Abstract

We have studied the competition between the F324I1124 and F324I1324 gain channels in the Nd:Ba5(PO4)3F random laser. The strength of stimulated emission transitions was influenced by adding to the Nd-doped powder the powder of Cr4+:Y3Al5O12, absorbing light at λ=1.06μm, and the 1.32μm mirror, which provided an extra stimulated emission feedback. We have demonstrated a robustness of the Nd random laser to contamination. A much better control of the spectrum of the stimulated emission can be obtained by means of wavelength-selective external mirrors.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. V. S. Letokhov, "Stimulated emission of an ensemble of scattering particles with negative absorption," JETP Lett. 5, 212-215 (1967).
  2. V. M. Markushev, V. F. Zolin, and Ch. M. Briskina, "Luminescence and stimulated emission of neodymium in sodium lanthanum molybdate powders," Sov. J. Quantum Electron. 16, 281-283 (1986).
    [CrossRef]
  3. N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, "Laser action in strongly scattering medium," Nature 368, 436-438 (1994).
    [CrossRef]
  4. W. L. Sha, C.-H. Liu, and R. R. Alfano, "Spectral and temporal measurements of laser action of rhodamine 640 dye in strongly scattering media," Opt. Lett. 19, 1922-1924 (1994).
    [CrossRef] [PubMed]
  5. M. A. Noginov, N. E. Noginova, H. J. Caulfield, P. Venkateswarlu, and M. Mahdi, "Line narrowing in the dye solution with scattering centers," Opt. Commun. 118, 430-437 (1995).
    [CrossRef]
  6. R. M. Balachandran, A. Pacheco, and N. M. Lawandy, "Photonic textile fibers," in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, 1995), pp. 114-115.
  7. F. Hide, B. J. Schwartz, M. A. Diaz-Garsia, and A. J. Heeger, "Laser emission from solutions and films containing semiconducting polymer and titanium dioxide nanocrystals," Chem. Phys. Lett. 256, 424-430 (1996).
    [CrossRef]
  8. F. Hide, M. A. Días-García, B. J. Schwartz, M. R. Andersson, Q. Pei, and A. J. Heeger, "Semiconducting polymers: a new class of solid-state laser materials," Science 273, 1833-1836 (1996).
    [CrossRef]
  9. M. A. Días-García, F. Hide, B. J. Schwartz, M. R. Andersson, A. J. Heeger, and Q. Pei, "Plastic lasers: semiconducting polymers as a new class of solid-state laser materials," Synth. Met. 84, 455-462 (1997).
    [CrossRef]
  10. H. Cao, Y. G. Zhao, C. H. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, "Ultraviolet lasing in resonators formed by scattering in semiconductor polycrystalline films," Appl. Phys. Lett. 73, 3656-3658 (1998).
    [CrossRef]
  11. H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, "Random laser action in semiconductor powder," Phys. Rev. Lett. 82, 2278-2281 (1999).
    [CrossRef]
  12. H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chan, S. T. Ho, E. W. Seelig, S. Liu, and R. P. H. Chang, "Spatial confinement of laser light in active random media," Phys. Rev. Lett. 84, 5584-5587 (2000).
    [CrossRef] [PubMed]
  13. N. E. Ter-Gabrielyan, V. M. Markusev, V. R. Belan, Ch. M. Briskina, and V. F. Zolin, "Stimulated emission spectra of powders of double sodium and lanthanum tetramolybdate," IEEE J. Quantum Electron. 21, 32-33 (1991).
    [CrossRef]
  14. Ch. M. Briskina, V. M. Markushev, and N. E. Ter-Gabrielyan, "Use of a model of coupled microcavities in the interpretation of experiments on powder lasers," Quantum Electron. 26, 923-927 (1996).
    [CrossRef]
  15. M. A. Noginov, N. E. Noginova, H. J. Caulfield, P. Venkateswarlu, T. Thompson, M. Mahdi, and V. Ostroumov, "Short-pulsed stimulated emission in the powders of NdAl3(BO3)4, NdSc3(BO3)4, and Nd:Sr5(PO4)3F laser crystals," J. Opt. Soc. Am. B 13, 2024-2033 (1996).
    [CrossRef]
  16. M. A. Noginov, N. Noginova, S. U. Egarievwe, J. C. Wang, and H. J. Caulfield, "New advances in solid state powder lasers: the effects of external seeding and external mirrors," http://spie.org/x648.xml?productlowbarid=340064 Proc. SPIE 3733, 223-227 (1999).
    [CrossRef]
  17. M. A. Noginov, G. Zhu, C. Small, and J. Novak, "Neodymium random laser with external mirrors," Appl. Phys. B 84, 269-273 (2006).
    [CrossRef]
  18. O. Svelto, Principles of Lasers, 4th ed. (Plenum, 1998).
  19. A. Rapaport and M. Bass, "The role of stimulated emission in luminescence decay," J. Lumin. 97, 180-189 (2002).
    [CrossRef]
  20. M. A. Noginov, I. N. Fowlkes, G. Zhu, and J. Novak, "Random laser thresholds in cw and pulsed regimes," Phys. Rev. A 70, 043811 (2004).
    [CrossRef]
  21. G. B. Loutts, C. Bonner, C. Meegoda, H. Ries, M. A. Noginov, N. Noginova, M. Curley, P. Venkateswarlu, A. Rapaport, and M. Bass, "Crystal growth, spectroscopic characterization, and laser performance of a new efficient laser material Nd:Ba5(PO4)3F," Appl. Phys. Lett. 71, 303-305 (1997).
    [CrossRef]
  22. S. Kueck, K. Petermann, U. Pohlmann, and G. Huber, "Electronic and vibronic transitions of the Cr4+-doped garnets Lu3Al5O12, Y3Al5O12, Y3Ga5O12, and Gd3Ga5O12," J. Lumin. 68, 1-14 (1996).
    [CrossRef]
  23. B. F. Aull and H. P. Jenssen, "Vibronic interaction in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections," IEEE J. Quantum Electron. QE-18, 925-930 (1982).
    [CrossRef]
  24. M. A. Noginov, G. B. Loutts, B. D. Lucas, D. Fider, P. T. Higgins, A. Troung, N. Noginova, N. P. Barnes, and S. Kueck, "Development of Nd-doped solid-state laser materials for 944-nm operation," IEEE J. Quantum Electron. 37, 469-480 (2001).
    [CrossRef]
  25. M. A. Noginov, Solid-State Random Lasers (Springer, 2005).
  26. M. Bahoura, K. J. Morris, G. Zhu, and M. A. Noginov, "Dependence of the neodymium random laser threshold on the diameter of the pumped spot," IEEE J. Quantum Electron. 41, 677-685 (2005).
    [CrossRef]
  27. A. G. Okhrimchuk and A. V. Shestakov, "Performance of YAG:Cr4+ laser crystal," Opt. Mater. 3, 1-13 (1994).
    [CrossRef]
  28. S. Kueck, K. Peterman, U. Pohlmann, and G. Huber, "Near-infrared emission of Cr4+-doped garnets: lifetimes, quantum efficiencies, and emission cross sections," Phys. Rev. B 51, 17323-17331 (1995).
    [CrossRef]
  29. M. A. Noginov, J. Novak, D. Grigsby, G. Zhu, and M. Bahoura, "Optimization of the transport mean free path and the absorption length in random lasers with non-resonant feedback," Opt. Express 13, 8829-8836 (2005).
    [CrossRef] [PubMed]

