modeling of laser-pumped Tm and Ho lasers accounting for up conversion and ground-state depletion,” IEEE J. Quantum Electron. **32**(9), 1645–1656 (1996). [CrossRef]

34. Y. F. Chen, Y. P. Lan, and S. C. Wang, “Modeling of diode-end-pumped Q-switched solid-state lasers: influence of energy-transfer upconversion,” J. Opt. Soc. Am. B **19**(7), 1558–1563 (2002). [CrossRef]

35. J. Degnan, “Theory of the optimally coupled Q-switched laser,” IEEE J. Quantum Electron. **25**(2), 214–220 (1989). [CrossRef]

## 2. Pumping stage

**93**(2-3), 269–316 (2008). [CrossRef]

36. T. Y. Fan, “Aperture guiding in quasi-three-level lasers,” Opt. Lett. **19**(8), 554–556 (1994). [CrossRef] [PubMed]

*S*

_{0}is equal to the pump beam area averaged over gain medium.

5. R. J. Beach, “CW Theory of quasi-three level end-pumped laser oscillators,” Opt. Commun. **123**(1-3), 385–393 (1996). [CrossRef]

7. G. L. Bourdet, “Theoretical investigation of quasi-three-level longitudinally pumped continuous wave lasers,” Appl. Opt. **39**(6), 966–971 (2000). [CrossRef] [PubMed]

**93**(2-3), 269–316 (2008). [CrossRef]

32. G. Rustad and K. Stenersen, “Modeling of laser-pumped Tm and Ho lasers accounting for up conversion and ground-state depletion,” IEEE J. Quantum Electron. **32**(9), 1645–1656 (1996). [CrossRef]

34. Y. F. Chen, Y. P. Lan, and S. C. Wang, “Modeling of diode-end-pumped Q-switched solid-state lasers: influence of energy-transfer upconversion,” J. Opt. Soc. Am. B **19**(7), 1558–1563 (2002). [CrossRef]

*z*in the crystal and time

*t*. We neglect here transverse spatial distribution of pump beam and operate with averaged across beam pump densities

*I*

_{p}(

*z,t*) and population of upper 2-nd level

*N*

_{2}(

*z,t*). After some transformations, problem can be defined as follows:where:

^{( + )}forward,

^{(-)}backward directions,

*N*− population of 2-nd upper laser level,

_{2}*k*

_{etu}− coefficient of ETU [32

**32**(9), 1645–1656 (1996). [CrossRef]

34. Y. F. Chen, Y. P. Lan, and S. C. Wang, “Modeling of diode-end-pumped Q-switched solid-state lasers: influence of energy-transfer upconversion,” J. Opt. Soc. Am. B **19**(7), 1558–1563 (2002). [CrossRef]

*τ*− lifetime of upper laser level. The information about structure of QTL medium is contained in un-dimensional parameters:

*A, γ*(see details [20

_{p}20. G. L. Bourdet and G. Lescroart, “Theoretical modeling and design of a Tm:YVO_{4} microchip lasers,” Opt. Commun. **149**(4-6), 404–414 (1998). [CrossRef]

*γ*= 1 and

_{p}*A*is the measure of quantum efficiency (including for example cross-relaxation) of pumping process between

*A*=

*f*

_{a}’,

*f*

_{a}’,

*f*

_{b}’ are fractional occupations of (

_{a}’) lower and (

_{b}’) upper levels of pumping process (see e.g [5

5. R. J. Beach, “CW Theory of quasi-three level end-pumped laser oscillators,” Opt. Commun. **123**(1-3), 385–393 (1996). [CrossRef]

8. G. L. Bourdet, “New evaluation of ytterbium-doped materials for CW laser applications,” Opt. Commun. **198**(4-6), 411–417 (2001). [CrossRef]

9. C. Lim and Y. Izawa, “Modeling of end-pumped CW quasi-three-level lasers,” IEEE J. Quantum Electron. **38**(3), 306–311 (2002). [CrossRef]

*R*

_{2}– pumping rate into 2-nd upper level defined as follows:where:

*h*– Planck constant,

*ν*

_{p}=

*c*/

*λ*

_{p}– frequency of pump wave,

*c*– light speed,

*λ*

_{p}– pump wavelength. Let us introduce the un-dimensional variables

*t’*,

*ζ*and functions

*x*

_{2},

*α*

_{0}– absorption coefficient,

*I*

_{p,sat}– saturation density for pump wavelength defined for indirect and direct pumping as follows:

