Abstract

The Energy Transfer Upconversion (ETU) macroparameter is measured for Nd-doped GdVO4 and YVO4 samples at temperatures ranging from Room Temperature (RT) to 450K, by means of a simple and automated z-scan technique. Furthermore, the ground state absorption cross section into the 2H9/2 + 4F5/2 energy levels is characterised for both crystals over the same range of temperatures. The 808 nm π-polarisation absorption cross section is found to decrease from (58.6 ± 0.2) pm2 to (30.9 ± 0.6) pm2 for Nd:YVO4 and (54.0 ± 0.3) pm2 to (25.7 ± 0.5) pm2 for Nd:GdVO4, from RT to 450K. Over the same range the ETU coefficient decreases from (3.2 ± 0.7) 10−16 cm3/s to (1.8 ± 0.4 10−16 cm3/s and (5.0 ± 0.5) 10−16 cm3/s to (3.4±0.2) 10−16 cm3/s for 0.6 at. % and 1 at. % Nd:YVO4 respectively, and (3.3 ± 0.5) 10−16 cm3/s to (0.8 ± 0.2) 10−16 cm3/s and (5.5 ± 0.5) 10−16 cm3/s to (3.1 ± 0.3) 10−16 cm3/s for 0.5 at.% and 1.1 at.% Nd:GdVO4.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Full Article  |  PDF Article
OSA Recommended Articles
Concentration dependence of energy transfer upconversion in Nd:YAG

S. J. Yoon, R. P. Yan, S. J. Beecher, and J. I. Mackenzie
Opt. Mater. Express 5(5) 926-931 (2015)

Improvement of passive Q-switching performance reached with a new Nd-doped mixed vanadate crystal Nd:Gd0.64Y0.36VO4

Junhai Liu, Zhengping Wang, Xianlin Meng, Zongshu Shao, Bernd Ozygus, Adalbert Ding, and Horst Weber
Opt. Lett. 28(23) 2330-2332 (2003)

Influence of energy-transfer upconversion and excited-state absorption on a high power Nd:YVO4 laser at 1.34 μm

Yayun Ma, Yuanji Li, Jinxia Feng, and Kuanshou Zhang
Opt. Express 26(9) 12106-12120 (2018)

