Abstract

The temperature dependence of the reflectivity of volume Bragg grating mirrors is shown to determine the performance of a solid-state laser. Mirrors with reflectivities that vary with temperature are then considered that make the temperature-independent operation of Nd:YAG (and other) lasers possible.

© 2006 Optical Society of America

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References

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  1. M. Bass, L. Weichman, S. Vigil, and B. Brickeen, "The temperature dependence of Nd3+ doped solid-state lasers," IEEE J. Quantum Electron. 39, 741-748 (2003).
    [CrossRef]
  2. T.-Y. Chung, V. Smimov, M. Hemmer, L. B. Glebov, M. C. Richardson, and M. Bass, "Unexpected properties of a laser resonator with volumetric Bragg grating end mirrors," in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science, (OSA, 2006), paper CFBS.
  3. R. Corless, G. Gonnet, D. Hare, D. Jeffrey, and D. Knuth, "On the Lambert W function," Adv. Comput. Math. 5, 329-359 (1996).
    [CrossRef]
  4. E. W. Weisstein, "From MathWorld--A Wolfram Web Resource," http://mathworld.wolfram.com/LambertW-Function.html.
  5. The calculations leading to Eqs. (9) and (10) are long and complicated and will be published separately.
  6. G. Xiao and M. Bass, "A generalized model for passively Q-switched lasers including excited state absorption in the saturable absorber," IEEE J. Quantum Electron. 33, 41-44 (1997).
    [CrossRef]
  7. O. M. Efimov, L. B. Glebov, L. N. Glebova, and V. I. Smirnov, "Process for production of high efficiency volume diffractive elements in photo-thermo-refractive glass," U.S. patent 6,586,141 B1 (1 July 2003).
  8. O. M. Efimov, L. B. Glebov, and V. I. Smirnov, "High efficiency volume diffractive elements in photo-thermo-refractive glass," U.S. patent 6,673,497 B2 (6 January 2004).

2003

M. Bass, L. Weichman, S. Vigil, and B. Brickeen, "The temperature dependence of Nd3+ doped solid-state lasers," IEEE J. Quantum Electron. 39, 741-748 (2003).
[CrossRef]

1997

G. Xiao and M. Bass, "A generalized model for passively Q-switched lasers including excited state absorption in the saturable absorber," IEEE J. Quantum Electron. 33, 41-44 (1997).
[CrossRef]

1996

R. Corless, G. Gonnet, D. Hare, D. Jeffrey, and D. Knuth, "On the Lambert W function," Adv. Comput. Math. 5, 329-359 (1996).
[CrossRef]

Bass, M.

M. Bass, L. Weichman, S. Vigil, and B. Brickeen, "The temperature dependence of Nd3+ doped solid-state lasers," IEEE J. Quantum Electron. 39, 741-748 (2003).
[CrossRef]

G. Xiao and M. Bass, "A generalized model for passively Q-switched lasers including excited state absorption in the saturable absorber," IEEE J. Quantum Electron. 33, 41-44 (1997).
[CrossRef]

T.-Y. Chung, V. Smimov, M. Hemmer, L. B. Glebov, M. C. Richardson, and M. Bass, "Unexpected properties of a laser resonator with volumetric Bragg grating end mirrors," in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science, (OSA, 2006), paper CFBS.

Brickeen, B.

M. Bass, L. Weichman, S. Vigil, and B. Brickeen, "The temperature dependence of Nd3+ doped solid-state lasers," IEEE J. Quantum Electron. 39, 741-748 (2003).
[CrossRef]

Chung, T.-Y.

T.-Y. Chung, V. Smimov, M. Hemmer, L. B. Glebov, M. C. Richardson, and M. Bass, "Unexpected properties of a laser resonator with volumetric Bragg grating end mirrors," in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science, (OSA, 2006), paper CFBS.

Corless, R.

R. Corless, G. Gonnet, D. Hare, D. Jeffrey, and D. Knuth, "On the Lambert W function," Adv. Comput. Math. 5, 329-359 (1996).
[CrossRef]

Efimov, O. M.

