Abstract

Theoretical and experimental results of a study that investigates cw thermal loading in solid-state saturable absorbers with low heat conductivities are presented. In addition to the temperature dependence of the refractive index, the proposed model considers the temperature dependence of the fluorescence lifetime to account for the local variations in the saturation intensity resulting from thermal gradients. In the calculations an iterative scheme is employed to calculate first the temperature distribution produced by the pump beam subject to saturable absorption with a constant saturation intensity and then the resulting modifications in the propagation parameters that are due to the presence of the calculated temperature distribution. Excellent agreement is obtained between the numerically calculated results and experimentally measured cw transmission data obtained with use of a Cr:YAG saturable absorber. Because the absorption cross section of the medium is used as one of the fitting parameters to yield the best fit between theory and experiment, the model further offers an accurate method whereby the cw power transmission data can be used to determine the absorption cross section of a saturable absorber subject to thermal loading.

© 1997 Optical Society of America

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References

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    [CrossRef]
  10. A. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 293.
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    [CrossRef]

1997

1996

1995

1994

1993

1992

A. K. Cousins, “Temperature and thermal stress scaling in finite-length end-pumped laser rods,” IEEE J. Quantum Electron. 28, 1057–1069 (1992).
[CrossRef]

1988

N. B. Angert, N. I. Borodin, V. M. Garmash, V. A. Zhitnyuk, A. G. Okhrimchuk, O. G. Siyuchenko, and A. V. Shestakov, “Lasing due to impurity color centers in yttrium aluminum garnet crystals at wavelengths in the range 1.35–1.45 μm,” Sov. J. Quantum Electron. 18, 73–74 (1988).
[CrossRef]

Angert, N. B.

N. B. Angert, N. I. Borodin, V. M. Garmash, V. A. Zhitnyuk, A. G. Okhrimchuk, O. G. Siyuchenko, and A. V. Shestakov, “Lasing due to impurity color centers in yttrium aluminum garnet crystals at wavelengths in the range 1.35–1.45 μm,” Sov. J. Quantum Electron. 18, 73–74 (1988).
[CrossRef]

Askar, A.

Atay, F. M.

Ben-Amar Baranga, A.

Y. Shimony, Z. Burshtein, A. Ben-Amar Baranga, Y. Kalisky, and M. Strauss, “Repetitive Q-switching of a cw Nd:YAG laser using Cr4+:YAG saturable absorbers,” IEEE J. Quantum Electron. 32, 305–310 (1996).
[CrossRef]

Bergman, K.

Borodin, N. I.

N. B. Angert, N. I. Borodin, V. M. Garmash, V. A. Zhitnyuk, A. G. Okhrimchuk, O. G. Siyuchenko, and A. V. Shestakov, “Lasing due to impurity color centers in yttrium aluminum garnet crystals at wavelengths in the range 1.35–1.45 μm,” Sov. J. Quantum Electron. 18, 73–74 (1988).
[CrossRef]

Brignon, A.

Burshtein, Z.

Y. Shimony, Z. Burshtein, A. Ben-Amar Baranga, Y. Kalisky, and M. Strauss, “Repetitive Q-switching of a cw Nd:YAG laser using Cr4+:YAG saturable absorbers,” IEEE J. Quantum Electron. 32, 305–310 (1996).
[CrossRef]

Chai, B. H. T.

Collings, B. C.

Cousins, A. K.

A. K. Cousins, “Temperature and thermal stress scaling in finite-length end-pumped laser rods,” IEEE J. Quantum Electron. 28, 1057–1069 (1992).
[CrossRef]

Cunningham, J. E.

French, P. M. W.

Garmash, V. M.

N. B. Angert, N. I. Borodin, V. M. Garmash, V. A. Zhitnyuk, A. G. Okhrimchuk, O. G. Siyuchenko, and A. V. Shestakov, “Lasing due to impurity color centers in yttrium aluminum garnet crystals at wavelengths in the range 1.35–1.45 μm,” Sov. J. Quantum Electron. 18, 73–74 (1988).
[CrossRef]

Huignard, J.-P.

Jan, W. Y.

Kalisky, Y.

