Abstract

A 2.3 W single transverse mode thulium-doped fluoride fiber laser based on fiber Bragg gratings is presented. The laser has a conversion efficiency of 65% to be compared to the quantum limit of 72%. The performances of the laser are compared for two pump wavelengths of 1040 and 1064 nm and are analyzed based on a rate equation analysis.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. N. Islam, "Overview of Raman amplification in telecommunications," in Raman amplifiers for telecommunications 1 (Springer 2004), Chap. 1.
    [CrossRef]
  2. J. Bromage, "Raman amplification for fiber communications systems," J. Lightwave Technol. 22, 79-93 (2004).
    [CrossRef]
  3. Y. Nagashima, S. Onuki, Y. Shimose, A. Yamada, and T. Kikugawa, "1480-nm pump laser with asymmetric quaternary cladding structure achieving high output power >1.2W with low power consumption," IEEE 19th Semicond. Laser Conf. Digest., 47-48 (Sept. 2004).
    [CrossRef]
  4. A. Guermache, V. Voirot, N. Bouche, F. Lelarge, D. Locatelli, R. M. Capella, and J. Jacquet, "1W fiber coupled power InGaAsP/InP 14xx pump laser for Raman amplification," Electron. Lett. 40, 1535-1536 (2004).
    [CrossRef]
  5. C. Headley, M. Mermelstein, and J. C. Bouteiller, "Raman fiber laser, " in Raman amplifiers for telecommunications 2 (Springer 2004), Chap. 11.
    [CrossRef]
  6. R. M. El-Agmy, W. Lüthy, T. Graf, and H. P. Weber, "1.47 µm Tm3+:ZBLAN fibre laser pumped at 1.064µm," Electron. Lett. 39, 507-508 (2003).
    [CrossRef]
  7. Y. Miyajima, T. Komukai, and T. Sugawa, "1-W CW Tm-doped fluoride fibre laser at 1.47 µm," Electron. Lett. 29, 660-661 (1993).
    [CrossRef]
  8. T. Komukai, T. Yamamoto, T. Sugawa, and Y. Miyajima, "Efficient upconversion pumping at 1.064 µm of Tm3+-doped fluoride fiber laser operating at 1.47 µm," Electron. Lett. 28, 830-831 (1992).
    [CrossRef]
  9. R. M. Percival, D. Szebesta, and J. R. Williams, "Highly efficient 1.064 µm pumped 1.47 µm thulium doped fluoride fiber laser," Electron. Lett. 30, 1057-1058 (1994).
    [CrossRef]
  10. T. Komukai, T. Yamamoto, T. Sugawa, and Y. Miyajima, "Upconversion pumped thulium-doped fluoride fiber amplifier and laser operating at 1.47 µm," IEEE J. Quantum. Electron. 31, 1880-1889 (1995).
    [CrossRef]
  11. M. Bernier, D. Faucher, R. Vallée, A. Salimina, G. Androz, Y. Sheng, and S. L. Chin, "Bragg gratings photoinduced in ZBLAN fiber by femtosecond pulses at 800 nm," Opt. Lett. 32, 454-456 (2007).
    [CrossRef] [PubMed]
  12. G. Androz, D. Faucher, M. Bernier, and R. Vallée, "Monolithic fluoride-fiber laser at 1480 nm using fiber Bragg gratings," Opt. Lett. 32, 1302-1304 (2007).
    [CrossRef] [PubMed]
  13. B. Jacquier, L. Bigot, S. Guy, and A. M. Jurdyc, "Rare earth doped confined structures for lasers and amplifiers," in Spectroscopic properties of rare earths in optical materials, G. Liu and B. Jacquier, eds., (Springer, 2005), pp. 450-452.
  14. R. M. Percival, D. Szebesta, C. P. Seltzer, S. D. Perrin, S. T. Davey, and M. Louka, "A 1.6-µm pumped 1.9-µm thulium-doped fluoride fiber laser and amplifier of very high efficiency," IEEE J. Quantum Electron. 31, 489-493 (1995).
    [CrossRef]
  15. P. Laperle, "Etude de lasers à fibre émettant à 480 nm et du phénomène de coloration dans la fibre de ZBLAN dopée au thulium," Ph.D. Thesis, Université Laval (2003).
  16. M. Eichhorn, "Numerical modeling of Tm-doped double-clad floride fiber amplifiers," IEEE J. Quantum. Electron. 41, 1574-1581 (2005).
    [CrossRef]
  17. W. J. Lee, B. Min, J. Park, and N. Park, "Study on the pumping wavelength dependency of S-band fluoride based thulium doped fiber amplifiers," in Optical Fiber Communication Conference, Vol. 2 of 2001 OSA Technical Digest Series (Optical Society of America, 2001), paper TuQ5.
  18. X. Zhu and R. Jain, "10-W-level diode-pumped compact 2.78 µm ZBLAN fiber laser," Opt. Lett. 32, 26-28 (2007).
    [CrossRef]

