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.

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2009

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

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]

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. 39(5), 410–414 (2009).
[CrossRef]

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]

2008

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]

2007

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]

M. Schellhorn, M. Eichhorn, C. Kieleck, and A. Hirth, “High repetition rate mid-infrared laser source,” C. R. Phys. 8(10), 1151–1161 (2007).
[CrossRef]

J. K. Jabczynski, W. Zendzian, J. Kwiatkowski, H. Jelínková, J. Šulc, and M. Němec, “Actively Q-switched diode pumped thulium laser,” Laser Phys. Lett. 4(12), 863–867 (2007).
[CrossRef]

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]

2006

X. Zhang, Y. Ju, and Y. Wang, “Theoretical and experimental investigation of actively Q-switched Tm,Ho:YLF lasers,” Opt. Express 14(17), 7745–7750 (2006).
[CrossRef] [PubMed]

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 84(3), 389–393 (2006).
[CrossRef]

2005

P. Cemy and D. Burns, “Modeling and experimental investigation of a diode-pumped Tm:YAlO3 laser with a- and b-cut orientation,” IEEE J. Sel. Top. Quantum Electron. 11(3), 674–681 (2005).
[CrossRef]

2002

2001

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

2000

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

G. L. Bourdet, “Gain and absorption saturation coupling in end pumped Tm:YVO4 and Tm:Ho:YLF amplifiers,” Opt. Commun. 173(1-6), 333–340 (2000).
[CrossRef]

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. 6(4), 629–635 (2000).
[CrossRef]

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

1999

1998

G. L. Bourdet and G. Lescroart, “Theoretical modeling and design of a Tm:YVO4 microchip lasers,” Opt. Commun. 149(4-6), 404–414 (1998).
[CrossRef]

1997

1996

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]

L. B. Shaw, R. S. F. Chang, and N. Djeu, “Measurement of up-conversion energy-transfer probabilities in Ho:Y3Al5O12 and Tm:Y3Al5O12,” Phys. Rev. B 50, 6009–6019 (1996).

P. Peterson, M. P. Sharma, and A. Gavrielides, “Extraction efficiency and thermal lensing in Tm:YAG lasers,” Opt. Quantum Electron. 28(6), 695–707 (1996).
[CrossRef]

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]

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

1994

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

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

1992

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

1989

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

1988

Antipov, O. L.

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. 39(5), 410–414 (2009).
[CrossRef]

Barnes, N. P.

Beach, R. J.

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]

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

Betterton, J. G.

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 84(3), 389–393 (2006).
[CrossRef]

Bourdet, G. L.

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

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

G. L. Bourdet, “Gain and absorption saturation coupling in end pumped Tm:YVO4 and Tm:Ho:YLF amplifiers,” Opt. Commun. 173(1-6), 333–340 (2000).
[CrossRef]

G. L. Bourdet and G. Lescroart, “Theoretical modeling and design of a Tm:Ho:YLiF4 microchip laser,” Appl. Opt. 38(15), 3275–3281 (1999).
[CrossRef] [PubMed]

G. L. Bourdet and G. Lescroart, “Theoretical modeling and design of a Tm:YVO4 microchip lasers,” Opt. Commun. 149(4-6), 404–414 (1998).
[CrossRef]

Budni, P. A.

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. 6(4), 629–635 (2000).
[CrossRef]

Burns, D.

P. Cemy and D. Burns, “Modeling and experimental investigation of a diode-pumped Tm:YAlO3 laser with a- and b-cut orientation,” IEEE J. Sel. Top. Quantum Electron. 11(3), 674–681 (2005).
[CrossRef]

Byer, R. L.

Cemy, P.

P. Cemy and D. Burns, “Modeling and experimental investigation of a diode-pumped Tm:YAlO3 laser with a- and b-cut orientation,” IEEE J. Sel. Top. Quantum Electron. 11(3), 674–681 (2005).
[CrossRef]

Chang, R. S. F.

L. B. Shaw, R. S. F. Chang, and N. Djeu, “Measurement of up-conversion energy-transfer probabilities in Ho:Y3Al5O12 and Tm:Y3Al5O12,” Phys. Rev. B 50, 6009–6019 (1996).

Chen, Y. F.