*a*

_{0}) where

*a*

_{0}= α

_{p}

*l*

_{0}–absorbance of gain medium. Let us notice that:

*y*

_{2}averaged relative population of 2-nd laser level as follows:where:

*y*

_{2}– averaged relative population of 2-nd laser level defined as follows:

*r*(

_{p}*y*) is the relative averaged pump rate. Let us consider two cases:

_{2}*i)*pumping from 1 (left) end of rod with

*R*

_{p}≥ 0 – reflection coefficient of the latter one,

*ii)*pumping from both ends with

*R*

_{p}= 0.

*i*

_{p,0}– relative pump density,

*η*

_{0}(

*x*) – initial absorption efficiency defined as follows:

*P*–pump power,

_{0}*S*– averaged area of pump beam.

_{p}### 2.1. Semi-analytical solution of pumping equation

*t’*,

*y*

_{2}increases, causing depletion of ground state and decrease in pump rate

*r*(

_{p}*y*). The 1-st order differential Eq. (8) does not have analytical solution for function

_{2}*r*(

_{p}*y*). However, for constant coefficients, it is the nonlinear differential equation of Ricatti type [37] and has the following analytical solution:

_{2}*y*

_{2,0}=

*y*

_{2}(

*t*

_{0}’) – initial value of

*y*

_{2}for time

*t*

_{0}’ ; Δ

*t*’ =

*t*’-

*t*

_{0}’,

*y*

_{2,0}= 0) we obtain the following formula on

*y*

_{2,h}(Δ

*t’*):which is basically the same as in [32

**32**(9), 1645–1656 (1996). [CrossRef]

*t’*and

*p*

_{0}, because it leads to contradiction (unlimited increase in

*y*

_{2}) as a result of lack of ground state depletion causing decrease in pump rate. Nevertheless, both formulae can be applied for a case of small

*y*

_{2}<< 1. To overcome these limitations, we have proposed the semi-analytical procedure consisting in application of exact analytical formula (12) for small interval Δ

*t’*<< 1 in a 1-st step of calculation, and applying to the following steps of procedure the value of

*y*

_{2}(Δ

*t’*), obtained in previous step as the initial condition. Such simple procedure describes the pumping of gain medium considering ground state depletion and nonlinear relaxation effects defined by ETU parameter for a wide class of practical cases. The examples of calculations of

*y*

_{2}in dependence on relative time

*t*’ for different relative pump density

*i*

_{p0}and

*k*– up-conversion parameters are shown in Fig. 2 .

*y*

_{2,st}. In such a case pump rate is balanced by linear and nonlinear (via ETU effects) relaxation. The value of

*y*

_{2,st}can be determined as a solution of transcendent equation:

*y*

_{2,st}determines the maximal inversion, gain and stored energy for given set of pumping parameters.

## 3. Analytical model of Q-switching regime for QTL laser

*τ*, the high loss of a cavity is immediately switched off to low value, enabling the giant pulse formation. For analysis of such a case, let us start from the modified for QTL medium averaged rate equation set:

*f*– are fractional occupations of (

_{a}, f_{b}_{a}) lower and (

_{b}) upper levels of laser transition (see e.g [3

**28**(12), 2692–2697 (1992). [CrossRef]

5. R. J. Beach, “CW Theory of quasi-three level end-pumped laser oscillators,” Opt. Commun. **123**(1-3), 385–393 (1996). [CrossRef]

_{c}– cavity length, t

_{rt}= 2l

_{c}/c – round trip time of cavity, σ

_{e}– emission cross section,

*l*– gain medium length,

_{0}*N*– concentration of dopant,

_{tot}*T*

_{oc}– output transmission,

*δ*

_{pas}– passive losses of cavity.

**93**(2-3), 269–316 (2008). [CrossRef]

16. N. P. Barnes, K. E. Murray, and M. G. Jani, “Flash-lamp-pumped Ho:Tm:Cr:YAG and Ho:Tm:Er:YLF lasers: modeling of a single, long pulse length comparison,” Appl. Opt. **36**(15), 3363–3374 (1997). [CrossRef] [PubMed]

36. T. Y. Fan, “Aperture guiding in quasi-three-level lasers,” Opt. Lett. **19**(8), 554–556 (1994). [CrossRef] [PubMed]

*θ =*0 ; Δ

*y*

_{2}= Δ

*y*,

_{2,i}*ϕ*= 0.

