Abstract

Rate-equation analysis has been used in an investigation of the role of saturation and excited-state absorption in the power transmission characteristics and thermal lensing of an absorber. Use of an iterative approach gives explicit analytical results for power transmission and thermal focal length in the presence of excited-state absorption. Sample calculations indicate that pump absorption can increase or decrease with increasing incident pump power, depending on the relative strength of the excited-state absorption cross section with respect to the ground-state absorption cross section. In the case of thermal lensing, results further indicate that saturation and excited-state absorption act as two competing effects, the former reducing the strength of the thermal lens and the latter causing the opposite effect. The analytical formulas derived in this analysis should prove useful to experimentalists in determination of ground-state and excited-state absorption cross sections from experimental power transmission and lensing data.

© 1999 Optical Society of America

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References

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  1. V. Petricevic, S. K. Gayen, R. R. Alfano, K. Yamagashi, H. Anzai, Y. Yamaguchi, “Laser action in chromium-doped forsterite,” Appl. Phys. Lett. 52, 1040–1042 (1988).
    [CrossRef]
  2. N. B. Angert, N. I. Borodin, V. M. Garmash, V. A. Zhitnyuk, A. G. Okhrimchuk, O. G. Siyuchenko, 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]
  3. C. Deka, B. H. T. Chai, Y. Shimony, X. X. Zhang, E. Munin, M. Bass, “Laser performance of Cr4+:Y2SiO5,” Appl. Phys. Lett. 61, 2141–2143 (1992).
    [CrossRef]
  4. V. Petricevic, A. B. Bykov, J. M. Evans, R. R. Alfano, “Room-temperature near-infrared tunable laser operation of Cr4+:Ca2GeO4,” Opt. Lett. 21, 1750–1752 (1996).
    [CrossRef]
  5. V. P. Mikhailov, N. I. Zhavoronkov, N. V. Kuleshov, A. S. Avtukh, V. G. Scherbitsky, “Saturation of visible absorption in chromium-doped silicates,” Opt. Quantum Electron. 27, 767–776 (1995).
    [CrossRef]
  6. Y. Shimony, Z. Burshtein, A. Ben-Amar Baranga, Y. Kalisky, 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]
  7. A. Sennaroglu, “Continuous-wave thermal loading in saturable absorbers: theory and experiment,” Appl. Opt. 36, 9528–9535 (1997).
    [CrossRef]
  8. K. V. Yumashev, N. V. Kuleshov, P. V. Prokoshin, A. M. Malyarevich, V. P. Mikhailov, “Excited-state absorption of Cr4+ ion in forsterite,” Appl. Phys. Lett. 70, 2523–2525 (1997).
    [CrossRef]
  9. Z. Burshtein, P. Blau, Y. Kalisky, Y. Shimony, M. R. Kokta, “Excited-state absorption studies of Cr4+ ions in several garnet host crystals,” IEEE J. Quantum Electron. 34, 292–299 (1998).
    [CrossRef]
  10. A. K. Cousins, “Temperature and thermal stress scaling in finite-length end-pumped laser rods,” IEEE J. Quantum Electron. 28, 1057–1069 (1992).
    [CrossRef]
  11. M. E. Innocenzi, H. T. Yura, C. L. Fincher, R. A. Fields, “Thermal modeling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56, 1831–1833 (1990).
    [CrossRef]

1998

Z. Burshtein, P. Blau, Y. Kalisky, Y. Shimony, M. R. Kokta, “Excited-state absorption studies of Cr4+ ions in several garnet host crystals,” IEEE J. Quantum Electron. 34, 292–299 (1998).
[CrossRef]

1997

K. V. Yumashev, N. V. Kuleshov, P. V. Prokoshin, A. M. Malyarevich, V. P. Mikhailov, “Excited-state absorption of Cr4+ ion in forsterite,” Appl. Phys. Lett. 70, 2523–2525 (1997).
[CrossRef]

A. Sennaroglu, “Continuous-wave thermal loading in saturable absorbers: theory and experiment,” Appl. Opt. 36, 9528–9535 (1997).
[CrossRef]

