Abstract

Taking the improved SRS threshold formula into consideration, the power scaling of tandem-pumped Yb-doped silica fiber lasers and amplifiers is analyzed by new models. The results show that the power scaling of tandem-pumped Yb-doped fiber lasers and amplifiers is primarily limited by optical damage, SRS and thermal lens, while the pump brightness induced limitation is almost removed. It is also found that tandem-pumped Yb-doped fiber lasers and amplifiers, based upon state-of-art fiber technology, have the potential to achieve a power limit of 70.7 kW with a core diameter of 63.4 μm, and in the case of a strict single-mode fiber, the power limit is about 13.3 kW with a core numerical aperture of 0.03.

© 2011 OSA

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References

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  1. Y. Jeong, J. K. Sahu, D. N. Payne, and J. Nilsson, “Ytterbium-doped large-core fiber laser with 1.36 kW continuous-wave output power,” Opt. Express 12(25), 6088–6092 (2004).
    [CrossRef] [PubMed]
  2. J. Limpert, F. Röser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tünnermann, “The rising power of fiber lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 537–545 (2007).
    [CrossRef]
  3. Y. Jeong, A. J. Boyland, J. K. Sahu, S. Chung, J. Nilsson, and D. N. Payne, “Multi-kilowatt single-mode ytterbium-doped large-core fiber laser,” J. Opt. Soc. Korea 13(4), 416–422 (2009).
    [CrossRef]
  4. T. Ehrenreich, R. Leveille, I. Majid, and K. Tankala, “1 kW, all-glass Tm: fiber lasers,” presented at SPIE Photonics West 2010: Fiber Lasers VII: Technology, Systems and Applications, January 28, 2010.
  5. A. Tünnermann, T. Schreiber, and J. Limpert, “Fiber lasers and amplifiers: an ultrafast performance evolution,” Appl. Opt. 49(25), F71–F78 (2010).
    [CrossRef] [PubMed]
  6. D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber lasers: current status and future perspectives,” J. Opt. Soc. Am. B 27(11), B63–B92 (2010).
    [CrossRef]
  7. V. Fomin, M. Abramov, A. Ferin, A. Abramov, D. Mochalov, N. Platonov, and V. Gapontsev, “10 kW single-mode fiber laser,” presented at 5th International Symposium on High-Power Fiber Lasers and Their Applications, St. Petersburg, June 28-July 1, 2010.
  8. Y. Ma, X. Wang, J. Leng, H. Xiao, X. Dong, J. Zhu, W. Du, P. Zhou, X. Xu, L. Si, Z. Liu, and Y. Zhao, “Coherent beam combination of 1.08 kW fiber amplifier array using single frequency dithering technique,” Opt. Lett. 36(6), 951–953 (2011).
    [CrossRef] [PubMed]
  9. J. W. Dawson, M. J. Messerly, R. J. Beach, M. Y. Shverdin, E. A. Stappaerts, A. K. Sridharan, P. H. Pax, J. E. Heebner, C. W. Siders, and C. P. J. Barty, “Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power,” Opt. Express 16(17), 13240–13266 (2008).
    [CrossRef] [PubMed]
  10. J. W. Dawson, M. J. Messerly, J. E. Heebner, P. H. Paxa, A. K. Sridharana, A. L. Bullingtona, R. J. Beacha, C. W. Sidersa, C. P. J. Bartya, and M. Dubinskiib, “Power scaling analysis of fiber lasers and amplifiers based on nonsilica materials,” Proc. SPIE 7886, 1–12 (2010).
  11. C. A. Codemard, J. K. Sahu, and J. Nilsson, “Tandem cladding-pumping for control of excess gain in Ytterbium-Doped fiber amplifiers,” IEEE J. Quantum Electron. 46(12), 1860–1869 (2010).
    [CrossRef]
  12. C. Jauregui, J. Limpert, and A. Tünnermann, “On the Raman threshold of passive large mode area fibers,” Proc. SPIE 7914, 791408, 791408-6 (2011).
    [CrossRef]
  13. D. C. Brown and H. J. Hoffman, “Thermal, stress, and thermo-optic effects in high average power double-clad silica fiber lasers,” IEEE J. Quantum Electron. 37(2), 207–217 (2001).
    [CrossRef]
  14. H. Xiao, J. Leng, W. Wu, P. Zhou, X. Xu, and G. Zhao, “High efficiency tandem-pumped fiber amplifier,” Acta Phys. Sin (to be published).
  15. R. G. Smith, “Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and brillouin scattering,” Appl. Opt. 11(11), 2489–2494 (1972).
    [CrossRef] [PubMed]
  16. C. Jauregui, J. Limpert, and A. Tünnermann, “Derivation of Raman treshold formulas for CW double-clad fiber amplifiers,” Opt. Express 17(10), 8476–8490 (2009).
    [CrossRef] [PubMed]
  17. A. V. Smith, B. T. Do, G. R. Hadley, and R. L. Farrow, “Optical damage limits to pulse energy from fibers,” IEEE J. Sel. Top. Quantum Electron. 15(1), 153–158 (2009).
    [CrossRef]
  18. J. Hecht, “Fiber laser ramp up the power,” Laser Focus World 12, 52–57 (2009).