_{i}*y*satisfies the threshold condition:

_{2,i}*y*> 0 satisfies the following transcendent equation:

_{2,f}36. T. Y. Fan, “Aperture guiding in quasi-three-level lasers,” Opt. Lett. **19**(8), 554–556 (1994). [CrossRef] [PubMed]

## 4. Optimization of output of QTL laser

*l*,

_{c}*x*

_{oc},

*δ*

_{pas}}, gain medium parameters {

*α*

_{p},

*l*

_{0},

*σ*

_{p},

*σ*

_{e},

*τ*,

*γ*

_{p},

*A*,

*γ*,

_{l}*β*,

_{l}*k*

_{ETU}} and pump parameters {

*y*,

_{2,0}*t*,

_{pump}*P*,

_{0}*S*}. In general case of optimization of Q-switched laser the merit function is output energy, control variables of optimization are output coupling losses

_{p}*x*

_{oc}and gain medium length

*l*

_{0}. The rest of parameters are constant, given data. For definite initial gain (i.e. definite values of pump density, pump duration and gain medium length) the modified Degnan’s method can be adopted [11

**93**(2-3), 269–316 (2008). [CrossRef]

**19**(8), 554–556 (1994). [CrossRef] [PubMed]

*y*is a function of pump power

_{2,i}*P*

_{0}and pump duration

*t*. For repetitively Q-switching, the final inversion has to be considered because it affects on the gain reached in the end of the following period of pumping. Thus, directly Degnan’s approach is not adequate for such a case because we cannot separate pumping and Q-switching processes.

_{pump}### 4.1. Procedure of optimization of CW regime of QTL laser

*R*

_{p}= 0, the output laser density of QTL laser is given by:where:

**123**(1-3), 385–393 (1996). [CrossRef]

7. G. L. Bourdet, “Theoretical investigation of quasi-three-level longitudinally pumped continuous wave lasers,” Appl. Opt. **39**(6), 966–971 (2000). [CrossRef] [PubMed]

**93**(2-3), 269–316 (2008). [CrossRef]

*y*

_{2},_{t}(see formulae (15), (21)). The absorption efficiency is determined by the threshold population

*y*

_{2,t}as follows:

*a*

_{0,opt,cw}as follows:for relative pump density

*i*

_{p,0}>

*i*

_{t,cw}. It is easy to show, that optimal length

*l*

_{opt,cw}increases with pump density and OC losses. The effect of ETU is contrary; increase in

*k*causes the decrease in optimal length.

*x*

_{OC,opt,cw}for CW case can be found as a solution of the following equation:

*x*

_{OC,opt,cw},

*l*

_{opt,cw}are coupled pair of parameters, because the value of

*x*

_{OC}effects on the absorption efficiency in a case of CW generation, unlike in the case of Q-switching regime, where the inversion is determined by incident pump density and duration and does not depend on out-coupling losses of cavity. The above presented procedure can be applied for optimization of Q-switched lasers operating with high repetition rates.

### 4.2. Procedure of optimization of Q-switching regime for quasi-stationary inversion

*l*results in change of averaged pump area, thus we should consider this combined effect in calculation of incident pump density, quasi-stationary inversion etc. To simplify approach, in analysis presented below, we do not consider optimization or change of pump area (which depends on gain medium length) and assume the same pump and mode area

_{0}*S*

_{0}. Such approximation is valid for quasi-coherent pumping, for which the Rayleigh range of pumping beam is much longer than gain medium length and absorption depth.

**19**(8), 554–556 (1994). [CrossRef] [PubMed]

*z*– initial gain ratio for quasi-stationary (long pulse) pumping

_{st}*y*- quasi-stationary population of 2-nd level determined as a solution of the Eq. (15). Let us notice, that unlike in a case of CW regime, now we have to solve (15) with respect to population

_{2,st}*y*

_{2,st}whereas pump density

*i*

_{p,0}is a given parameter. The Eq. (33) defines the

*extremal curve*in the 2D space of (

*x*

_{oc},

*l*

_{0}) tracing the route to the global maximum on the 2D surface of output energy density. The output energy density determined on the extremal curve (33) is given by the following formula:where

*J*

_{sat,e}=

*h*ν

_{l}/σ

_{e}– saturation energy density.