Chicklis, E. P.

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. 6(4), 629–635 (2000).
[CrossRef]

Clarkson, W. A.

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 84(3), 389–393 (2006).
[CrossRef]

Contag, K.

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

Degnan, J.

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

Djeu, N.

L. B. Shaw, R. S. F. Chang, and N. Djeu, “Measurement of up-conversion energy-transfer probabilities in Ho:Y3Al5O12 and Tm:Y3Al5O12,” Phys. Rev. B 50, 6009–6019 (1996).

Dubinskii, M.

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]

Eichhorn, M.

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]

M. Schellhorn, M. Eichhorn, C. Kieleck, and A. Hirth, “High repetition rate mid-infrared laser source,” C. R. Phys. 8(10), 1151–1161 (2007).
[CrossRef]

Emanuel, M. A.

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]

Eremeikin, O. N.

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. 39(5), 410–414 (2009).
[CrossRef]

Fan, T. Y.

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

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

Frolov, Y. N.

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. 39(5), 410–414 (2009).
[CrossRef]

Garbuzov, D.

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]

Gavrielides, A.

P. Peterson, M. P. Sharma, and A. Gavrielides, “Extraction efficiency and thermal lensing in Tm:YAG lasers,” Opt. Quantum Electron. 28(6), 695–707 (1996).
[CrossRef]

Giesen, A.

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

Gorajek, L.

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]

Gorton, E. K.

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 84(3), 389–393 (2006).
[CrossRef]

Hirth, A.

M. Schellhorn, M. Eichhorn, C. Kieleck, and A. Hirth, “High repetition rate mid-infrared laser source,” C. R. Phys. 8(10), 1151–1161 (2007).
[CrossRef]

Honea, E. C.

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]

Hugel, H.

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

Izawa, Y.

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

Jabczynski, J. K.

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]

J. K. Jabczynski, W. Zendzian, J. Kwiatkowski, H. Jelínková, J. Šulc, and M. Němec, “Actively Q-switched diode pumped thulium laser,” Laser Phys. Lett. 4(12), 863–867 (2007).
[CrossRef]

Jackson, S. D.

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]

Jani, M. G.

Jelínková, H.

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]

J. K. Jabczynski, W. Zendzian, J. Kwiatkowski, H. Jelínková, J. Šulc, and M. Němec, “Actively Q-switched diode pumped thulium laser,” Laser Phys. Lett. 4(12), 863–867 (2007).
[CrossRef]

Ju, Y.

Kieleck, C.

M. Schellhorn, M. Eichhorn, C. Kieleck, and A. Hirth, “High repetition rate mid-infrared laser source,” C. R. Phys. 8(10), 1151–1161 (2007).
[CrossRef]

Koranda, P.

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]

Kudryashov, I.

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]

Kuzmin, V. V.

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]

Kwiatkowski, J.

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]

J. K. Jabczynski, W. Zendzian, J. Kwiatkowski, H. Jelínková, J. Šulc, and M. Němec, “Actively Q-switched diode pumped thulium laser,” Laser Phys. Lett. 4(12), 863–867 (2007).
[CrossRef]

Lan, Y. P.

Larionov, M.

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

Lemons, M. L.

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. 6(4), 629–635 (2000).
[CrossRef]

Lescroart, G.

G. L. Bourdet and G. Lescroart, “Theoretical modeling and design of a Tm:Ho:YLiF4 microchip laser,” Appl. Opt. 38(15), 3275–3281 (1999).
[CrossRef] [PubMed]

G. L. Bourdet and G. Lescroart, “Theoretical modeling and design of a Tm:YVO4 microchip lasers,” Opt. Commun. 149(4-6), 404–414 (1998).
[CrossRef]

Lim, C.

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

Louchev, O. A.

Mackenzie, J. I.

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 84(3), 389–393 (2006).
[CrossRef]

Mishchenko, G. M.

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. 39(5), 410–414 (2009).
[CrossRef]

Mitchell, S. C.

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]

Mosto, J. R.

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. 6(4), 629–635 (2000).
[CrossRef]

Murray, K. E.

Nabors, C. D.

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

Nemec, M.