References

  • View by:
  • |
  • |
  • |

  1. T. Y. Fan and R. L. Byer, “Modeling and CW Operation of a Quasi-Three-Level 946 nm Nd:YAG Laser,” IEEE J. Quantum Electron. 23(5), 605–612 (1987).
    [Crossref]
  2. W. P. Risk, “Modeling of longitudinally pumped solid-state lasers exhibiting reabsorption losses,” J. Opt. Soc. Am. B 5(7), 1412–1423(1988).
    [Crossref]
  3. S. Bjurshagen and R. Koch, “Modeling of Energy-Transfer Upconversion and Thermal Effects in End-Pumped Quasi-Three-Level Lasers,” Appl. Opt. 43(24), 4753–4767 (2004).
    [Crossref] [PubMed]
  4. V. Ostroumov, T. Jensen, J.-P. Meyn, G. Huber, and M. A. Noginov, “Study of luminescence concentration quenching and energy transfer upconversion in Nd-doped LaSc3(BO3)4 and GdVO4 laser crystals,” J. Opt. Soc. Am. B 15(3), 1025–1060 (1998).
    [Crossref]
  5. Y. F. Chen, C. C. Liao, Y. P. Lan, and S. C. Wang, “Determination of the Auger upconversion rate in fiber-coupled diode end-pumped Nd:YAG and Nd:YVO4 crystals,” Appl. Phys. B 70(4), 487–490 (2000).
    [Crossref]
  6. R. Yan, S. J. Yoon, S. J. Beecher, and J. I. Mackenzie, “Measuring the elevated temperature dependence of upconversion in Nd:YAG,” IEEE J. Sel. Top. Quantum Electron. 21(1), 1–7 (2015).
  7. Y. Sato and T. Taira, “Temperature dependencies of stimulated emission cross section for Nd-doped solid-state laser materials,” Opt. Mater. Express 2(8), 1076–1087 (2012).
    [Crossref]
  8. J. O. White and C. E. Mungan, “Measurement of up-conversion in Er:YAG via z-scan,” J. Opt. Soc. Am. B 28(10), 2358–2361 (2011).
    [Crossref]
  9. S. J. Yoon, R. P. Yan, S. J. Beecher, and J. I. Mackenzie, “Concentration dependence of energy transfer upconversion in Nd:YAG,” Opt. Mater. Express 5(5), 926–931 (2015).
    [Crossref]
  10. W. J. Lima, V. M. Martins, A. F. G. Monte, D. N. Messias, N. O. Dantas, M. J. V. Bell, and T. Catunda, “Energy transfer upconversion on neodymium doped phosphate glasses investigated by Z-scan technique,” Opt. Mater. Express 35(9), 1724–1727 (2013).
    [Crossref]
  11. S. Goldring, R. Lavi, and V. Lupei, “Decay dynamics of excited Nd3+ ions in YVO4 following weak excitation,” IEEE J. Quantum Electron.  46(2), 169–181 (2010).
    [Crossref]
  12. S. Guy, C. L. Bonner, D. P. Shepherd, D. C. Hanna, A. C. Tropper, and B. Ferrand, “High-inversion densities in Nd:YAG: up-conversion and bleaching,” IEEE J. Quantum Electron. 34(5), 900–909 (1998).
    [Crossref]
  13. C. Czeranowsky, “Resonatorinterne Frequenzverdopplung von diodengepumpten Neodym-Lasern mit hohen Ausgangsleistungen im blauen Spektralbereich,” Dissertation, Universitat Hamburg (2002).
  14. J. W. Kim, J. I. Mackenzie, and W. A. Clarkson, “Influence of energy-transfer-upconversion on threshold pump power in quasi-three-level solid-state lasers,” Opt. Express 17(14), 11935–11943 (2009).
    [Crossref] [PubMed]
  15. D. C. Brown, R. Nelson, and L. Billings, “End-cooled Nd:YVO4 Diode-pumped Laser,” Appl. Opt.  36(33), 2–4 (1991).

2015 (2)

S. J. Yoon, R. P. Yan, S. J. Beecher, and J. I. Mackenzie, “Concentration dependence of energy transfer upconversion in Nd:YAG,” Opt. Mater. Express 5(5), 926–931 (2015).
[Crossref]

R. Yan, S. J. Yoon, S. J. Beecher, and J. I. Mackenzie, “Measuring the elevated temperature dependence of upconversion in Nd:YAG,” IEEE J. Sel. Top. Quantum Electron. 21(1), 1–7 (2015).

2013 (1)

W. J. Lima, V. M. Martins, A. F. G. Monte, D. N. Messias, N. O. Dantas, M. J. V. Bell, and T. Catunda, “Energy transfer upconversion on neodymium doped phosphate glasses investigated by Z-scan technique,” Opt. Mater. Express 35(9), 1724–1727 (2013).
[Crossref]

2012 (1)

2011 (1)

2010 (1)

S. Goldring, R. Lavi, and V. Lupei, “Decay dynamics of excited Nd3+ ions in YVO4 following weak excitation,” IEEE J. Quantum Electron.  46(2), 169–181 (2010).
[Crossref]

2009 (1)

2004 (1)

2000 (1)

Y. F. Chen, C. C. Liao, Y. P. Lan, and S. C. Wang, “Determination of the Auger upconversion rate in fiber-coupled diode end-pumped Nd:YAG and Nd:YVO4 crystals,” Appl. Phys. B 70(4), 487–490 (2000).
[Crossref]

1998 (2)