*y*

_{opt}of the following form:where:

*a*

_{opt,Qsw}= α

_{0}

*l*

_{0,opt,qsw}is given by:and resulting maximal gain ratio

*z*

_{max}:

*k*= 0 (i.e. for medium with negligible ETU processes), we have obtained

*explicté*formula on optimal absorbance: where:

*a*

_{opt,0},

*y*

_{opt,0},

*z*

_{max,0}- optimal absorbance, 2-nd level population and maximal gain ratio respectively.

*i*/ the search for optimal absorbance of gain medium with respect to maximum of initial gain ratio according to formulae (37) –(40)*ii*/ the determination of optimal OC losses according to formula (33).

*l*

_{0,}_{opt,qsw}is here control parameter dependent on pumping parameters set {

*i*

_{p,0}, α

_{0},

*k*}, whereas the optimal OC loss

*x*

_{OC,opt,qsw}is the variable dependent on

*l*

_{0,}_{opt,qsw}and other parameters.

### 4.3. Role of gain medium absorbance and passive losses

*i*

_{p,0}> 1).

## 5. Conclusions

*explicte*formulae for ETU-less (

*k*= 0) gain medium were derived. The novel method of optimization of QTL laser in CW regime was proposed and applied to compare results of absorbance optimization for both regimes. The procedure for CW regime optimization can be applied for actively Q-switched lasers operating with high repetition rates. Analysis of role of ETU parameter and passive losses was performed for two important for practice cases: negligible ETU (

*k*= 0) and significant ETU (

*k*= 8) cases.

## Appendix

*f*(

*x,y*)], where:

*f(x,y)*- normalized gain ratio (40) determined in the 2D space of

*x = a*− absorbance,

*y = y*– averaged relative stationary population of 2-nd level, assuming the boundary condition

_{st}.*G*(

*x,y*) = 0, which is pumping equation for quasi-stationary inversion (15):where:

*i*

_{p,0}– incident relative pump density,

*β*– lower laser level relative population factor defined by (17),

_{l}*k*– relative parameter of ETU defined by (6). Let us introduce the multiplier Λ and a new function

*F*(

*x,y*) as follows:

*x, y*, Λ):

*x*variable in the following way:

*y*

_{opt}:

*z*

_{max,st}is given by:

*a*

_{opt,0}, 2-nd level population

*y*

_{opt,0}and maximal gain ratio

*z*

_{max,0}as follows:

## Acknowledgments

## References and links

1. | H. Svelto, |

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

3. | T. Y. Fan, “Optimizing the efficiency and stored energy in quasi-three-level lasers,” IEEE J. Quantum Electron. |

4. | C. D. Nabors, “Q-switched operation of quasi-three-level lasers,” IEEE J. Quantum Electron. |

5. | R. J. Beach, “CW Theory of quasi-three level end-pumped laser oscillators,” Opt. Commun. |

6. | C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hugel, “A 1-kW CW thin disk laser,” IEEE J. Sel. Top. Quantum Electron. |

7. | G. L. Bourdet, “Theoretical investigation of quasi-three-level longitudinally pumped continuous wave lasers,” Appl. Opt. |

8. | G. L. Bourdet, “New evaluation of ytterbium-doped materials for CW laser applications,” Opt. Commun. |

9. | C. Lim and Y. Izawa, “Modeling of end-pumped CW quasi-three-level lasers,” IEEE J. Quantum Electron. |

10. | T. Taira, W. M. Tulloch, and R. L. Byer, “Modeling of quasi-three-level lasers and operation of cw Yb:YAG lasers,” Appl. Opt. |

11. | M. Eichhorn, “Quasi-three-level solid-state lasers in the near and mid infrared based on trivalent rare earth ions,” Appl. Phys. B |

12. | I. Kudryashov, D. Garbuzov, and M. Dubinskii, “Latest developments in resonantly diode-pumped Er:YAG lasers,” in |

13. | B. M. Walsh, “Review of Tm and Ho Materials; Spectroscopy and Lasers,” Laser Phys. |

14. | E. P. Chicklis, J. R. Mosto, M. L. Lemons, and P. A. Budni, “High-Power/High-Brightness Diode-Pumped 1.9-μm Thulium and resonantly Pumped 2.1-μm Holmium Lasers,” IEEE J. Sel. Top. Quantum Electron. |