2007

2005

M. Eichhorn, "Numerical modeling of Tm-doped double-clad floride fiber amplifiers," IEEE J. Quantum. Electron. 41, 1574-1581 (2005).
[CrossRef]

2004

J. Bromage, "Raman amplification for fiber communications systems," J. Lightwave Technol. 22, 79-93 (2004).
[CrossRef]

A. Guermache, V. Voirot, N. Bouche, F. Lelarge, D. Locatelli, R. M. Capella, and J. Jacquet, "1W fiber coupled power InGaAsP/InP 14xx pump laser for Raman amplification," Electron. Lett. 40, 1535-1536 (2004).
[CrossRef]

2003

R. M. El-Agmy, W. Lüthy, T. Graf, and H. P. Weber, "1.47 µm Tm3+:ZBLAN fibre laser pumped at 1.064µm," Electron. Lett. 39, 507-508 (2003).
[CrossRef]

1995

R. M. Percival, D. Szebesta, C. P. Seltzer, S. D. Perrin, S. T. Davey, and M. Louka, "A 1.6-µm pumped 1.9-µm thulium-doped fluoride fiber laser and amplifier of very high efficiency," IEEE J. Quantum Electron. 31, 489-493 (1995).
[CrossRef]

T. Komukai, T. Yamamoto, T. Sugawa, and Y. Miyajima, "Upconversion pumped thulium-doped fluoride fiber amplifier and laser operating at 1.47 µm," IEEE J. Quantum. Electron. 31, 1880-1889 (1995).
[CrossRef]

1994

R. M. Percival, D. Szebesta, and J. R. Williams, "Highly efficient 1.064 µm pumped 1.47 µm thulium doped fluoride fiber laser," Electron. Lett. 30, 1057-1058 (1994).
[CrossRef]

1993

Y. Miyajima, T. Komukai, and T. Sugawa, "1-W CW Tm-doped fluoride fibre laser at 1.47 µm," Electron. Lett. 29, 660-661 (1993).
[CrossRef]

1992

T. Komukai, T. Yamamoto, T. Sugawa, and Y. Miyajima, "Efficient upconversion pumping at 1.064 µm of Tm3+-doped fluoride fiber laser operating at 1.47 µm," Electron. Lett. 28, 830-831 (1992).
[CrossRef]

Androz, G.

Bernier, M.

Bouche, N.

A. Guermache, V. Voirot, N. Bouche, F. Lelarge, D. Locatelli, R. M. Capella, and J. Jacquet, "1W fiber coupled power InGaAsP/InP 14xx pump laser for Raman amplification," Electron. Lett. 40, 1535-1536 (2004).
[CrossRef]

Bromage, J.

Capella, R. M.

A. Guermache, V. Voirot, N. Bouche, F. Lelarge, D. Locatelli, R. M. Capella, and J. Jacquet, "1W fiber coupled power InGaAsP/InP 14xx pump laser for Raman amplification," Electron. Lett. 40, 1535-1536 (2004).
[CrossRef]

Chin, S. L.

Davey, S. T.

R. M. Percival, D. Szebesta, C. P. Seltzer, S. D. Perrin, S. T. Davey, and M. Louka, "A 1.6-µm pumped 1.9-µm thulium-doped fluoride fiber laser and amplifier of very high efficiency," IEEE J. Quantum Electron. 31, 489-493 (1995).
[CrossRef]

Eichhorn, M.

M. Eichhorn, "Numerical modeling of Tm-doped double-clad floride fiber amplifiers," IEEE J. Quantum. Electron. 41, 1574-1581 (2005).
[CrossRef]

El-Agmy, R. M.

R. M. El-Agmy, W. Lüthy, T. Graf, and H. P. Weber, "1.47 µm Tm3+:ZBLAN fibre laser pumped at 1.064µm," Electron. Lett. 39, 507-508 (2003).
[CrossRef]

Faucher, D.

Graf, T.