2011 (2)

2010 (4)

A. Tünnermann, T. Schreiber, and J. Limpert, “Fiber lasers and amplifiers: an ultrafast performance evolution,” Appl. Opt. 49(25), F71–F78 (2010).
[CrossRef] [PubMed]

D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber lasers: current status and future perspectives,” J. Opt. Soc. Am. B 27(11), B63–B92 (2010).
[CrossRef]

J. W. Dawson, M. J. Messerly, J. E. Heebner, P. H. Paxa, A. K. Sridharana, A. L. Bullingtona, R. J. Beacha, C. W. Sidersa, C. P. J. Bartya, and M. Dubinskiib, “Power scaling analysis of fiber lasers and amplifiers based on nonsilica materials,” Proc. SPIE 7886, 1–12 (2010).

C. A. Codemard, J. K. Sahu, and J. Nilsson, “Tandem cladding-pumping for control of excess gain in Ytterbium-Doped fiber amplifiers,” IEEE J. Quantum Electron. 46(12), 1860–1869 (2010).
[CrossRef]

2009 (4)

2008 (1)

2007 (1)

J. Limpert, F. Röser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tünnermann, “The rising power of fiber lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 537–545 (2007).
[CrossRef]

2004 (1)

2001 (1)

D. C. Brown and H. J. Hoffman, “Thermal, stress, and thermo-optic effects in high average power double-clad silica fiber lasers,” IEEE J. Quantum Electron. 37(2), 207–217 (2001).
[CrossRef]

1972 (1)

Barty, C. P. J.

Bartya, C. P. J.

J. W. Dawson, M. J. Messerly, J. E. Heebner, P. H. Paxa, A. K. Sridharana, A. L. Bullingtona, R. J. Beacha, C. W. Sidersa, C. P. J. Bartya, and M. Dubinskiib, “Power scaling analysis of fiber lasers and amplifiers based on nonsilica materials,” Proc. SPIE 7886, 1–12 (2010).

Beach, R. J.

Beacha, R. J.

J. W. Dawson, M. J. Messerly, J. E. Heebner, P. H. Paxa, A. K. Sridharana, A. L. Bullingtona, R. J. Beacha, C. W. Sidersa, C. P. J. Bartya, and M. Dubinskiib, “Power scaling analysis of fiber lasers and amplifiers based on nonsilica materials,” Proc. SPIE 7886, 1–12 (2010).

Boyland, A. J.

Brown, D. C.

D. C. Brown and H. J. Hoffman, “Thermal, stress, and thermo-optic effects in high average power double-clad silica fiber lasers,” IEEE J. Quantum Electron. 37(2), 207–217 (2001).
[CrossRef]

Bullingtona, A. L.

J. W. Dawson, M. J. Messerly, J. E. Heebner, P. H. Paxa, A. K. Sridharana, A. L. Bullingtona, R. J. Beacha, C. W. Sidersa, C. P. J. Bartya, and M. Dubinskiib, “Power scaling analysis of fiber lasers and amplifiers based on nonsilica materials,” Proc. SPIE 7886, 1–12 (2010).