15. | J. Kwiatkowski, J. K. Jabczynski, Ł. Gorajek, W. Zendzian, H. Jelínková, J. Sulc, M. Nemec, and P. Koranda, “Resonantly pumped tunable Ho:YAG laser,” Laser Phys. Lett. |

16. | N. P. Barnes, K. E. Murray, and M. G. Jani, “Flash-lamp-pumped Ho:Tm:Cr:YAG and Ho:Tm:Er:YLF lasers: modeling of a single, long pulse length comparison,” Appl. Opt. |

17. | E. C. Honea, R. J. Beach, S. B. Sutton, J. A. Speth, S. C. Mitchell, J. A. Skidmore, M. A. Emanuel, and S. A. Payne, “115-W Tm:YAG diode-pumped solid-state laser,” IEEE J. Quantum Electron. |

18. | P. Peterson, M. P. Sharma, and A. Gavrielides, “Extraction efficiency and thermal lensing in Tm:YAG lasers,” Opt. Quantum Electron. |

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

20. | G. L. Bourdet and G. Lescroart, “Theoretical modeling and design of a Tm:YVO |

21. | S. So, J. I. Mackenzie, D. P. Shepherd, W. A. Clarkson, J. G. Betterton, and E. K. Gorton, “A power-scaling strategy for longitudinally diode-pumped Tm:YLF lasers,” Appl. Phys. B |

22. | M. Schellhorn, M. Eichhorn, C. Kieleck, and A. Hirth, “High repetition rate mid-infrared laser source,” C. R. Phys. |

23. | J. K. Jabczynski, W. Zendzian, J. Kwiatkowski, H. Jelínková, J. Šulc, and M. Němec, “Actively Q-switched diode pumped thulium laser,” Laser Phys. Lett. |

24. | N. G. Zakharov, O. L. Antipov, A. P. Savikin, V. V. Sharkov, O. N. Eremeikin, Y. N. Frolov, G. M. Mishchenko, and S. D. Velikanov, “Efficient emission at 1908 nm in a diode-pumped Tm:YLF laser,” Quantum Electron. |

25. | J. K. Jabczynski, L. Gorajek, W. Zendzian, J. Kwiatkowski, H. Jelinkova, J. Sulc, and M. Nemec, “Actively Q-switched thulium lasers,” in |

26. | S. D. Jackson, “The spectroscopic and energy transfer characteristics of the rare earth ions used for silicate glass fibre lasers operating in the shortwave infrared,” Laser & Photon. Rev. |

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

28. | G. L. Bourdet, “Gain and absorption saturation coupling in end pumped Tm:YVO |

29. | J. M. Sousa, J. R. Salcedo, and V. V. Kuzmin, “Simulation of laser dynamics and active Q-switching in Tm,Ho:YAG and Tm:YAG lasers,” Appl. Phys. B |

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

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

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

33. | L. B. Shaw, R. S. F. Chang, and N. Djeu, “Measurement of up-conversion energy-transfer probabilities in Ho:Y |

34. | Y. F. Chen, Y. P. Lan, and S. C. Wang, “Modeling of diode-end-pumped Q-switched solid-state lasers: influence of energy-transfer upconversion,” J. Opt. Soc. Am. B |

35. | J. Degnan, “Theory of the optimally coupled Q-switched laser,” IEEE J. Quantum Electron. |

36. | T. Y. Fan, “Aperture guiding in quasi-three-level lasers,” Opt. Lett. |

37. | I. N. Bronstein, K. A. Semendjajew, G. Musiol, and H. Muehling, |

**OCIS Codes**

(140.3460) Lasers and laser optics : Lasers

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

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

(140.5560) Lasers and laser optics : Pumping

(140.5680) Lasers and laser optics : Rare earth and transition metal solid-state lasers

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: March 29, 2011

Revised Manuscript: June 14, 2011

Manuscript Accepted: June 23, 2011

Published: August 1, 2011

**Citation**

Jan K. Jabczynski, Lukasz Gorajek, Jacek Kwiatkowski, Mateusz Kaskow, and Waldemar Zendzian, "Optimization of end-pumped, actively Q-switched quasi-III-level lasers," Opt. Express **19**, 15652-15668 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-17-15652

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### References

- H. Svelto, Principles of Lasers (Plenum Press, 1998).
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