O. M. Efimov, L. B. Glebov, L. N. Glebova, and V. I. Smirnov, "Process for production of high efficiency volume diffractive elements in photo-thermo-refractive glass," U.S. patent 6,586,141 B1 (1 July 2003).

O. M. Efimov, L. B. Glebov, and V. I. Smirnov, "High efficiency volume diffractive elements in photo-thermo-refractive glass," U.S. patent 6,673,497 B2 (6 January 2004).

Glebov, L. B.

O. M. Efimov, L. B. Glebov, and V. I. Smirnov, "High efficiency volume diffractive elements in photo-thermo-refractive glass," U.S. patent 6,673,497 B2 (6 January 2004).

O. M. Efimov, L. B. Glebov, L. N. Glebova, and V. I. Smirnov, "Process for production of high efficiency volume diffractive elements in photo-thermo-refractive glass," U.S. patent 6,586,141 B1 (1 July 2003).

T.-Y. Chung, V. Smimov, M. Hemmer, L. B. Glebov, M. C. Richardson, and M. Bass, "Unexpected properties of a laser resonator with volumetric Bragg grating end mirrors," in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science, (OSA, 2006), paper CFBS.

Glebova, L. N.

O. M. Efimov, L. B. Glebov, L. N. Glebova, and V. I. Smirnov, "Process for production of high efficiency volume diffractive elements in photo-thermo-refractive glass," U.S. patent 6,586,141 B1 (1 July 2003).

Gonnet, G.

R. Corless, G. Gonnet, D. Hare, D. Jeffrey, and D. Knuth, "On the Lambert W function," Adv. Comput. Math. 5, 329-359 (1996).
[CrossRef]

Hare, D.

R. Corless, G. Gonnet, D. Hare, D. Jeffrey, and D. Knuth, "On the Lambert W function," Adv. Comput. Math. 5, 329-359 (1996).
[CrossRef]

Hemmer, M.

T.-Y. Chung, V. Smimov, M. Hemmer, L. B. Glebov, M. C. Richardson, and M. Bass, "Unexpected properties of a laser resonator with volumetric Bragg grating end mirrors," in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science, (OSA, 2006), paper CFBS.

Jeffrey, D.

R. Corless, G. Gonnet, D. Hare, D. Jeffrey, and D. Knuth, "On the Lambert W function," Adv. Comput. Math. 5, 329-359 (1996).
[CrossRef]

Knuth, D.

R. Corless, G. Gonnet, D. Hare, D. Jeffrey, and D. Knuth, "On the Lambert W function," Adv. Comput. Math. 5, 329-359 (1996).
[CrossRef]

Richardson, M. C.

T.-Y. Chung, V. Smimov, M. Hemmer, L. B. Glebov, M. C. Richardson, and M. Bass, "Unexpected properties of a laser resonator with volumetric Bragg grating end mirrors," in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science, (OSA, 2006), paper CFBS.

Smimov, V.

T.-Y. Chung, V. Smimov, M. Hemmer, L. B. Glebov, M. C. Richardson, and M. Bass, "Unexpected properties of a laser resonator with volumetric Bragg grating end mirrors," in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science, (OSA, 2006), paper CFBS.

Smirnov, V. I.

O. M. Efimov, L. B. Glebov, L. N. Glebova, and V. I. Smirnov, "Process for production of high efficiency volume diffractive elements in photo-thermo-refractive glass," U.S. patent 6,586,141 B1 (1 July 2003).

O. M. Efimov, L. B. Glebov, and V. I. Smirnov, "High efficiency volume diffractive elements in photo-thermo-refractive glass," U.S. patent 6,673,497 B2 (6 January 2004).

Vigil, S.

M. Bass, L. Weichman, S. Vigil, and B. Brickeen, "The temperature dependence of Nd3+ doped solid-state lasers," IEEE J. Quantum Electron. 39, 741-748 (2003).
[CrossRef]

Weichman, L.

M. Bass, L. Weichman, S. Vigil, and B. Brickeen, "The temperature dependence of Nd3+ doped solid-state lasers," IEEE J. Quantum Electron. 39, 741-748 (2003).
[CrossRef]

Weisstein, E. W.

E. W. Weisstein, "From MathWorld--A Wolfram Web Resource," http://mathworld.wolfram.com/LambertW-Function.html.

Xiao, G.