V. Ostroumov, T. Jensen, J.-P. Meyn, G. Huber, and M. A. Noginov, “Study of luminescence concentration quenching and energy transfer upconversion in Nd-doped LaSc3(BO3)4 and GdVO4 laser crystals,” J. Opt. Soc. Am. B 15(3), 1025–1060 (1998).
[Crossref]

S. Guy, C. L. Bonner, D. P. Shepherd, D. C. Hanna, A. C. Tropper, and B. Ferrand, “High-inversion densities in Nd:YAG: up-conversion and bleaching,” IEEE J. Quantum Electron. 34(5), 900–909 (1998).
[Crossref]

1991 (1)

D. C. Brown, R. Nelson, and L. Billings, “End-cooled Nd:YVO4 Diode-pumped Laser,” Appl. Opt.  36(33), 2–4 (1991).

1988 (1)

1987 (1)

T. Y. Fan and R. L. Byer, “Modeling and CW Operation of a Quasi-Three-Level 946 nm Nd:YAG Laser,” IEEE J. Quantum Electron. 23(5), 605–612 (1987).
[Crossref]

Beecher, S. J.

R. Yan, S. J. Yoon, S. J. Beecher, and J. I. Mackenzie, “Measuring the elevated temperature dependence of upconversion in Nd:YAG,” IEEE J. Sel. Top. Quantum Electron. 21(1), 1–7 (2015).

S. J. Yoon, R. P. Yan, S. J. Beecher, and J. I. Mackenzie, “Concentration dependence of energy transfer upconversion in Nd:YAG,” Opt. Mater. Express 5(5), 926–931 (2015).
[Crossref]

Bell, M. J. V.

W. J. Lima, V. M. Martins, A. F. G. Monte, D. N. Messias, N. O. Dantas, M. J. V. Bell, and T. Catunda, “Energy transfer upconversion on neodymium doped phosphate glasses investigated by Z-scan technique,” Opt. Mater. Express 35(9), 1724–1727 (2013).
[Crossref]

Billings, L.

D. C. Brown, R. Nelson, and L. Billings, “End-cooled Nd:YVO4 Diode-pumped Laser,” Appl. Opt.  36(33), 2–4 (1991).

Bjurshagen, S.

Bonner, C. L.

S. Guy, C. L. Bonner, D. P. Shepherd, D. C. Hanna, A. C. Tropper, and B. Ferrand, “High-inversion densities in Nd:YAG: up-conversion and bleaching,” IEEE J. Quantum Electron. 34(5), 900–909 (1998).
[Crossref]

Brown, D. C.

D. C. Brown, R. Nelson, and L. Billings, “End-cooled Nd:YVO4 Diode-pumped Laser,” Appl. Opt.  36(33), 2–4 (1991).

Byer, R. L.

T. Y. Fan and R. L. Byer, “Modeling and CW Operation of a Quasi-Three-Level 946 nm Nd:YAG Laser,” IEEE J. Quantum Electron. 23(5), 605–612 (1987).
[Crossref]

Catunda, T.

W. J. Lima, V. M. Martins, A. F. G. Monte, D. N. Messias, N. O. Dantas, M. J. V. Bell, and T. Catunda, “Energy transfer upconversion on neodymium doped phosphate glasses investigated by Z-scan technique,” Opt. Mater. Express 35(9), 1724–1727 (2013).
[Crossref]

Chen, Y. F.

Y. F. Chen, C. C. Liao, Y. P. Lan, and S. C. Wang, “Determination of the Auger upconversion rate in fiber-coupled diode end-pumped Nd:YAG and Nd:YVO4 crystals,” Appl. Phys. B 70(4), 487–490 (2000).
[Crossref]

Clarkson, W. A.

Czeranowsky, C.

C. Czeranowsky, “Resonatorinterne Frequenzverdopplung von diodengepumpten Neodym-Lasern mit hohen Ausgangsleistungen im blauen Spektralbereich,” Dissertation, Universitat Hamburg (2002).

Dantas, N. O.