1996

V. Petricevic, A. B. Bykov, J. M. Evans, R. R. Alfano, “Room-temperature near-infrared tunable laser operation of Cr4+:Ca2GeO4,” Opt. Lett. 21, 1750–1752 (1996).
[CrossRef]

Y. Shimony, Z. Burshtein, A. Ben-Amar Baranga, Y. Kalisky, 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]

1995

V. P. Mikhailov, N. I. Zhavoronkov, N. V. Kuleshov, A. S. Avtukh, V. G. Scherbitsky, “Saturation of visible absorption in chromium-doped silicates,” Opt. Quantum Electron. 27, 767–776 (1995).
[CrossRef]

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]

C. Deka, B. H. T. Chai, Y. Shimony, X. X. Zhang, E. Munin, M. Bass, “Laser performance of Cr4+:Y2SiO5,” Appl. Phys. Lett. 61, 2141–2143 (1992).
[CrossRef]

1990

M. E. Innocenzi, H. T. Yura, C. L. Fincher, R. A. Fields, “Thermal modeling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56, 1831–1833 (1990).
[CrossRef]

1988

V. Petricevic, S. K. Gayen, R. R. Alfano, K. Yamagashi, H. Anzai, Y. Yamaguchi, “Laser action in chromium-doped forsterite,” Appl. Phys. Lett. 52, 1040–1042 (1988).
[CrossRef]

N. B. Angert, N. I. Borodin, V. M. Garmash, V. A. Zhitnyuk, A. G. Okhrimchuk, O. G. Siyuchenko, 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]

Alfano, R. R.

V. Petricevic, A. B. Bykov, J. M. Evans, R. R. Alfano, “Room-temperature near-infrared tunable laser operation of Cr4+:Ca2GeO4,” Opt. Lett. 21, 1750–1752 (1996).
[CrossRef]

V. Petricevic, S. K. Gayen, R. R. Alfano, K. Yamagashi, H. Anzai, Y. Yamaguchi, “Laser action in chromium-doped forsterite,” Appl. Phys. Lett. 52, 1040–1042 (1988).
[CrossRef]

Angert, N. B.

N. B. Angert, N. I. Borodin, V. M. Garmash, V. A. Zhitnyuk, A. G. Okhrimchuk, O. G. Siyuchenko, 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]

Anzai, H.

V. Petricevic, S. K. Gayen, R. R. Alfano, K. Yamagashi, H. Anzai, Y. Yamaguchi, “Laser action in chromium-doped forsterite,” Appl. Phys. Lett. 52, 1040–1042 (1988).
[CrossRef]

Avtukh, A. S.

V. P. Mikhailov, N. I. Zhavoronkov, N. V. Kuleshov, A. S. Avtukh, V. G. Scherbitsky, “Saturation of visible absorption in chromium-doped silicates,” Opt. Quantum Electron. 27, 767–776 (1995).
[CrossRef]

Bass, M.

C. Deka, B. H. T. Chai, Y. Shimony, X. X. Zhang, E. Munin, M. Bass, “Laser performance of Cr4+:Y2SiO5,” Appl. Phys. Lett. 61, 2141–2143 (1992).
[CrossRef]

Ben-Amar Baranga, A.

Y. Shimony, Z. Burshtein, A. Ben-Amar Baranga, Y. Kalisky, 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]

Blau, P.

Z. Burshtein, P. Blau, Y. Kalisky, Y. Shimony, M. R. Kokta, “Excited-state absorption studies of Cr4+ ions in several garnet host crystals,” IEEE J. Quantum Electron. 34, 292–299 (1998).
[CrossRef]

Borodin, N. I.

N. B. Angert, N. I. Borodin, V. M. Garmash, V. A. Zhitnyuk, A. G. Okhrimchuk, O. G. Siyuchenko, 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]

Burshtein, Z.

Z. Burshtein, P. Blau, Y. Kalisky, Y. Shimony, M. R. Kokta, “Excited-state absorption studies of Cr4+ ions in several garnet host crystals,” IEEE J. Quantum Electron. 34, 292–299 (1998).
[CrossRef]

Y. Shimony, Z. Burshtein, A. Ben-Amar Baranga, Y. Kalisky, 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]

Bykov, A. B.