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]

J. K. Jabczynski, W. Zendzian, J. Kwiatkowski, H. Jelínková, J. Šulc, and M. Němec, “Actively Q-switched diode pumped thulium laser,” Laser Phys. Lett. 4(12), 863–867 (2007).
[CrossRef]

Payne, S. A.

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]

Peterson, P.

P. Peterson, M. P. Sharma, and A. Gavrielides, “Extraction efficiency and thermal lensing in Tm:YAG lasers,” Opt. Quantum Electron. 28(6), 695–707 (1996).
[CrossRef]

Risk, W. P.

Rustad, G.

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]

Salcedo, J. R.

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]

Savikin, A. P.

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. 39(5), 410–414 (2009).
[CrossRef]

Schellhorn, M.

M. Schellhorn, M. Eichhorn, C. Kieleck, and A. Hirth, “High repetition rate mid-infrared laser source,” C. R. Phys. 8(10), 1151–1161 (2007).
[CrossRef]

Sharkov, V. V.

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. 39(5), 410–414 (2009).
[CrossRef]

Sharma, M. P.

P. Peterson, M. P. Sharma, and A. Gavrielides, “Extraction efficiency and thermal lensing in Tm:YAG lasers,” Opt. Quantum Electron. 28(6), 695–707 (1996).
[CrossRef]

Shaw, L. B.

L. B. Shaw, R. S. F. Chang, and N. Djeu, “Measurement of up-conversion energy-transfer probabilities in Ho:Y3Al5O12 and Tm:Y3Al5O12,” Phys. Rev. B 50, 6009–6019 (1996).

Shepherd, D. P.

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 84(3), 389–393 (2006).
[CrossRef]

Skidmore, J. A.

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]

So, S.

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 84(3), 389–393 (2006).
[CrossRef]

Sousa, J. M.

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]

Speth, J. A.

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]

Stenersen, K.

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]

Stewen, C.

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

Sulc, J.

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]

Šulc, J.

J. K. Jabczynski, W. Zendzian, J. Kwiatkowski, H. Jelínková, J. Šulc, and M. Němec, “Actively Q-switched diode pumped thulium laser,” Laser Phys. Lett. 4(12), 863–867 (2007).
[CrossRef]

Sutton, S. B.

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]

Taira, T.

Tulloch, W. M.

Urata, Y.

Velikanov, S. D.

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. 39(5), 410–414 (2009).
[CrossRef]

Wada, S.

Walsh, B. M.

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

Wang, S. C.

Wang, Y.

Zakharov, N. G.

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. 39(5), 410–414 (2009).
[CrossRef]

Zendzian, W.

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]

J. K. Jabczynski, W. Zendzian, J. Kwiatkowski, H. Jelínková, J. Šulc, and M. Němec, “Actively Q-switched diode pumped thulium laser,” Laser Phys. Lett. 4(12), 863–867 (2007).
[CrossRef]

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Appl. Opt.

Appl. Phys. B

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]

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 84(3), 389–393 (2006).
[CrossRef]

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]

C. R. Phys.

M. Schellhorn, M. Eichhorn, C. Kieleck, and A. Hirth, “High repetition rate mid-infrared laser source,” C. R. Phys. 8(10), 1151–1161 (2007).
[CrossRef]

IEEE J. Quantum Electron.

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

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

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

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]

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]

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

IEEE J. Sel. Top. Quantum Electron.

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. 6(4), 629–635 (2000).
[CrossRef]

P. Cemy and D. Burns, “Modeling and experimental investigation of a diode-pumped Tm:YAlO3 laser with a- and b-cut orientation,” IEEE J. Sel. Top. Quantum Electron. 11(3), 674–681 (2005).
[CrossRef]

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

J. Opt. Soc. Am. B

Laser & Photon. Rev.

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).
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Laser Phys.

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

Laser Phys. Lett.

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]

J. K. Jabczynski, W. Zendzian, J. Kwiatkowski, H. Jelínková, J. Šulc, and M. Němec, “Actively Q-switched diode pumped thulium laser,” Laser Phys. Lett. 4(12), 863–867 (2007).
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Opt. Commun.