Y. Shimony, Z. Burshtein, A. Ben-Amar Baranga, Y. Kalisky, and M. Strauss, “Repetitive Q-switching of a cw Nd:YAG laser using Cr4+:YAG saturable absorbers,” IEEE J. Quantum Electron. 32, 305–310 (1996).
[CrossRef]

Knox, W. H.

Nathel, H.

Okhrimchuk, A. G.

N. B. Angert, N. I. Borodin, V. M. Garmash, V. A. Zhitnyuk, A. G. Okhrimchuk, O. G. Siyuchenko, and A. V. Shestakov, “Lasing due to impurity color centers in yttrium aluminum garnet crystals at wavelengths in the range 1.35–1.45 μm,” Sov. J. Quantum Electron. 18, 73–74 (1988).
[CrossRef]

Pathak, R.

Pollock, C. R.

Rizvi, N. H.

Sennaroglu, A.

Shestakov, A. V.

Shimony, Y.

Y. Shimony, Z. Burshtein, A. Ben-Amar Baranga, Y. Kalisky, and M. Strauss, “Repetitive Q-switching of a cw Nd:YAG laser using Cr4+:YAG saturable absorbers,” IEEE J. Quantum Electron. 32, 305–310 (1996).
[CrossRef]

Siegman, A.

A. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 293.

Siyuchenko, O. G.

N. B. Angert, N. I. Borodin, V. M. Garmash, V. A. Zhitnyuk, A. G. Okhrimchuk, O. G. Siyuchenko, and A. V. Shestakov, “Lasing due to impurity color centers in yttrium aluminum garnet crystals at wavelengths in the range 1.35–1.45 μm,” Sov. J. Quantum Electron. 18, 73–74 (1988).
[CrossRef]

Stark, J. B.

Strauss, M.

Y. Shimony, Z. Burshtein, A. Ben-Amar Baranga, Y. Kalisky, and M. Strauss, “Repetitive Q-switching of a cw Nd:YAG laser using Cr4+:YAG saturable absorbers,” IEEE J. Quantum Electron. 32, 305–310 (1996).
[CrossRef]

Sutherland, J. M.

Taylor, J. R.

Tong, Y. P.

Tsuda, S.

Zhitnyuk, V. A.

N. B. Angert, N. I. Borodin, V. M. Garmash, V. A. Zhitnyuk, A. G. Okhrimchuk, O. G. Siyuchenko, and A. V. Shestakov, “Lasing due to impurity color centers in yttrium aluminum garnet crystals at wavelengths in the range 1.35–1.45 μm,” Sov. J. Quantum Electron. 18, 73–74 (1988).
[CrossRef]

IEEE J. Quantum Electron.

Y. Shimony, Z. Burshtein, A. Ben-Amar Baranga, Y. Kalisky, and M. Strauss, “Repetitive Q-switching of a cw Nd:YAG laser using Cr4+:YAG saturable absorbers,” IEEE J. Quantum Electron. 32, 305–310 (1996).
[CrossRef]

A. K. Cousins, “Temperature and thermal stress scaling in finite-length end-pumped laser rods,” IEEE J. Quantum Electron. 28, 1057–1069 (1992).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Sov. J. Quantum Electron.

N. B. Angert, N. I. Borodin, V. M. Garmash, V. A. Zhitnyuk, A. G. Okhrimchuk, O. G. Siyuchenko, and A. V. Shestakov, “Lasing due to impurity color centers in yttrium aluminum garnet crystals at wavelengths in the range 1.35–1.45 μm,” Sov. J. Quantum Electron. 18, 73–74 (1988).
[CrossRef]

Other

A. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 293.

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Figures (10)

Fig. 1
Fig. 1

Measured variation of the fluorescence lifetime as a function of the crystal temperature for a Cr:YAG saturable absorber between 5 and 50 °C. The line is the best linear fit to the data.

Fig. 2
Fig. 2

Calculated variation of h(r, z) and h a (r, z) as a function of r at z = 1 cm for P i = 3.94 W, T b = 21 °C, z f = 0.2 cm, α0 = 1.48 cm-1, and σ a = 5.8 × 10-19 cm2.