Chung, S.

Clarkson, W. A.

Codemard, C. A.

C. A. Codemard, J. K. Sahu, and J. Nilsson, “Tandem cladding-pumping for control of excess gain in Ytterbium-Doped fiber amplifiers,” IEEE J. Quantum Electron. 46(12), 1860–1869 (2010).
[CrossRef]

Dawson, J. W.

J. W. Dawson, M. J. Messerly, J. E. Heebner, P. H. Paxa, A. K. Sridharana, A. L. Bullingtona, R. J. Beacha, C. W. Sidersa, C. P. J. Bartya, and M. Dubinskiib, “Power scaling analysis of fiber lasers and amplifiers based on nonsilica materials,” Proc. SPIE 7886, 1–12 (2010).

J. W. Dawson, M. J. Messerly, R. J. Beach, M. Y. Shverdin, E. A. Stappaerts, A. K. Sridharan, P. H. Pax, J. E. Heebner, C. W. Siders, and C. P. J. Barty, “Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power,” Opt. Express 16(17), 13240–13266 (2008).
[CrossRef] [PubMed]

Do, B. T.

A. V. Smith, B. T. Do, G. R. Hadley, and R. L. Farrow, “Optical damage limits to pulse energy from fibers,” IEEE J. Sel. Top. Quantum Electron. 15(1), 153–158 (2009).
[CrossRef]

Dong, X.

Du, W.

Dubinskiib, M.

J. W. Dawson, M. J. Messerly, J. E. Heebner, P. H. Paxa, A. K. Sridharana, A. L. Bullingtona, R. J. Beacha, C. W. Sidersa, C. P. J. Bartya, and M. Dubinskiib, “Power scaling analysis of fiber lasers and amplifiers based on nonsilica materials,” Proc. SPIE 7886, 1–12 (2010).

Eberhardt, R.

J. Limpert, F. Röser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tünnermann, “The rising power of fiber lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 537–545 (2007).
[CrossRef]

Farrow, R. L.

A. V. Smith, B. T. Do, G. R. Hadley, and R. L. Farrow, “Optical damage limits to pulse energy from fibers,” IEEE J. Sel. Top. Quantum Electron. 15(1), 153–158 (2009).
[CrossRef]

Hadley, G. R.

A. V. Smith, B. T. Do, G. R. Hadley, and R. L. Farrow, “Optical damage limits to pulse energy from fibers,” IEEE J. Sel. Top. Quantum Electron. 15(1), 153–158 (2009).
[CrossRef]

Hecht, J.

J. Hecht, “Fiber laser ramp up the power,” Laser Focus World 12, 52–57 (2009).

Heebner, J. E.

J. W. Dawson, M. J. Messerly, J. E. Heebner, P. H. Paxa, A. K. Sridharana, A. L. Bullingtona, R. J. Beacha, C. W. Sidersa, C. P. J. Bartya, and M. Dubinskiib, “Power scaling analysis of fiber lasers and amplifiers based on nonsilica materials,” Proc. SPIE 7886, 1–12 (2010).

J. W. Dawson, M. J. Messerly, R. J. Beach, M. Y. Shverdin, E. A. Stappaerts, A. K. Sridharan, P. H. Pax, J. E. Heebner, C. W. Siders, and C. P. J. Barty, “Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power,” Opt. Express 16(17), 13240–13266 (2008).
[CrossRef] [PubMed]

Hoffman, H. J.

D. C. Brown and H. J. Hoffman, “Thermal, stress, and thermo-optic effects in high average power double-clad silica fiber lasers,” IEEE J. Quantum Electron. 37(2), 207–217 (2001).
[CrossRef]

Jauregui, C.

C. Jauregui, J. Limpert, and A. Tünnermann, “On the Raman threshold of passive large mode area fibers,” Proc. SPIE 7914, 791408, 791408-6 (2011).
[CrossRef]

C. Jauregui, J. Limpert, and A. Tünnermann, “Derivation of Raman treshold formulas for CW double-clad fiber amplifiers,” Opt. Express 17(10), 8476–8490 (2009).
[CrossRef] [PubMed]

Jeong, Y.