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

G. L. Bourdet and G. Lescroart, “Theoretical modeling and design of a Tm:YVO4 microchip lasers,” Opt. Commun. 149(4-6), 404–414 (1998).
[CrossRef]

G. L. Bourdet, “Gain and absorption saturation coupling in end pumped Tm:YVO4 and Tm:Ho:YLF amplifiers,” Opt. Commun. 173(1-6), 333–340 (2000).
[CrossRef]

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Opt. Lett.

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P. Peterson, M. P. Sharma, and A. Gavrielides, “Extraction efficiency and thermal lensing in Tm:YAG lasers,” Opt. Quantum Electron. 28(6), 695–707 (1996).
[CrossRef]

Phys. Rev. B

L. B. Shaw, R. S. F. Chang, and N. Djeu, “Measurement of up-conversion energy-transfer probabilities in Ho:Y3Al5O12 and Tm:Y3Al5O12,” Phys. Rev. B 50, 6009–6019 (1996).

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[CrossRef]

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J. K. Jabczynski, L. Gorajek, W. Zendzian, J. Kwiatkowski, H. Jelinkova, J. Sulc, and M. Nemec, “Actively Q-switched thulium lasers,” in Advances in Solid State Lasers: Development and Applications IN-TECH, Vienna, (2010).

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Figures (6)

Fig. 1
Fig. 1

Scheme of indirect pumping.

Fig. 2
Fig. 2

y 2- relative population of upper level vs. relative time t’ = t/τ for different relative pump density i p,0 = 1,2,4 and ETU parameters k = 0 (plot a)), k = 8 (plot b)).

Fig. 3
Fig. 3

Optimal absorbance vs. relative pump density for ETU parameter k = 8 (blue curves) and ETU parameter k = 0 (red curves) for Q-switched (continuous curves) and CW (dashed curves).

Fig. 4
Fig. 4

Output energy density vs. absorbance for different relative pump densities i p,0 = 1,2,4; ETU parameters k = 0 (plot a)) and k = 8 (plot b)) .

Fig. 5
Fig. 5

(a) Normalized output energy density vs. absorbance for different passive losses; ETU parameters k = 0, relative pump density i p,0 = 2. (b) Normalized output energy density vs. absorbance for different passive losses δpas; ETU parameters k = 8, relative pump density i p,0 = 2.

Fig. 6
Fig. 6

Normalized output energy density vs. passive losses for ETU parameter k = 0 (continuous curves) and ETU parameter k = 8 (dotted curves) and several relative pump density: i p,0 = 2 (red curves), i p,0 = 4 (blue curves).

Equations (58)