G. Xiao and M. Bass, "A generalized model for passively Q-switched lasers including excited state absorption in the saturable absorber," IEEE J. Quantum Electron. 33, 41-44 (1997).
[CrossRef]

Adv. Comput. Math.

R. Corless, G. Gonnet, D. Hare, D. Jeffrey, and D. Knuth, "On the Lambert W function," Adv. Comput. Math. 5, 329-359 (1996).
[CrossRef]

IEEE J. Quantum Electron.

M. Bass, L. Weichman, S. Vigil, and B. Brickeen, "The temperature dependence of Nd3+ doped solid-state lasers," IEEE J. Quantum Electron. 39, 741-748 (2003).
[CrossRef]

G. Xiao and M. Bass, "A generalized model for passively Q-switched lasers including excited state absorption in the saturable absorber," IEEE J. Quantum Electron. 33, 41-44 (1997).
[CrossRef]

Other

O. M. Efimov, L. B. Glebov, L. N. Glebova, and V. I. Smirnov, "Process for production of high efficiency volume diffractive elements in photo-thermo-refractive glass," U.S. patent 6,586,141 B1 (1 July 2003).

O. M. Efimov, L. B. Glebov, and V. I. Smirnov, "High efficiency volume diffractive elements in photo-thermo-refractive glass," U.S. patent 6,673,497 B2 (6 January 2004).

T.-Y. Chung, V. Smimov, M. Hemmer, L. B. Glebov, M. C. Richardson, and M. Bass, "Unexpected properties of a laser resonator with volumetric Bragg grating end mirrors," in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science, (OSA, 2006), paper CFBS.

E. W. Weisstein, "From MathWorld--A Wolfram Web Resource," http://mathworld.wolfram.com/LambertW-Function.html.

The calculations leading to Eqs. (9) and (10) are long and complicated and will be published separately.

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Figures (2)

Fig. 1
Fig. 1

P out versus P in of the X cavity Ti:sapphire laser with VBG end mirrors for five VBG temperature differences. The lines are linear fits to the data.

Fig. 2
Fig. 2

Reflectivity versus Nd:YAG gain medium temperature. The dashed–dotted curve is for the case of long pulse operation, the dotted curve is for the case of an actively Q-switched laser with constant pump energy, the dashed curve is for the case of the actively Q-switched laser pumped to the ASE limit, and the solid curve is for the case of the Cr:YAG passively Q-switched laser.

Tables (2)

Tables Icon

Table 1 Common Parameters for the Nd:YAG Lasers Evaluated

Tables Icon

Table 2 Saturable Absorber Properties Used in the Passive Q-Switch Example

Equations (72)