W. J. Lima, V. M. Martins, A. F. G. Monte, D. N. Messias, N. O. Dantas, M. J. V. Bell, and T. Catunda, “Energy transfer upconversion on neodymium doped phosphate glasses investigated by Z-scan technique,” Opt. Mater. Express 35(9), 1724–1727 (2013).
[Crossref]

Fan, T. Y.

T. Y. Fan and R. L. Byer, “Modeling and CW Operation of a Quasi-Three-Level 946 nm Nd:YAG Laser,” IEEE J. Quantum Electron. 23(5), 605–612 (1987).
[Crossref]

Ferrand, B.

S. Guy, C. L. Bonner, D. P. Shepherd, D. C. Hanna, A. C. Tropper, and B. Ferrand, “High-inversion densities in Nd:YAG: up-conversion and bleaching,” IEEE J. Quantum Electron. 34(5), 900–909 (1998).
[Crossref]

Goldring, S.

S. Goldring, R. Lavi, and V. Lupei, “Decay dynamics of excited Nd3+ ions in YVO4 following weak excitation,” IEEE J. Quantum Electron.  46(2), 169–181 (2010).
[Crossref]

Guy, S.

S. Guy, C. L. Bonner, D. P. Shepherd, D. C. Hanna, A. C. Tropper, and B. Ferrand, “High-inversion densities in Nd:YAG: up-conversion and bleaching,” IEEE J. Quantum Electron. 34(5), 900–909 (1998).
[Crossref]

Hanna, D. C.

S. Guy, C. L. Bonner, D. P. Shepherd, D. C. Hanna, A. C. Tropper, and B. Ferrand, “High-inversion densities in Nd:YAG: up-conversion and bleaching,” IEEE J. Quantum Electron. 34(5), 900–909 (1998).
[Crossref]

Huber, G.

V. Ostroumov, T. Jensen, J.-P. Meyn, G. Huber, and M. A. Noginov, “Study of luminescence concentration quenching and energy transfer upconversion in Nd-doped LaSc3(BO3)4 and GdVO4 laser crystals,” J. Opt. Soc. Am. B 15(3), 1025–1060 (1998).
[Crossref]

Jensen, T.

V. Ostroumov, T. Jensen, J.-P. Meyn, G. Huber, and M. A. Noginov, “Study of luminescence concentration quenching and energy transfer upconversion in Nd-doped LaSc3(BO3)4 and GdVO4 laser crystals,” J. Opt. Soc. Am. B 15(3), 1025–1060 (1998).
[Crossref]

Kim, J. W.

Koch, R.

Lan, Y. P.

Y. F. Chen, C. C. Liao, Y. P. Lan, and S. C. Wang, “Determination of the Auger upconversion rate in fiber-coupled diode end-pumped Nd:YAG and Nd:YVO4 crystals,” Appl. Phys. B 70(4), 487–490 (2000).
[Crossref]

Lavi, R.

S. Goldring, R. Lavi, and V. Lupei, “Decay dynamics of excited Nd3+ ions in YVO4 following weak excitation,” IEEE J. Quantum Electron.  46(2), 169–181 (2010).
[Crossref]

Liao, C. C.

Y. F. Chen, C. C. Liao, Y. P. Lan, and S. C. Wang, “Determination of the Auger upconversion rate in fiber-coupled diode end-pumped Nd:YAG and Nd:YVO4 crystals,” Appl. Phys. B 70(4), 487–490 (2000).
[Crossref]

Lima, W. J.

W. J. Lima, V. M. Martins, A. F. G. Monte, D. N. Messias, N. O. Dantas, M. J. V. Bell, and T. Catunda, “Energy transfer upconversion on neodymium doped phosphate glasses investigated by Z-scan technique,” Opt. Mater. Express 35(9), 1724–1727 (2013).
[Crossref]

Lupei, V.

S. Goldring, R. Lavi, and V. Lupei, “Decay dynamics of excited Nd3+ ions in YVO4 following weak excitation,” IEEE J. Quantum Electron.  46(2), 169–181 (2010).
[Crossref]

Mackenzie, J. I.