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{ dI p ± dz = ( N tot γ p N 2 ) σ p I p ± dN 2 dt =   A   R 2 N 2 τ k E T U N 2 2 ,
R 2 = N 1 σ p I p + + I p h ν p = ( N t o t γ p N 2 ) σ p I p + + I p h ν p ,
t ' = t / τ ; ζ = α 0 z ; x 2 = N 2 / N t o t ; i p ± = I p ± / I p , s a t ,
α 0 = σ p N t o t ; I p , s a t = h ν p A ​   σ p τ     ; γ p = 1 ; A = η 1 2 2 ,
α 0 = f a ' σ p N t o t ; I p , s a t = h ν p f a ' ​   σ p τ     ; γ p = 1 + f b ' / f a ' ; A = 1.
{ d i p ± d ξ = ( 1 γ p x 2 ) i p ± d x 2 d t ' = ( 1 γ p x 2 ) ( i p + + i p ) x 2 k x 2 2 ,
k = k E T U τ N t o t .
0 a 0 ( 1 γ p x 2 ) ( i p + + i p ) d ξ = 0 a 0 d i p 0 a 0 d i p + = i p + ( 0 ) i p + ( a 0 ) + i p ( a 0 ) i p ( 0 ) .
d y 2 d t ' = r p ( y 2 ) y 2 k y 2 2 ,
y 2 = x 2 ¯ = a 0 1 0 a 0 x 2 d ξ .
r p ( y 2 ) = i p , 0 a 0 { η 0 ( a 0 ( 1 γ p y 2 ) ) [ 1 + R p ( 1 η 0 ( a 0 ( 1 γ p y 2 ) ) ) ] f o r 1 e n d p u m p 2 η 0 ( a 0 ( 1 γ p y 2 ) )                 f o r 2 e n d p u m p ,
i p , 0 = P 0 S p I p , s a t ; η 0 ( x ) = 1 exp ( x ) .
y 2 ( Δ t ' ) = β 1 ( β 2 k y 2 , 0 ) exp ( β 1 Δ t ' ) β 2 ( β 1 k y 2 , 0 ) exp ( β 2 Δ t ' ) κ [ ( β 2 k y 2 , 0 ) exp ( β 1 Δ t ' ) ( β 1 k y 2 , 0 ) exp ( β 2 Δ t ' ) ] ,
β 1 = 1 2 ( 1 + 1 + 4 k p 0 ) , β 2 = 1 2 ( 1 1 + 4 k p 0 ) , p 0 = r p ( y 2 , 0 ) .
y 2 , h ( Δ t ' ) = 2 p 0 tanh ( 0.5 Δ t ' 1 + 4 k p 0 ) tanh ( 0.5 Δ t ' 1 + 4 k p 0 ) + 1 + 4 k p 0 ,
r p ( y 2 , s t ) y 2 , s t k y 2 , s t 2 = 0.
{ d ϕ l d t = Φ l t r t ( 2 σ e l 0 γ l ( N ¯ 2 β l N t o t ) x O C δ p a s ) d N ¯ 2 d t = A R ¯ 2 N ¯ 2 τ k E T U N ¯ 2 2 Φ l t r t l c l 0 ( 2 σ e l 0 γ l ( N ¯ 2 β l N t o t ) ) ,
γ l = ( f a + f b ) / f b ; β l = f a / ( f a + f b ) = ( γ l 1 ) / γ l ,
θ = t / t r t     ;     Δ y 2 =     ( N ¯ 2 β l N t o t ) / N t o t = y 2 β l ;     ϕ l = Φ l / N t o t .
{ d ϕ l d θ = 2 g 0 l 0 ( Δ y 2 Δ y 2 , t ) ϕ l d Δ y 2 d θ = l c l 0 2 g 0 l 0 Δ y 2 ϕ l ,
g 0 = γ l σ e N t o t ; Δ y 2 , t = ( x o c + δ p a s ) / 2 g 0 l 0 ,
y 2 , i > y 2 , t ( l 0 , x O C , δ p a s ) = ( x o c + δ p a s ) / 2 g 0 l 0 + β l .
ϕ l ( Δ y 2 ) = l 0 l c Δ y 2 , i Δ y 2 x Δ y 2 , t x d x = l 0 l c ( Δ y 2 , i Δ y 2 Δ y 2 , t ln ( Δ y 2 , i Δ y 2 ) ) .
Δ y 2 , i Δ y 2 , f Δ y 2 , t ln ( Δ y 2 , i Δ y 2 , f ) = 0.
J o u t = J 0 x o c x o c + δ p a s ( Δ y 2 , i Δ y 2 , f ) ,
J 0 = h ν l l 0 N t o t .
i l ( l 0 , x O C ; i p , 0 ) = η s l o p e , i ( x O C , δ p a s ) η a b s , t ( l 0 , x O C , δ p a s ) ( i p , 0 i t , c w ( l 0 , x O C , δ p a s ) ) ,
η s l o p e ( x O C , δ p a s ) = g 0 α 0 ( 1 R O C ) R p a s ( 1 R O C R p a s ) ( R O C + R p a s ) .
η a b s , t ( l 0 , x O C , δ p a s ) = 1 exp [ α 0 l 0 ( 1 γ p y 2 , t ( l 0 , x O C , δ p a s ) ) ] .