Klingebiel, S.

J. Limpert, F. Röser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tünnermann, “The rising power of fiber lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 537–545 (2007).
[CrossRef]

Leng, J.

Limpert, J.

C. Jauregui, J. Limpert, and A. Tünnermann, “On the Raman threshold of passive large mode area fibers,” Proc. SPIE 7914, 791408, 791408-6 (2011).
[CrossRef]

A. Tünnermann, T. Schreiber, and J. Limpert, “Fiber lasers and amplifiers: an ultrafast performance evolution,” Appl. Opt. 49(25), F71–F78 (2010).
[CrossRef] [PubMed]

C. Jauregui, J. Limpert, and A. Tünnermann, “Derivation of Raman treshold formulas for CW double-clad fiber amplifiers,” Opt. Express 17(10), 8476–8490 (2009).
[CrossRef] [PubMed]

J. Limpert, F. Röser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tünnermann, “The rising power of fiber lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 537–545 (2007).
[CrossRef]

Liu, Z.

Ma, Y.

Messerly, M. J.

J. W. Dawson, M. J. Messerly, J. E. Heebner, P. H. Paxa, A. K. Sridharana, A. L. Bullingtona, R. J. Beacha, C. W. Sidersa, C. P. J. Bartya, and M. Dubinskiib, “Power scaling analysis of fiber lasers and amplifiers based on nonsilica materials,” Proc. SPIE 7886, 1–12 (2010).

J. W. Dawson, M. J. Messerly, R. J. Beach, M. Y. Shverdin, E. A. Stappaerts, A. K. Sridharan, P. H. Pax, J. E. Heebner, C. W. Siders, and C. P. J. Barty, “Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power,” Opt. Express 16(17), 13240–13266 (2008).
[CrossRef] [PubMed]

Nilsson, J.

Pax, P. H.

Paxa, P. H.

J. W. Dawson, M. J. Messerly, J. E. Heebner, P. H. Paxa, A. K. Sridharana, A. L. Bullingtona, R. J. Beacha, C. W. Sidersa, C. P. J. Bartya, and M. Dubinskiib, “Power scaling analysis of fiber lasers and amplifiers based on nonsilica materials,” Proc. SPIE 7886, 1–12 (2010).

Payne, D. N.

Peschel, T.

J. Limpert, F. Röser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tünnermann, “The rising power of fiber lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 537–545 (2007).
[CrossRef]

Richardson, D. J.

Röser, F.

J. Limpert, F. Röser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tünnermann, “The rising power of fiber lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 537–545 (2007).
[CrossRef]

Sahu, J. K.

Schreiber, T.

A. Tünnermann, T. Schreiber, and J. Limpert, “Fiber lasers and amplifiers: an ultrafast performance evolution,” Appl. Opt. 49(25), F71–F78 (2010).
[CrossRef] [PubMed]

J. Limpert, F. Röser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tünnermann, “The rising power of fiber lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 537–545 (2007).
[CrossRef]

Shverdin, M. Y.

Si, L.

Siders, C. W.

Sidersa, C. W.

J. W. Dawson, M. J. Messerly, J. E. Heebner, P. H. Paxa, A. K. Sridharana, A. L. Bullingtona, R. J. Beacha, C. W. Sidersa, C. P. J. Bartya, and M. Dubinskiib, “Power scaling analysis of fiber lasers and amplifiers based on nonsilica materials,” Proc. SPIE 7886, 1–12 (2010).

Smith, A. V.

A. V. Smith, B. T. Do, G. R. Hadley, and R. L. Farrow, “Optical damage limits to pulse energy from fibers,” IEEE J. Sel. Top. Quantum Electron. 15(1), 153–158 (2009).
[CrossRef]

Smith, R. G.

Sridharan, A. K.

Sridharana, A. K.