Fig. 3
Fig. 3

Calculated variation of T(r, z) as a function of r at z = 1 cm for T b = 21 °C, z f = 0.2 cm, α0 = 1.48 cm-1, σ a = 5.8 × 10-19 cm2, and different levels of the incident pump power P i .

Fig. 4
Fig. 4

Calculated variation of the axial temperature distribution T 1 (z) between z = 0 and z = 2 cm for T b = 21 °C, z f = 0.2 cm, α0 = 1.48 cm-1, σ a = 5.8 × 10-19 cm2, and different levels of the incident pump power P i .

Fig. 5
Fig. 5

Calculated variation of the thermally loaded spot-size function ω T (z) between z = 0 and z = 2 cm for T b = 21 °C, z f = 0.2 cm, α0 = 1.48 cm-1, σ a = 5.8 × 10-19 cm2, and different levels of the incident pump power P i .

Fig. 6
Fig. 6

Schematic of the experimental setup used to measure the thermal lifetime coefficients and cw power transmission with the Cr:YAG crystal.

Fig. 7
Fig. 7

Time-resolved fluorescence intensity for Cr:YAG at 20 °C. The crystal is excited with 150-ns Nd:YAG pulses at 1.06 µm.

Fig. 8
Fig. 8

Measured and calculated variation of crystal transmission τP as a function of the crystal boundary temperature T b for P i = 3.94 W and z f = 0.2 cm.

Fig. 9
Fig. 9

Measured and calculated variation of the crystal transmission τ P as a function of the unperturbed beam focus location z f for P i = 3.92 W and T b = 21 °C.

Fig. 10
Fig. 10

Measured and calculated variation of the crystal transmission τ P as a function of the incident pump power P i for z f = 0.2 cm and T b = 21 °C.

Tables (1)

Tables Icon

Table 1 Representative Values of the Thermal and Optical Parameters Used to Characterize Cr:YAG Saturable Absorbers

Equations (40)

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Is=hν/σaτf,
2Ex+k2Ex=0.
k=k0n-iα2k0.
n=n0+nTT-Tr0,
α=α0+αTT-Tr11+I/Is,
τf=τf0-τfTT-Tr2.
Tr, z=T1z-T2zr2,
nr, z=n0+n1z+n2zr2,
αr, z=α1z+α2zr2.
k2r,z=kc21+κ1z+κ2zr2+Or4
κ1z=2n1zn0-iα1zkc,
κ2z=2n2zn0-iα2zkc.
Exr,z=E0 exp-iPz+kc2uzduzdzr2×exp-ikcz
dPdz=-iqz+kc2 κ1z
d2udz2-κ2zu=0.
ωTz=1Im-kc2uzdudz1/2.
u0z=z-zf+iz0,
I0r, z=2Piπω2zexp-2r2ωz2exp-α0z.
ωz=ω01+z-zfz021/2.
z0=nπω02λ.
δsa=2Piπω2zIs,
αr, z=α01+δsa exp-α01+δsi z-2rωz2,
δsi=2Piπω20Is.
Ir, z=2Piπω2zexp-α0z×1+δsa1+δsa exp-α0z1+δsi1+δsi exp-2r2ω2z.
1ydydζ=-11+δy,
yζ=exp-ζ1+δ1+δ exp-ζ1+δ1+δ.
1rdrrTr, zr=-hr, zκ,
hr, z=αr, zIr, z.
T2z=h0, z4κ.
h0z=h0, z,
whz=ωz2ln2+I0, zIs1/2.
T1z=Tb+h0zwhz24κ1+2 lnr0whz.
α1z=α01+δs0 exp-αz1+τfTτf0T1z-Tr2×δs0 exp-αz1+δs0 exp-αz,
α2z=-α0δs0 exp-αz1+δs0 exp-αz2-2ω2z+τfTτf0×T2z+2T1z-Tr2ω2z,
n1z=nTT1z-Tr0,
n2z=-T2znT.
u0=-zf+iz0, dudzz=0=1.
τP=ωT2LωT20u02uL2exp2 ImP2L-P20,
P2z=0zdzkc2κ1z
σa=σa0-σaTT,

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