Chai, B. H. T.

C. Deka, B. H. T. Chai, Y. Shimony, X. X. Zhang, E. Munin, M. Bass, “Laser performance of Cr4+:Y2SiO5,” Appl. Phys. Lett. 61, 2141–2143 (1992).
[CrossRef]

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]

Deka, C.

C. Deka, B. H. T. Chai, Y. Shimony, X. X. Zhang, E. Munin, M. Bass, “Laser performance of Cr4+:Y2SiO5,” Appl. Phys. Lett. 61, 2141–2143 (1992).
[CrossRef]

Evans, J. M.

Fields, R. A.

M. E. Innocenzi, H. T. Yura, C. L. Fincher, R. A. Fields, “Thermal modeling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56, 1831–1833 (1990).
[CrossRef]

Fincher, C. L.

M. E. Innocenzi, H. T. Yura, C. L. Fincher, R. A. Fields, “Thermal modeling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56, 1831–1833 (1990).
[CrossRef]

Garmash, V. M.

N. B. Angert, N. I. Borodin, V. M. Garmash, V. A. Zhitnyuk, A. G. Okhrimchuk, O. G. Siyuchenko, 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]

Gayen, S. K.

V. Petricevic, S. K. Gayen, R. R. Alfano, K. Yamagashi, H. Anzai, Y. Yamaguchi, “Laser action in chromium-doped forsterite,” Appl. Phys. Lett. 52, 1040–1042 (1988).
[CrossRef]

Innocenzi, M. E.

M. E. Innocenzi, H. T. Yura, C. L. Fincher, R. A. Fields, “Thermal modeling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56, 1831–1833 (1990).
[CrossRef]

Kalisky, Y.

Z. Burshtein, P. Blau, Y. Kalisky, Y. Shimony, M. R. Kokta, “Excited-state absorption studies of Cr4+ ions in several garnet host crystals,” IEEE J. Quantum Electron. 34, 292–299 (1998).
[CrossRef]

Y. Shimony, Z. Burshtein, A. Ben-Amar Baranga, Y. Kalisky, 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]

Kokta, M. R.

Z. Burshtein, P. Blau, Y. Kalisky, Y. Shimony, M. R. Kokta, “Excited-state absorption studies of Cr4+ ions in several garnet host crystals,” IEEE J. Quantum Electron. 34, 292–299 (1998).
[CrossRef]

Kuleshov, N. V.

K. V. Yumashev, N. V. Kuleshov, P. V. Prokoshin, A. M. Malyarevich, V. P. Mikhailov, “Excited-state absorption of Cr4+ ion in forsterite,” Appl. Phys. Lett. 70, 2523–2525 (1997).
[CrossRef]

V. P. Mikhailov, N. I. Zhavoronkov, N. V. Kuleshov, A. S. Avtukh, V. G. Scherbitsky, “Saturation of visible absorption in chromium-doped silicates,” Opt. Quantum Electron. 27, 767–776 (1995).
[CrossRef]

Malyarevich, A. M.

K. V. Yumashev, N. V. Kuleshov, P. V. Prokoshin, A. M. Malyarevich, V. P. Mikhailov, “Excited-state absorption of Cr4+ ion in forsterite,” Appl. Phys. Lett. 70, 2523–2525 (1997).
[CrossRef]

Mikhailov, V. P.

K. V. Yumashev, N. V. Kuleshov, P. V. Prokoshin, A. M. Malyarevich, V. P. Mikhailov, “Excited-state absorption of Cr4+ ion in forsterite,” Appl. Phys. Lett. 70, 2523–2525 (1997).
[CrossRef]

V. P. Mikhailov, N. I. Zhavoronkov, N. V. Kuleshov, A. S. Avtukh, V. G. Scherbitsky, “Saturation of visible absorption in chromium-doped silicates,” Opt. Quantum Electron. 27, 767–776 (1995).
[CrossRef]

Munin, E.