R. M. El-Agmy, W. Lüthy, T. Graf, and H. P. Weber, "1.47 µm Tm3+:ZBLAN fibre laser pumped at 1.064µm," Electron. Lett. 39, 507-508 (2003).
[CrossRef]

Guermache, A.

A. Guermache, V. Voirot, N. Bouche, F. Lelarge, D. Locatelli, R. M. Capella, and J. Jacquet, "1W fiber coupled power InGaAsP/InP 14xx pump laser for Raman amplification," Electron. Lett. 40, 1535-1536 (2004).
[CrossRef]

Jacquet, J.

A. Guermache, V. Voirot, N. Bouche, F. Lelarge, D. Locatelli, R. M. Capella, and J. Jacquet, "1W fiber coupled power InGaAsP/InP 14xx pump laser for Raman amplification," Electron. Lett. 40, 1535-1536 (2004).
[CrossRef]

Jain, R.

Komukai, T.

T. Komukai, T. Yamamoto, T. Sugawa, and Y. Miyajima, "Upconversion pumped thulium-doped fluoride fiber amplifier and laser operating at 1.47 µm," IEEE J. Quantum. Electron. 31, 1880-1889 (1995).
[CrossRef]

Y. Miyajima, T. Komukai, and T. Sugawa, "1-W CW Tm-doped fluoride fibre laser at 1.47 µm," Electron. Lett. 29, 660-661 (1993).
[CrossRef]

T. Komukai, T. Yamamoto, T. Sugawa, and Y. Miyajima, "Efficient upconversion pumping at 1.064 µm of Tm3+-doped fluoride fiber laser operating at 1.47 µm," Electron. Lett. 28, 830-831 (1992).
[CrossRef]

Lelarge, F.

A. Guermache, V. Voirot, N. Bouche, F. Lelarge, D. Locatelli, R. M. Capella, and J. Jacquet, "1W fiber coupled power InGaAsP/InP 14xx pump laser for Raman amplification," Electron. Lett. 40, 1535-1536 (2004).
[CrossRef]

Locatelli, D.

A. Guermache, V. Voirot, N. Bouche, F. Lelarge, D. Locatelli, R. M. Capella, and J. Jacquet, "1W fiber coupled power InGaAsP/InP 14xx pump laser for Raman amplification," Electron. Lett. 40, 1535-1536 (2004).
[CrossRef]

Louka, M.

R. M. Percival, D. Szebesta, C. P. Seltzer, S. D. Perrin, S. T. Davey, and M. Louka, "A 1.6-µm pumped 1.9-µm thulium-doped fluoride fiber laser and amplifier of very high efficiency," IEEE J. Quantum Electron. 31, 489-493 (1995).
[CrossRef]

Lüthy, W.

R. M. El-Agmy, W. Lüthy, T. Graf, and H. P. Weber, "1.47 µm Tm3+:ZBLAN fibre laser pumped at 1.064µm," Electron. Lett. 39, 507-508 (2003).
[CrossRef]

Miyajima, Y.

T. Komukai, T. Yamamoto, T. Sugawa, and Y. Miyajima, "Upconversion pumped thulium-doped fluoride fiber amplifier and laser operating at 1.47 µm," IEEE J. Quantum. Electron. 31, 1880-1889 (1995).
[CrossRef]

Y. Miyajima, T. Komukai, and T. Sugawa, "1-W CW Tm-doped fluoride fibre laser at 1.47 µm," Electron. Lett. 29, 660-661 (1993).
[CrossRef]

T. Komukai, T. Yamamoto, T. Sugawa, and Y. Miyajima, "Efficient upconversion pumping at 1.064 µm of Tm3+-doped fluoride fiber laser operating at 1.47 µm," Electron. Lett. 28, 830-831 (1992).
[CrossRef]

Percival, R. M.

R. M. Percival, D. Szebesta, C. P. Seltzer, S. D. Perrin, S. T. Davey, and M. Louka, "A 1.6-µm pumped 1.9-µm thulium-doped fluoride fiber laser and amplifier of very high efficiency," IEEE J. Quantum Electron. 31, 489-493 (1995).
[CrossRef]

R. M. Percival, D. Szebesta, and J. R. Williams, "Highly efficient 1.064 µm pumped 1.47 µm thulium doped fluoride fiber laser," Electron. Lett. 30, 1057-1058 (1994).
[CrossRef]

Perrin, S. D.