i t , c w ( l 0 , x O C , δ p a s ) = α 0 l 0 y 2 , t ( l 0 , x O C , δ p a s ) ( 1 + k y 2 , t ( l 0 , x O C , δ p a s ) ) 1 exp ( α 0 l 0 ( 1 γ p y 2 , t ( l 0 , x O C , δ p a s ) ) ) .
i p , 0 d d l 0 η a b s , t ( l 0 , x O C , δ p a s ) = d d l 0 α 0 l 0 [ 1 + k y 2 , t ( l 0 , x O C , δ p a s ) ] y 2 , t ( l 0 , x O C , δ p a s ) .
a 0 , o p t , c w = α 0 l o p t , c w = 1 1 γ p β l [ ln ( i p , 0 ( 1 + γ p β l ) β l ( 1 + β l k ) ) + α 0 γ p ( x O C + δ p a s ) 2 g 0 ] ,
d d x O C i l ( l o p t , c w ( x O C ; i p , 0 ) , x O C ; i p , 0 ) = 0.
x o c , o p t Q s w ( l 0 ; i p , 0 ) = δ p a s z s t ( l 0 ; i p , 0 ) 1 ln [ z s t ( l 0 ; i p , 0 ) ] ln [ z s t ( l 0 ; i p , 0 ) ] ,
z s t ( l 0 ; i p , 0 ) = 2 g 0 l 0 δ p a s [ y 2 , s t ( l 0 ; i p , 0 ) β l ] ,
J max ( l 0 ; i p , 0 ) = δ p a s J s a t , e 2 γ l ( z s t ( l 0 ; i p , 0 ) 1 ln [ z s t ( l 0 ; i p , 0 ) ] ) ,
d d l 0 J max ( l 0 ; i p , 0 ) = δ p a s J s a t , e 2 γ l ( z s t ( l 0 ; i p , 0 ) 1 z s t ( l 0 ; i p , 0 ) ) d z s t ( l 0 ; i p , 0 ) d l 0 = 0.
i p , 0 exp ( f 1 ( y o p t ) ( 1 y o p t 1 ) ) = i p 0 f 1 ( y o p t ) ( 1 + k y o p t ) ,
f 1 ( y ) = 1 1 + k y ( i p , 0 + 1 + 2 k y 1 + 2 k y k y 2 1 β l ) .
a o p t , Q s w = f 1 ( y o p t ) / y o p t ,
z max = 2 g 0 α 0 δ p a s a o p t , Q s w ( y o p t β l ) .
a o p t , 0 = i p , 0 β l 1 β l + ln ( i p , 0 ( 1 β l ) β l ) ,
y o p t , 0 = i p , 0 β l 1 β l i p , 0 β l 1 β l l + ln ( i p , 0 ( 1 β l ) β l ) ,
z max , 0 = 2 g 0 α 0 δ p a s [ i p , 0 ( 1 β l ) + β l ln ( i p , 0 ( 1 β l ) β l e ) ] ,
f ( x , y ) = x ( y β l ) G ( x , y ) = r p ( x , y ) y ( 1 + k y ) = 0
r p ( x , y ) = i p , 0 ( 1 exp ( x y x ) ) x - 1
F ( x , y ) = f ( x , y ) + Λ G ( x , y )
{ F ( x , y , Λ ) x = 0 F ( x , y , Λ ) y = 0 G ( x , y ) = 0
{ y β + Λ ( i p , 0 ( 1 y ) exp ( x y x ) y ( 1 + k y ) ) = 0 x Λ ( i p , 0 x exp ( x y x ) x ( 1 2 k y ) ) = 0 i p , 0 ( 1 - exp ( x y x ) ) x y ( 1 k y ) = 0
Λ = x i p , 0 exp ( x y x ) 1 2 k y
{ ( 1 β l ) ( i p , 0 exp ( x y x ) + 1 + 2 κ y ) = 1 + 2 κ y κ y 2 i p , 0 exp ( x y x ) = i p , 0 x y ( 1 + κ y )
x = f 1 ( y ) y - 1
f 1 ( y ) = 1 1 + k y ( i p , 0 + 1 + 2 κ y 1 + 2 k y k y 2 1 β l )
i p , 0 exp ( f 1 ( y o p t ) ( 1 y o p t 1 ) ) = i p , 0 f 1 ( y o p t ) ( 1 + y o p t )
z max , s t = 2 g 0 α 0 δ p a s ( 1 β l y o p t 1 ) f 1 ( y o p t )
a o p t , 0 = i p , 0 β l 1 β l + ln ( i p , 0 ( 1 β l ) β l )
y o p t , 0 = i p , 0 β l 1 β l i p , 0 β l 1 β l l + ln ( i p , 0 ( 1 β l ) β l )
z max , 0 = 2 g 0 α 0 δ p a s [ i p , 0 ( 1 β l ) + β l ln ( i p , 0 ( 1 β l ) β l e ) ]

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