C. Deka, B. H. T. Chai, Y. Shimony, X. X. Zhang, E. Munin, M. Bass, “Laser performance of Cr4+:Y2SiO5,” Appl. Phys. Lett. 61, 2141–2143 (1992).
[CrossRef]

Okhrimchuk, A. G.

N. B. Angert, N. I. Borodin, V. M. Garmash, V. A. Zhitnyuk, A. G. Okhrimchuk, O. G. Siyuchenko, 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]

Petricevic, V.

V. Petricevic, A. B. Bykov, J. M. Evans, R. R. Alfano, “Room-temperature near-infrared tunable laser operation of Cr4+:Ca2GeO4,” Opt. Lett. 21, 1750–1752 (1996).
[CrossRef]

V. Petricevic, S. K. Gayen, R. R. Alfano, K. Yamagashi, H. Anzai, Y. Yamaguchi, “Laser action in chromium-doped forsterite,” Appl. Phys. Lett. 52, 1040–1042 (1988).
[CrossRef]

Prokoshin, P. V.

K. V. Yumashev, N. V. Kuleshov, P. V. Prokoshin, A. M. Malyarevich, V. P. Mikhailov, “Excited-state absorption of Cr4+ ion in forsterite,” Appl. Phys. Lett. 70, 2523–2525 (1997).
[CrossRef]

Scherbitsky, V. G.

V. P. Mikhailov, N. I. Zhavoronkov, N. V. Kuleshov, A. S. Avtukh, V. G. Scherbitsky, “Saturation of visible absorption in chromium-doped silicates,” Opt. Quantum Electron. 27, 767–776 (1995).
[CrossRef]

Sennaroglu, A.

Shestakov, A. V.

N. B. Angert, N. I. Borodin, V. M. Garmash, V. A. Zhitnyuk, A. G. Okhrimchuk, O. G. Siyuchenko, 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]

Shimony, Y.

Z. Burshtein, P. Blau, Y. Kalisky, Y. Shimony, M. R. Kokta, “Excited-state absorption studies of Cr4+ ions in several garnet host crystals,” IEEE J. Quantum Electron. 34, 292–299 (1998).
[CrossRef]

Y. Shimony, Z. Burshtein, A. Ben-Amar Baranga, Y. Kalisky, 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]

C. Deka, B. H. T. Chai, Y. Shimony, X. X. Zhang, E. Munin, M. Bass, “Laser performance of Cr4+:Y2SiO5,” Appl. Phys. Lett. 61, 2141–2143 (1992).
[CrossRef]

Siyuchenko, O. G.

N. B. Angert, N. I. Borodin, V. M. Garmash, V. A. Zhitnyuk, A. G. Okhrimchuk, O. G. Siyuchenko, 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]

Strauss, M.

Y. Shimony, Z. Burshtein, A. Ben-Amar Baranga, Y. Kalisky, 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]

Yamagashi, K.

V. Petricevic, S. K. Gayen, R. R. Alfano, K. Yamagashi, H. Anzai, Y. Yamaguchi, “Laser action in chromium-doped forsterite,” Appl. Phys. Lett. 52, 1040–1042 (1988).
[CrossRef]

Yamaguchi, Y.

V. Petricevic, S. K. Gayen, R. R. Alfano, K. Yamagashi, H. Anzai, Y. Yamaguchi, “Laser action in chromium-doped forsterite,” Appl. Phys. Lett. 52, 1040–1042 (1988).
[CrossRef]

Yumashev, K. V.

K. V. Yumashev, N. V. Kuleshov, P. V. Prokoshin, A. M. Malyarevich, V. P. Mikhailov, “Excited-state absorption of Cr4+ ion in forsterite,” Appl. Phys. Lett. 70, 2523–2525 (1997).
[CrossRef]

Yura, H. T.

M. E. Innocenzi, H. T. Yura, C. L. Fincher, R. A. Fields, “Thermal modeling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56, 1831–1833 (1990).
[CrossRef]

Zhang, X. X.

C. Deka, B. H. T. Chai, Y. Shimony, X. X. Zhang, E. Munin, M. Bass, “Laser performance of Cr4+:Y2SiO5,” Appl. Phys. Lett. 61, 2141–2143 (1992).
[CrossRef]

Zhavoronkov, N. I.