R. M. Percival, D. Szebesta, C. P. Seltzer, S. D. Perrin, S. T. Davey, and M. Louka, "A 1.6-µm pumped 1.9-µm thulium-doped fluoride fiber laser and amplifier of very high efficiency," IEEE J. Quantum Electron. 31, 489-493 (1995).
[CrossRef]

Salimina, A.

Seltzer, C. P.

R. M. Percival, D. Szebesta, C. P. Seltzer, S. D. Perrin, S. T. Davey, and M. Louka, "A 1.6-µm pumped 1.9-µm thulium-doped fluoride fiber laser and amplifier of very high efficiency," IEEE J. Quantum Electron. 31, 489-493 (1995).
[CrossRef]

Sheng, Y.

Sugawa, T.

T. Komukai, T. Yamamoto, T. Sugawa, and Y. Miyajima, "Upconversion pumped thulium-doped fluoride fiber amplifier and laser operating at 1.47 µm," IEEE J. Quantum. Electron. 31, 1880-1889 (1995).
[CrossRef]

Y. Miyajima, T. Komukai, and T. Sugawa, "1-W CW Tm-doped fluoride fibre laser at 1.47 µm," Electron. Lett. 29, 660-661 (1993).
[CrossRef]

T. Komukai, T. Yamamoto, T. Sugawa, and Y. Miyajima, "Efficient upconversion pumping at 1.064 µm of Tm3+-doped fluoride fiber laser operating at 1.47 µm," Electron. Lett. 28, 830-831 (1992).
[CrossRef]

Szebesta, D.

R. M. Percival, D. Szebesta, C. P. Seltzer, S. D. Perrin, S. T. Davey, and M. Louka, "A 1.6-µm pumped 1.9-µm thulium-doped fluoride fiber laser and amplifier of very high efficiency," IEEE J. Quantum Electron. 31, 489-493 (1995).
[CrossRef]

R. M. Percival, D. Szebesta, and J. R. Williams, "Highly efficient 1.064 µm pumped 1.47 µm thulium doped fluoride fiber laser," Electron. Lett. 30, 1057-1058 (1994).
[CrossRef]

Vallée, R.

Voirot, V.

A. Guermache, V. Voirot, N. Bouche, F. Lelarge, D. Locatelli, R. M. Capella, and J. Jacquet, "1W fiber coupled power InGaAsP/InP 14xx pump laser for Raman amplification," Electron. Lett. 40, 1535-1536 (2004).
[CrossRef]

Weber, H. P.

R. M. El-Agmy, W. Lüthy, T. Graf, and H. P. Weber, "1.47 µm Tm3+:ZBLAN fibre laser pumped at 1.064µm," Electron. Lett. 39, 507-508 (2003).
[CrossRef]

Williams, J. R.

R. M. Percival, D. Szebesta, and J. R. Williams, "Highly efficient 1.064 µm pumped 1.47 µm thulium doped fluoride fiber laser," Electron. Lett. 30, 1057-1058 (1994).
[CrossRef]

Yamamoto, T.

T. Komukai, T. Yamamoto, T. Sugawa, and Y. Miyajima, "Upconversion pumped thulium-doped fluoride fiber amplifier and laser operating at 1.47 µm," IEEE J. Quantum. Electron. 31, 1880-1889 (1995).
[CrossRef]

T. Komukai, T. Yamamoto, T. Sugawa, and Y. Miyajima, "Efficient upconversion pumping at 1.064 µm of Tm3+-doped fluoride fiber laser operating at 1.47 µm," Electron. Lett. 28, 830-831 (1992).
[CrossRef]

Zhu, X.

Electron. Lett.

R. M. El-Agmy, W. Lüthy, T. Graf, and H. P. Weber, "1.47 µm Tm3+:ZBLAN fibre laser pumped at 1.064µm," Electron. Lett. 39, 507-508 (2003).
[CrossRef]

Y. Miyajima, T. Komukai, and T. Sugawa, "1-W CW Tm-doped fluoride fibre laser at 1.47 µm," Electron. Lett. 29, 660-661 (1993).
[CrossRef]

T. Komukai, T. Yamamoto, T. Sugawa, and Y. Miyajima, "Efficient upconversion pumping at 1.064 µm of Tm3+-doped fluoride fiber laser operating at 1.47 µm," Electron. Lett. 28, 830-831 (1992).
[CrossRef]

R. M. Percival, D. Szebesta, and J. R. Williams, "Highly efficient 1.064 µm pumped 1.47 µm thulium doped fluoride fiber laser," Electron. Lett. 30, 1057-1058 (1994).
[CrossRef]

A. Guermache, V. Voirot, N. Bouche, F. Lelarge, D. Locatelli, R. M. Capella, and J. Jacquet, "1W fiber coupled power InGaAsP/InP 14xx pump laser for Raman amplification," Electron. Lett. 40, 1535-1536 (2004).
[CrossRef]

IEEE J. Quantum Electron.