Martins, V. M.

W. J. Lima, V. M. Martins, A. F. G. Monte, D. N. Messias, N. O. Dantas, M. J. V. Bell, and T. Catunda, “Energy transfer upconversion on neodymium doped phosphate glasses investigated by Z-scan technique,” Opt. Mater. Express 35(9), 1724–1727 (2013).
[Crossref]

Messias, D. N.

W. J. Lima, V. M. Martins, A. F. G. Monte, D. N. Messias, N. O. Dantas, M. J. V. Bell, and T. Catunda, “Energy transfer upconversion on neodymium doped phosphate glasses investigated by Z-scan technique,” Opt. Mater. Express 35(9), 1724–1727 (2013).
[Crossref]

Meyn, J.-P.

V. Ostroumov, T. Jensen, J.-P. Meyn, G. Huber, and M. A. Noginov, “Study of luminescence concentration quenching and energy transfer upconversion in Nd-doped LaSc3(BO3)4 and GdVO4 laser crystals,” J. Opt. Soc. Am. B 15(3), 1025–1060 (1998).
[Crossref]

Monte, A. F. G.

W. J. Lima, V. M. Martins, A. F. G. Monte, D. N. Messias, N. O. Dantas, M. J. V. Bell, and T. Catunda, “Energy transfer upconversion on neodymium doped phosphate glasses investigated by Z-scan technique,” Opt. Mater. Express 35(9), 1724–1727 (2013).
[Crossref]

Mungan, C. E.

Nelson, R.

D. C. Brown, R. Nelson, and L. Billings, “End-cooled Nd:YVO4 Diode-pumped Laser,” Appl. Opt.  36(33), 2–4 (1991).

Noginov, M. A.

V. Ostroumov, T. Jensen, J.-P. Meyn, G. Huber, and M. A. Noginov, “Study of luminescence concentration quenching and energy transfer upconversion in Nd-doped LaSc3(BO3)4 and GdVO4 laser crystals,” J. Opt. Soc. Am. B 15(3), 1025–1060 (1998).
[Crossref]

Ostroumov, V.

V. Ostroumov, T. Jensen, J.-P. Meyn, G. Huber, and M. A. Noginov, “Study of luminescence concentration quenching and energy transfer upconversion in Nd-doped LaSc3(BO3)4 and GdVO4 laser crystals,” J. Opt. Soc. Am. B 15(3), 1025–1060 (1998).
[Crossref]

Risk, W. P.

Sato, Y.

Shepherd, D. P.

S. Guy, C. L. Bonner, D. P. Shepherd, D. C. Hanna, A. C. Tropper, and B. Ferrand, “High-inversion densities in Nd:YAG: up-conversion and bleaching,” IEEE J. Quantum Electron. 34(5), 900–909 (1998).
[Crossref]

Taira, T.

Tropper, A. C.

S. Guy, C. L. Bonner, D. P. Shepherd, D. C. Hanna, A. C. Tropper, and B. Ferrand, “High-inversion densities in Nd:YAG: up-conversion and bleaching,” IEEE J. Quantum Electron. 34(5), 900–909 (1998).
[Crossref]

Wang, S. C.

Y. F. Chen, C. C. Liao, Y. P. Lan, and S. C. Wang, “Determination of the Auger upconversion rate in fiber-coupled diode end-pumped Nd:YAG and Nd:YVO4 crystals,” Appl. Phys. B 70(4), 487–490 (2000).
[Crossref]

White, J. O.

Yan, R.

R. Yan, S. J. Yoon, S. J. Beecher, and J. I. Mackenzie, “Measuring the elevated temperature dependence of upconversion in Nd:YAG,” IEEE J. Sel. Top. Quantum Electron. 21(1), 1–7 (2015).

Yan, R. P.

Yoon, S. J.