V. P. Mikhailov, N. I. Zhavoronkov, N. V. Kuleshov, A. S. Avtukh, V. G. Scherbitsky, “Saturation of visible absorption in chromium-doped silicates,” Opt. Quantum Electron. 27, 767–776 (1995).
[CrossRef]

Zhitnyuk, V. A.

N. B. Angert, N. I. Borodin, V. M. Garmash, V. A. Zhitnyuk, A. G. Okhrimchuk, O. G. Siyuchenko, 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]

Appl. Opt.

Appl. Phys. Lett.

C. Deka, B. H. T. Chai, Y. Shimony, X. X. Zhang, E. Munin, M. Bass, “Laser performance of Cr4+:Y2SiO5,” Appl. Phys. Lett. 61, 2141–2143 (1992).
[CrossRef]

K. V. Yumashev, N. V. Kuleshov, P. V. Prokoshin, A. M. Malyarevich, V. P. Mikhailov, “Excited-state absorption of Cr4+ ion in forsterite,” Appl. Phys. Lett. 70, 2523–2525 (1997).
[CrossRef]

V. Petricevic, S. K. Gayen, R. R. Alfano, K. Yamagashi, H. Anzai, Y. Yamaguchi, “Laser action in chromium-doped forsterite,” Appl. Phys. Lett. 52, 1040–1042 (1988).
[CrossRef]

M. E. Innocenzi, H. T. Yura, C. L. Fincher, R. A. Fields, “Thermal modeling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56, 1831–1833 (1990).
[CrossRef]

IEEE J. Quantum Electron.

Z. Burshtein, P. Blau, Y. Kalisky, Y. Shimony, M. R. Kokta, “Excited-state absorption studies of Cr4+ ions in several garnet host crystals,” IEEE J. Quantum Electron. 34, 292–299 (1998).
[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]

Y. Shimony, Z. Burshtein, A. Ben-Amar Baranga, Y. Kalisky, 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]

Opt. Lett.

Opt. Quantum Electron.

V. P. Mikhailov, N. I. Zhavoronkov, N. V. Kuleshov, A. S. Avtukh, V. G. Scherbitsky, “Saturation of visible absorption in chromium-doped silicates,” Opt. Quantum Electron. 27, 767–776 (1995).
[CrossRef]

Sov. J. Quantum Electron.

N. B. Angert, N. I. Borodin, V. M. Garmash, V. A. Zhitnyuk, A. G. Okhrimchuk, O. G. Siyuchenko, 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]

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Figures (4)

Fig. 1
Fig. 1

Energy-level diagram of a saturable absorber subject to excited-state absorption.

Fig. 2
Fig. 2

Variation of the cw power transmission as a function of incident pump power P i for various values of f p .

Fig. 3
Fig. 3

Variation of the transmission correction factor τ* as a function of the incident pump power P i for various values of f p .

Fig. 4
Fig. 4

Variation of the pump-induced thermal focal length as a function of the incident pump power P i for two values of f p .

Tables (1)

Tables Icon

Table 1 Values of Fixed Material Parameters Used in the Power Transmission and Thermal Lensing Calculations

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

dN2dt=σaIphνp Ng-σesaIphνp N2-N2τf-σeILhνL,
1IpdIpdz=-αp01+2fpIp/Isa1+1+fpIp/Isa=-αp,
Ip0, z=δsaIsa exp-αp1z.
αp1=αp01+2fδsi1+1+fδsi,
δsa=2Piπωp2z1Isa.
τP=exp-αp0L0×1+δsa1+fpexp-αp1L01+δsa1+fpfp-1fp+11+δsi1+fp1+2fpδsi.
hr, z=ηHαpr, zIpr, z,
Tr, z=T1z-T2zr2+Or4.
T2z=h0, z4κ.
1fT=nT2κ0L0dzh0, z,
1fT=nTηT2κ1+δsi1+fp1+2fpδsiδsaIsa1-fpδsa1+fp2×ln1+δsa1+fp1+δsa1+fpexp-αp1L0+2fp1+fp×1-exp(-αp1L0.

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