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 3F4, 5I7, 3H4 and 3H5 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

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References

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  1. 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]
  2. 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).
  3. 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]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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2007 (1)

2006 (2)

2004 (3)

2003 (1)

2000 (1)

1999 (1)

1998 (4)

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]

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]

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]

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]

1996 (4)

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. 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]

1995 (2)

1992 (2)

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]

1991 (1)

1989 (2)

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]

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]

1988 (1)

Appl. Opt. (4)

IEEE J. of Quantum Electron. (1)

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]

IEEE J. Quantum Electron. (3)

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]

J. Appl. Phys. (2)

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]

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]

J. Opt. Soc. Am. B (3)

Opt. Commun. (1)

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]

Opt. Express (2)

Opt. Lett. (6)

Opt. Mater. (1)

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]

Phys. Rev. B (1)

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).

Quantum Electron. (1)

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]

Other (2)

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]

W. Koechner, Solid -State Laser Engineering, 6th Edition (New-York, Springer, 2006).

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Figures (5)

Fig. 1.
Fig. 1.

Energy transfer processes in co-doped Tm,Ho materials and energy differences used in Eq. (16).

Fig. 2.
Fig. 2.

Simulation of G-pulse generation: pulse power versus time.

Fig. 3.
Fig. 3.

Energy balance versus time during laser operation: (a) energy pumping and release and (b) optical loss by spontaneous radiation from different levels.

Fig. 4.
Fig. 4.

Temperature distribution inside the operating Tm,Ho:YLF crystal and thermal boundary layer for single G-pulse generation for h=104 W/m2K (δ T ≈60 µm, water temperature T w=290 K).

Fig. 5.
Fig. 5.

20 and 50 Hz G-pulse laser operation: (a) G-pulse power modification with time and (b) temperature increase in the operating crystal versus time for h=104 W/m2 K for crystal axis and surface.

Equations (23)

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dn 1 dt = R p ( t ) + n 2 τ 2 + p 28 n 2 n 8 p 71 n 7 n 1 p 41 n 4 n 1 + p 22 n 2 2 ,
+ p 27 n 2 n 7 p 51 n 5 n 1 p 61 n 6 n 1 + p 38 n 3 n 8
dn 2 dt = n 2 τ 2 + n 3 τ 3 p 28 n 2 n 8 + p 71 n 7 n 1 + 2 p 41 n 4 n 1 2 p 22 n 2 2 ,
p 27 n 2 n 7 + p 51 n 5 n 1
dn 3 dt = n 3 τ 3 + n 4 τ 4 + p 61 n 6 n 1 p 38 n 3 n 8 ,
dn 4 dt = R p ( t , z , r ) n 4 τ 4 p 41 n 4 n 1 p 22 n 2 2 ,
dn 5 dt = n 5 τ 5 + p 27 n 7 n 2 p 51 n 5 n 1 ,
dn 6 dt = n 6 τ 6 + n 5 τ 5 p 61 n 6 n 1 p 38 n 8 n 3 .
dn 7 dt = n 7 τ 7 + n 6 τ 6 p 28 n 2 n 8 p 71 n 7 n 1 p 27 n 2 n 7 + p 51 n 5 n 1 c σ se η ( f 7 n 7 f 8 n 8 ) ϕ ( t , r ) .
dn 8 dt = n 7 τ 7 p 28 n 2 n 8 + p 71 n 7 n 1 + p 61 n 6 n 1 p 38 n 3 n 8 c σ se η ( f 7 n 7 f 8 n 8 ) ϕ ( t , r ) ,
d Φ 0 ( t ) dt = Φ 0 ( t ) c σ se η V cr ( f 7 n 7 f 8 n 8 ) ϕ 0 ( r , z ) dV Φ 0 ( t ) τ c + ε τ 7 V cr n 7 dV ,
τ c 1 = c 2 L opt [ ln R 1 ln ( 1 T out ) + β ] ,
ϕ 0 ( r ) = 2 π w 0 2 L cav exp ( 2 r 2 w 0 2 ) ,
I 0 ( t , r ) = Φ 0 ch ν las 2 L opt ln 1 1 T out × 2 π w 0 * 2 exp ( 2 r 2 w 0 * 2 ) ,
R p ( t ) η p η a Q p π d 2 L cr h ν p Δ t p × { 1 , t Δ t p 0 , t > Δ t p .
f i ( t , r ) = g i exp [ E i k B T ( t , r ) ] j g j exp [ E j k B T ( t , r ) ] ,
q cr ( t , r ) = i = 2 7 Δ E i n i τ inr ,
q cr ( t , r ) = R p ( t ) h ν p c σ se η 1 h ν l ( f 7 n 7 f 8 n 8 ) ϕ ( t , r ) i = 2 7 Δ E i n i τ ir i = 2 7 Δ E i * dn i dt ,
Δ T cr ( t , r ) 1 ρ c 0 t q cr ( t , r ) dt .
δ T k w h 6 600 μ m .
ρ i C i T i t = ( k i T i ) + q i ( t , r ) ,
q w ( t , r ) = R 0 r i J 0 i ( t ) α i exp [ α i ( r R 0 ) ] ,
J 0 i ( t ) = 1 S cr V Δ E i n i ( t , r ) τ ir dV .

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