R. M. Percival, D. Szebesta, C. P. Seltzer, S. D. Perrin, S. T. Davey, and M. Louka, "A 1.6-µm pumped 1.9-µm thulium-doped fluoride fiber laser and amplifier of very high efficiency," IEEE J. Quantum Electron. 31, 489-493 (1995).
[CrossRef]

IEEE J. Quantum. Electron.

M. Eichhorn, "Numerical modeling of Tm-doped double-clad floride fiber amplifiers," IEEE J. Quantum. Electron. 41, 1574-1581 (2005).
[CrossRef]

T. Komukai, T. Yamamoto, T. Sugawa, and Y. Miyajima, "Upconversion pumped thulium-doped fluoride fiber amplifier and laser operating at 1.47 µm," IEEE J. Quantum. Electron. 31, 1880-1889 (1995).
[CrossRef]

J. Lightwave Technol.

Opt. Lett.

Other

M. N. Islam, "Overview of Raman amplification in telecommunications," in Raman amplifiers for telecommunications 1 (Springer 2004), Chap. 1.
[CrossRef]

B. Jacquier, L. Bigot, S. Guy, and A. M. Jurdyc, "Rare earth doped confined structures for lasers and amplifiers," in Spectroscopic properties of rare earths in optical materials, G. Liu and B. Jacquier, eds., (Springer, 2005), pp. 450-452.

Y. Nagashima, S. Onuki, Y. Shimose, A. Yamada, and T. Kikugawa, "1480-nm pump laser with asymmetric quaternary cladding structure achieving high output power >1.2W with low power consumption," IEEE 19th Semicond. Laser Conf. Digest., 47-48 (Sept. 2004).
[CrossRef]

C. Headley, M. Mermelstein, and J. C. Bouteiller, "Raman fiber laser, " in Raman amplifiers for telecommunications 2 (Springer 2004), Chap. 11.
[CrossRef]

W. J. Lee, B. Min, J. Park, and N. Park, "Study on the pumping wavelength dependency of S-band fluoride based thulium doped fiber amplifiers," in Optical Fiber Communication Conference, Vol. 2 of 2001 OSA Technical Digest Series (Optical Society of America, 2001), paper TuQ5.

P. Laperle, "Etude de lasers à fibre émettant à 480 nm et du phénomène de coloration dans la fibre de ZBLAN dopée au thulium," Ph.D. Thesis, Université Laval (2003).

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 (12)

Fig. 1.
Fig. 1.

Setup of the laser. A FBG has been at the entrance of the fiber and the output coupler is either a 4% Fresnel reflection (as shown) or another FBG. The pump source is either a laser emitting at 1040 nm or at 1064 nm.

Fig. 2.
Fig. 2.

Partial energy level diagram of the Tm3+ ions illustrating the upconversion pumping scheme.

Fig. 3.
Fig. 3.

Experimental (scatter) and simulated (solid) laser output power as a function of the launched pump power at 1040 nm (blue squares) and 1064 nm (red circles). Fiber length is 5.45m, and the input and output coupler reflectivities are 90% and 4% respectively.

Fig. 4.
Fig. 4.

Energy level diagram used in the numerical model.

Fig. 5.
Fig. 5.

(a). Experimental (scatter) and simulated (solid) laser output power as a function of the absorbed pump power at 1040 nm and (b) Laser output power as a function of the pump power for different values of the GSA1480 cross section at the signal wavelength. The blue curve corresponds to a full value of the GSA1480 cross section, the green curve corresponds to the half value and the red one corresponds to the zero value.

Fig. 6.
Fig. 6.

Experimental (scatter) and simulated (solid) laser output power as a function of the absorbed pump power at 1040 nm (red circles) and 1064 nm (blue squares). A similar conversion efficiency of 65% is shown. Fiber length is 5.45m, and the input and output coupler reflectivities are 90% and 4% respectively.

Fig. 7.
Fig. 7.

Laser output power as a function of (a) the launched pump power or (b) the absorbed pump power for pumping wavelengths from 1030 nm to 1090 nm. Fiber length is 5.45m, and the input and output coupler reflectivities are 90% and 4% respectively.