S. J. Yoon, R. P. Yan, S. J. Beecher, and J. I. Mackenzie, “Concentration dependence of energy transfer upconversion in Nd:YAG,” Opt. Mater. Express 5(5), 926–931 (2015).
[Crossref]

R. Yan, S. J. Yoon, S. J. Beecher, and J. I. Mackenzie, “Measuring the elevated temperature dependence of upconversion in Nd:YAG,” IEEE J. Sel. Top. Quantum Electron. 21(1), 1–7 (2015).

Appl. Opt (1)

D. C. Brown, R. Nelson, and L. Billings, “End-cooled Nd:YVO4 Diode-pumped Laser,” Appl. Opt.  36(33), 2–4 (1991).

Appl. Opt. (1)

Appl. Phys. B (1)

Y. F. Chen, C. C. Liao, Y. P. Lan, and S. C. Wang, “Determination of the Auger upconversion rate in fiber-coupled diode end-pumped Nd:YAG and Nd:YVO4 crystals,” Appl. Phys. B 70(4), 487–490 (2000).
[Crossref]

IEEE J. Quantum Electron (1)

S. Goldring, R. Lavi, and V. Lupei, “Decay dynamics of excited Nd3+ ions in YVO4 following weak excitation,” IEEE J. Quantum Electron.  46(2), 169–181 (2010).
[Crossref]

IEEE J. Quantum Electron. (2)

S. Guy, C. L. Bonner, D. P. Shepherd, D. C. Hanna, A. C. Tropper, and B. Ferrand, “High-inversion densities in Nd:YAG: up-conversion and bleaching,” IEEE J. Quantum Electron. 34(5), 900–909 (1998).
[Crossref]

T. Y. Fan and R. L. Byer, “Modeling and CW Operation of a Quasi-Three-Level 946 nm Nd:YAG Laser,” IEEE J. Quantum Electron. 23(5), 605–612 (1987).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

R. Yan, S. J. Yoon, S. J. Beecher, and J. I. Mackenzie, “Measuring the elevated temperature dependence of upconversion in Nd:YAG,” IEEE J. Sel. Top. Quantum Electron. 21(1), 1–7 (2015).

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

J. O. White and C. E. Mungan, “Measurement of up-conversion in Er:YAG via z-scan,” J. Opt. Soc. Am. B 28(10), 2358–2361 (2011).
[Crossref]

W. P. Risk, “Modeling of longitudinally pumped solid-state lasers exhibiting reabsorption losses,” J. Opt. Soc. Am. B 5(7), 1412–1423(1988).
[Crossref]

V. Ostroumov, T. Jensen, J.-P. Meyn, G. Huber, and M. A. Noginov, “Study of luminescence concentration quenching and energy transfer upconversion in Nd-doped LaSc3(BO3)4 and GdVO4 laser crystals,” J. Opt. Soc. Am. B 15(3), 1025–1060 (1998).
[Crossref]

Opt. Express (1)

Opt. Mater. Express (3)

S. J. Yoon, R. P. Yan, S. J. Beecher, and J. I. Mackenzie, “Concentration dependence of energy transfer upconversion in Nd:YAG,” Opt. Mater. Express 5(5), 926–931 (2015).
[Crossref]

W. J. Lima, V. M. Martins, A. F. G. Monte, D. N. Messias, N. O. Dantas, M. J. V. Bell, and T. Catunda, “Energy transfer upconversion on neodymium doped phosphate glasses investigated by Z-scan technique,” Opt. Mater. Express 35(9), 1724–1727 (2013).
[Crossref]

Y. Sato and T. Taira, “Temperature dependencies of stimulated emission cross section for Nd-doped solid-state laser materials,” Opt. Mater. Express 2(8), 1076–1087 (2012).
[Crossref]

Other (1)