J. W. Dawson, M. J. Messerly, J. E. Heebner, P. H. Paxa, A. K. Sridharana, A. L. Bullingtona, R. J. Beacha, C. W. Sidersa, C. P. J. Bartya, and M. Dubinskiib, “Power scaling analysis of fiber lasers and amplifiers based on nonsilica materials,” Proc. SPIE 7886, 1–12 (2010).

Stappaerts, E. A.

Tünnermann, A.

C. Jauregui, J. Limpert, and A. Tünnermann, “On the Raman threshold of passive large mode area fibers,” Proc. SPIE 7914, 791408, 791408-6 (2011).
[CrossRef]

A. Tünnermann, T. Schreiber, and J. Limpert, “Fiber lasers and amplifiers: an ultrafast performance evolution,” Appl. Opt. 49(25), F71–F78 (2010).
[CrossRef] [PubMed]

C. Jauregui, J. Limpert, and A. Tünnermann, “Derivation of Raman treshold formulas for CW double-clad fiber amplifiers,” Opt. Express 17(10), 8476–8490 (2009).
[CrossRef] [PubMed]

J. Limpert, F. Röser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tünnermann, “The rising power of fiber lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 537–545 (2007).
[CrossRef]

Wang, X.

Wirth, C.

J. Limpert, F. Röser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tünnermann, “The rising power of fiber lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 537–545 (2007).
[CrossRef]

Xiao, H.

Xu, X.

Zhao, Y.

Zhou, P.

Zhu, J.

Appl. Opt. (2)

IEEE J. Quantum Electron. (2)

C. A. Codemard, J. K. Sahu, and J. Nilsson, “Tandem cladding-pumping for control of excess gain in Ytterbium-Doped fiber amplifiers,” IEEE J. Quantum Electron. 46(12), 1860–1869 (2010).
[CrossRef]

D. C. Brown and H. J. Hoffman, “Thermal, stress, and thermo-optic effects in high average power double-clad silica fiber lasers,” IEEE J. Quantum Electron. 37(2), 207–217 (2001).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

A. V. Smith, B. T. Do, G. R. Hadley, and R. L. Farrow, “Optical damage limits to pulse energy from fibers,” IEEE J. Sel. Top. Quantum Electron. 15(1), 153–158 (2009).
[CrossRef]

J. Limpert, F. Röser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tünnermann, “The rising power of fiber lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 537–545 (2007).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Opt. Soc. Korea (1)

Laser Focus World (1)

J. Hecht, “Fiber laser ramp up the power,” Laser Focus World 12, 52–57 (2009).

Opt. Express (3)

Opt. Lett. (1)

Proc. SPIE (2)

J. W. Dawson, M. J. Messerly, J. E. Heebner, P. H. Paxa, A. K. Sridharana, A. L. Bullingtona, R. J. Beacha, C. W. Sidersa, C. P. J. Bartya, and M. Dubinskiib, “Power scaling analysis of fiber lasers and amplifiers based on nonsilica materials,” Proc. SPIE 7886, 1–12 (2010).

C. Jauregui, J. Limpert, and A. Tünnermann, “On the Raman threshold of passive large mode area fibers,” Proc. SPIE 7914, 791408, 791408-6 (2011).
[CrossRef]

Other (3)

T. Ehrenreich, R. Leveille, I. Majid, and K. Tankala, “1 kW, all-glass Tm: fiber lasers,” presented at SPIE Photonics West 2010: Fiber Lasers VII: Technology, Systems and Applications, January 28, 2010.

V. Fomin, M. Abramov, A. Ferin, A. Abramov, D. Mochalov, N. Platonov, and V. Gapontsev, “10 kW single-mode fiber laser,” presented at 5th International Symposium on High-Power Fiber Lasers and Their Applications, St. Petersburg, June 28-July 1, 2010.

H. Xiao, J. Leng, W. Wu, P. Zhou, X. Xu, and G. Zhao, “High efficiency tandem-pumped fiber amplifier,” Acta Phys. Sin (to be published).

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Figures (6)

Fig. 1
Fig. 1

Dependence of the physical limits of tandem-pumped Yb-doped fiberlasers and amplifiers on the diameter and length of fiber. In cyan region the limit is optical damage, in red region the limit is thermal lens, in blue region the limit is SRS, and in yellow region the limit is pump brightness.