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50 ° C
+ 50 ° C
P out
P in
Δ T
Δ T
Δ T
21 ° C
Δ T
Δ T
Δ T
d E out ( T ) / d T
E out ( T ) = η s ( T ) [ E in E t h ( T ) ] ,
E in
E t h ( T )
E t h ( T ) = A h ν p σ ( T ) τ f η pe { L ln [ R ( T ) ] } t p .
η pe
τ f
t p
η s ( T ) = 2 1 R ( T ) 1 + R ( T ) 1 L ln [ R ( T ) ] .
d E out ( T ) / d T = 0
d R ( T ) d T = R ( T ) { L ln [ R ( T ) ] } σ ( T ) + 1 R 2 ( T ) + 2 { L ln [ R ( T ) ] } R ( T ) 1 × 1 R 2 ( T ) E in E th ( T ) 1 d σ ( T ) d T .
T 0
d R / d T
1.24 × 10 3
n t ( T ) = L ln [ R ( T ) ] 2 l σ ( T ) .
n i
n f
n f ( T ) n i n t ( T ) ln [ n f ( T ) n i ( T ) ] = 0.
n f ( T ) = n t ( T ) W [ n i n t ( T ) e n i / n t ( T ) ] ,
E out ( T ) = V h ν γ ln [ R ( T ) ] L ln [ R ( T ) ] [ n i n f ( T ) ] ,
d R ( T ) d T = ξ ( T ) 1 ξ ( T ) R ( T ) L ln [ R ( T ) ] σ ( T ) d σ ( T ) d T ,
ξ ( T ) = W [ n i n t ( T ) e n i / n t ( T ) ] L { 1 + W [ n i n t ( T ) e n i / n t ( T ) ] }
n i
1.5 × 10 24     m 3
2.17 × 10 4
n i ( T ) = ln [ R AR R ( T ) ] 2 l σ ( T ) ,
R AR
d R ( T ) d T = R ( T ) ln [ R ( T ) ] σ ( T ) { L ln [ R ( T ) ] } W [ n i t ( T ) e n i t ( T ) ] n i t ( T ) ln [ R AR R ( T ) ] { W [ n i t ( T ) e n i t ( T ) ] + 1 } { L ln [ R ( T ) ] } n i t ( T ) [ n i t ( T ) 1 ] ln [ R ( T ) ] d σ ( T ) d T ,
n i t ( T )
n i t ( T ) = n i ( T ) n t ( T ) = ln [ R AR R ( T ) ] L - ln [ R ( T ) ] .
R AR
6.09 × 10 3
n i
n i ( T ) = 2 σ gs l s n 0 ln [ R ( T ) ] + L 2 l σ ( T ) .
E out ( T ) = V h ν γ { ln [ R ( T ) ] L ln [ R ( T ) ] } [ n i ( T ) n f ( T ) ] ,
n f ( T ) n i ( T ) n t ( T ) ln [ n f ( T ) n i ( T ) ] + l s γ l γ s n 0 { 1 [ n f ( T ) n i ( T ) ] α } = 0 ,
α = σ gs / σ γ
γ s
γ s = [ 1 σ e s σ gs ] 1 .
σ e s
σ gs
γ s
n t ( T ) = 2 σ e s l s n 0 ln [ R ( T ) ] + L 2 l σ ( T ) .
α > 10
n i > n f
= 1
n f ( T ) n i ( T ) n t ( T ) ln [ n f ( T ) n i ( T ) ] + l s γ l γ s n 0 = 0.
n f ( T ) = 2 σ e s l s n 0 ln [ R ( T ) ] + L 2 l σ ( T ) W [ X ( T ) ] ,
X ( T )
X ( T ) = 2 σ g s l s n 0 ln [ R ( T ) ] + L 2 σ e s l s n 0 ln [ R ( T ) ] + L × exp [ 2 σ g s l s n 0 ln [ R ( T ) ] + L 2 l σ ( T ) l s γ l γ s n 0 2 σ e s l s n 0 ln [ R ( T ) ] + L 2 l σ ( T ) ] .
d R ( T ) d T = 2 l σ ( T ) R ( T ) { L ln [ R ( T ) ] } ln [ R ( T ) ] { 2 σ g s l s n 0 ln [ R ( T ) ] + L 2 l σ ( T ) 2 + P ( T ) W [ X ( T ) ] } D ( T ) d σ ( T ) d T ,
D ( T ) = { L 2 + { 2 σ e s l s n 0 + ln [ R ( T ) ] } L + 2 { L ln [ R ( T ) ] } l O ( T ) σ ( T ) R ( T ) ln [ R ( T ) ] } × W [ X ( T ) ] L 2 + { 2 σ gs l s n 0 + ln [ R ( T ) ] } L ln [ R ( T ) ] 2 ,
O ( T ) = 1 2 l σ ( T ) R ( T ) + 2 γ s ( σ gs l s n 0 σ e s l s n 0 ) 2 { 2 σ gs l s n 0 ln [ R ( T ) ] + L } l s γ n 0 σ ( T ) { 1 + W [ X ( T ) ] } { 2 σ e s l s n 0 ln [ R ( T ) ] + L } { 2 σ gs l s n 0 ln [ R ( T ) ] + L } l γ s n 0 R ( T ) σ ( T ) ,
P ( T ) = { 2 σ g s l s n 0 ln [ R ( T ) ] + L 2 l σ ( T ) 1 1 + W [ X ( T ) ] l s γ l γ s n 0 } 1 σ ( T ) .
2.09 × 10 3
( T 0 )
R ( T 0 )
T 0
n 0
P out
P in

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