C. Czeranowsky, “Resonatorinterne Frequenzverdopplung von diodengepumpten Neodym-Lasern mit hohen Ausgangsleistungen im blauen Spektralbereich,” Dissertation, Universitat Hamburg (2002).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1 Schematics of the Nd3+ Energy levels and ETU dynamics.
Fig. 2
Fig. 2 Automated ETU measurement setup. Lenses: L1 (f = 50 mm), L2 (f = 300 mm), L3 (f = 200 mm), L4 (f = 175 mm); high reflectivity mirrors at 808 nm: M1 and M2 flat, M3 curved (radius or curvature=100 mm); glass wedges: W1 and W2; Si photodiodes: PD1, PD2 and PD3.
Fig. 3
Fig. 3 Sample of waveforms collected at each z-scan step. Solid lines: PD1 and PD2 signals [V], in red and pink respectively; dashed lines: small-signal and high irradiance regimes fluorescence normalised signals [a.u.], in blue and green respectively.
Fig. 4
Fig. 4 Absorption measurements setup.
Fig. 5
Fig. 5 Nd:YVO4 absorption cross section.
Fig. 6
Fig. 6 Nd:GdVO4 absorption cross section.
Fig. 7
Fig. 7 Polynomial fits to the dependence of absorption cross section peaks vs temperature. Secondary y-axis: FWHM (Δλ) for the π-pol peaks vs temperature.
Fig. 8
Fig. 8 Results for the ETU parameter measurements.
Fig. 9
Fig. 9 Pth vs Temperature for a 1mm thick Nd:YVO4 sample.

Tables (2)

Tables Icon

Table 1 Doping Ion Concentration Measurements: Results And Associated Uncertainties.

Tables Icon

Table 2 Second Degree Polynomial Fit Coefficients For σabs Vs T Dependence.

Equations (15)

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

I o u t ( λ ) = I i n ( λ ) e α a b s ( λ ) L = I i n ( λ ) e σ a b s ( λ ) C % N 0 L
α a b s ( λ ) N 0 = σ a b s ( λ ) C % = ln ( I i n ( λ ) I o u t ( λ ) ) N 0 L
C % = α a b s ( λ * ) σ a b s ( λ * ) N 0 = ln ( I i n ( λ * ) I o u t ( λ * ) ) σ a b s ( λ * ) N 0 L
C % = 1 N i = 1 N c % , i = 1 N i = 1 N α a b s ( λ i ) σ a b s ( λ i ) N 0
Δ C % = 1 N 1 i = 1 N | c % , i C % | 2
N 1 ( r , z ) t = I p ( r , z ) h v p σ a b s N 1 ( r , z ) + N 2 ( r , z ) τ f + W E T U N 2 ( r , z ) 2
N 2 ( r , z ) t = I p ( r , z ) h v p σ a b s N 1 ( r , z ) N 2 ( r , z ) τ f W E T U N 2 ( r , z ) 2
d I p ( r , z ) d z = I p ( r , z ) ( σ a b s N 1 ( r , z ) )
N 2 ( r , z ) = N t o t N 1 ( r , z ) = C % N 0 N 1 ( r , z )
N 1 ( r , z ) = b ± b 2 4 a c 2 a a = W E T U b = I p ( r , z ) h v p σ a b s 1 τ f 2 W E T U N t o t c = N t o t τ f + W E T U N t o t 2
S 2 ( W E T U ) = z [ ( T z T t h ( z , W E T U ) ) 2 ]
V ( t ) = V 0 e t τ f
I i n ( λ ) I o u t ( λ ) = P i n ( λ ) P o u t ( λ )
σ a b s ( T ) = p 1 + p 2 T + p 3 T 2
P t h h v p π w p 2 2 ( f 1 + f 2 ) σ τ f η q η L P η a ( L T + 2 f 1 σ η L P N t o t l r ) [ 1 + W E T U τ f α a b s 4 ( f 1 + f 2 ) σ η L P ( L T + 2 f 1 σ η L P N t o t l r ) ] = = P t h ( w i t h o u t E T U ) [ 1 + W E T U τ α a b s 4 ( f 1 + f 2 ) σ η L P ( L T + 2 f 1 σ η L P N t o t l r ) ]

Metrics