Fig. 2
Fig. 2

Boundary lines of physical limits of tandem-pumped Yb-doped fiber lasers and amplifiers.

Fig. 3
Fig. 3

Dependence of the power scaling of tandem-pumped Yb-doped fiber lasers and amplifiers on the core diameter.

Fig. 4
Fig. 4

Dependence of the strict single-mode power scaling of tandem-pumped Yb-doped fiber lasers and amplifiers on the core numerical aperture.

Fig. 5
Fig. 5

Dependence of the physical limits on the core diameter and length of fiber when using the traditional SRS threshold formula in the models.

Fig. 6
Fig. 6

Dependence of the power scaling on the core diameter and length of fiber when using the traditional SRS threshold formula in the models.

Equations (23)

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

P T F = 4 η l a s e r π R m L η h e a t ( 1 - a 2 2 b 2 )
P M C = 4 η l a s e r π k ( T m T c ) L η h e a t ( 1 + 2 k b h + 2 ln ( b a ) )
P T L = η l a s e r π k λ 2 L 2 η h e a t d n d T a 2
P S R S 16 A e f f g R L e f f
P S R S = 20.3 ln β + ln ( A e f f g R L e f f ) g R L e f f A e f f
A e f f = Γ 2 π a 2 L e f f G L ln ( G )
P S R S = [ 20.3 ln β + ln ( Γ 2 π a 2 g R G L / ln ( G ) ) ] g R L / ln ( G ) × ( Γ 2 π a 2 )
P O D = Γ 2 π a 2 I d a m a g e
P P B = η l a s e r I p u m p ( π b 2 ) ( π N A 2 )
( 20.3 ln β + ln ( Γ 2 π ln ( G ) g R G ) ) × a 4 L 2 + ln ( a 2 L ) × a 4 L 2 g R Γ 2 π ln ( G ) × η l a s e r π k λ 2 2 η h e a t d n d T = 0
P = 20.3 ln β + ln ( Γ 2 π ln ( G ) g R G ) , Q = g R Γ 2 π ln ( G ) × η l a s e r π k λ 2 2 η h e a t d n d T
P × a 4 L 2 + ln ( a 2 L ) × a 4 L 2 Q = 0
L S R S L e n s = a 2 exp { 1 2 × l a m b e r t w [ 2 × Q × exp ( 2 × P ) ] P } = a 2 5.03 × 10 11
P S R S L e n s = η l a s e r π k λ 2 2 η h e a t d n d T exp { 1 2 × l a m b e r t w [ 2 × Q × exp ( 2 × P ) ] P } = 70.7 k W
L S R S D a m a g e = a 2 exp { l a m b e r t w [ g R I d a m a g e ln ( G ) × a 2 × exp ( P ) ] P }
L D a m a g e L e n s = 2 η h e a t I d a m a g e Γ 2 d n d T η l a s e r k λ 2 × a 4
L D a m a g e P u m p = I d a m a g e Γ 2 A η l a s e r I p u m p π N A 2 α c o r e = 0.325 m
d P L = ( 8 k λ 2 A η h e a t I p u m p π N A 2 α c o r e d n d T ) 1 4 = 22.6 μ m
P D a m a g e L e n s = η l a s e r π k λ 2 L D a m a g e L e n s 2 η h e a t d n d T a 2
P D a m a g e P u m p = η l a s e r I p u m p π 2 ( N A ) 2 α c o r e A L D a m a g e P u m p a 2
P = { P P u m p D a m a g e P D a m a g e L e n s P S R S L e n s 0 d d P L d P L d d D S L d d D S L
d D S L = 2 g R I d a m a g e exp ( P ) exp { 1 2 × l a m b e r t w [ 2 × Q × exp ( 2 × P ) ] } × ln ( G ) × l a m b e r t w [ 2 × Q × exp ( 2 × P ) ] g R I d a m a g e exp ( P ) = 63.4 μ m
V = 2 π a ( N A c o r e ) λ < 2.405

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