Fig. 8.
Fig. 8.

Net gain for the 3H43F4 transition (given by Eq. (4)) as a function of the pump wavelength for different pump powers. The peak gain is marked with an open circle. Fiber length is 5.45m, and the input and output coupler reflectivities are 90% and 4% respectively.

Fig. 9.
Fig. 9.

Optimal fiber length and the corresponding laser output power at various pump wavelengths for a launched pump power of 1.5 W. Input and output coupler reflectivities are 90% and 4% respectively.

Fig. 10.
Fig. 10.

Evolution of the laser output power as a function of the fiber length for a launched pump power of 1.5 W at 1053 nm. Input coupler reflectivity is 90%. Circles indicate the maximum output power at each reflectivity.

Fig. 11.
Fig. 11.

Experimental (scatter) and simulated (solid) laser output power as a function of the launched pump power at 1040 nm and output spectrum (inset). Fiber length is 5.45m, and input and output coupler reflectivities are 90% and 4% at entrance and output respectively.

Fig. 12.
Fig. 12.

Experimental (scatter) and simulated (solid) laser output power as a function of the launched pump power at 1064 nm. The fiber length was 2.8 m, and input and output coupler reflectivities are 99% and 15% respectively.

Tables (4)

Tables Icon

Table 1. Cross-sections for the signals at 1480 nm (x10-25 m2)

Tables Icon

Table 2. Spontaneous emission rates (s-1)

Tables Icon

Table 3. CR coefficients (x10-25 m2.s-1)

Tables Icon

Table 4. Absorption and emission cross-sections at the pump wavelengths.

Equations (17)

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

d n 1 d t = ( R 01 + W 01 ) n 0 ( R 12 + W 12 + A 10 ) n 1 + ( W 21 + A 21 ) n 2 + A 31 n 3 + A 41 n 4 +
A 51 n 5 + X 0312 C n 0 n 3 + 2 X 0211 C n 0 n 0 + X 3315 C n 3 2 2 X 1102 C n 1 2 + X 2314 C n 2 n 3
d n 2 d t = ( R 12 + W 12 ) n 1 ( R 23 + W 21 + A 20 + A 21 ) n 2 + ( R 32 + W 32 + A 32 ) n 3 +
A 42 n 4 + A 52 n 5 X 0211 C n 0 n 2 + X 0312 C n 0 n 4 + 2 X 0422 C n 0 n 4 + X 3324 C n 3 2 +
X 1102 C n 1 2 X 2314 C n 2 n 3
d n 3 d t = R 23 n 2 ( R 32 + W 32 + W 34 + A 30 + A 31 + A 32 ) n 3 + ( W 43 + A 43 ) n 4 + A 53 n 5
X 0312 C n 0 n 3 2 X 3324 C n 3 2 2 X 3315 C n 3 2 X 2314 C n 2 n 3
d n 4 d t = W 34 n 3 ( R 45 + W 43 + A 40 + A 41 + A 42 + A 43 ) n 4 + ( W 54 + A 54 ) n 5
X 0422 C n 0 n 4 + X 3324 C n 3 2 + X 2314 C n 2 n 3
d n 5 d t = R 45 n 4 ( W 54 + A 50 + A 51 + A 52 + A 53 + A 54 ) n 5 + X 3315 C n 3 2
W i j ( λ s ) = λ s h c σ i j ( λ s ) P s
R i j ( λ p ) = λ p h c σ i j ( λ p ) P p
d P p ± d z = ± P p ± [ 2 π C 0 a ( σ 01 n 0 + σ 12 n 1 + σ 23 n 2 σ 32 n 3 + σ 45 n 4 ) Ψ p r d r α p ]
d P 1480 ± d z = ± P 1480 ± [ 2 π C 0 a ( σ 21 n 2 σ 12 n 1 σ 01 n 0 + σ 32 n 3 + σ 43 n 4 )
σ 34 n 3 + σ 54 n 5 ) Ψ 1480 r d r α 1480 ]
G ( dB ) = 10 log { exp ( 2 0 L [ 2 π C 0 a ( σ 21 n 2 σ 12 n 1 σ 01 n 0 + σ 32 n 3 + σ 43 n 4
σ 34 n 3 + σ 54 n 5 ) Ψ 1480 r d r α 1480 ] d z ) In ( 1 R 1 R 2 ) }

Metrics