2006 (1)

M. A. Noginov, G. Zhu, C. Small, and J. Novak, "Neodymium random laser with external mirrors," Appl. Phys. B 84, 269-273 (2006).
[CrossRef]

2005 (2)

M. Bahoura, K. J. Morris, G. Zhu, and M. A. Noginov, "Dependence of the neodymium random laser threshold on the diameter of the pumped spot," IEEE J. Quantum Electron. 41, 677-685 (2005).
[CrossRef]

M. A. Noginov, J. Novak, D. Grigsby, G. Zhu, and M. Bahoura, "Optimization of the transport mean free path and the absorption length in random lasers with non-resonant feedback," Opt. Express 13, 8829-8836 (2005).
[CrossRef] [PubMed]

2004 (1)

M. A. Noginov, I. N. Fowlkes, G. Zhu, and J. Novak, "Random laser thresholds in cw and pulsed regimes," Phys. Rev. A 70, 043811 (2004).
[CrossRef]

2002 (1)

A. Rapaport and M. Bass, "The role of stimulated emission in luminescence decay," J. Lumin. 97, 180-189 (2002).
[CrossRef]

2001 (1)

M. A. Noginov, G. B. Loutts, B. D. Lucas, D. Fider, P. T. Higgins, A. Troung, N. Noginova, N. P. Barnes, and S. Kueck, "Development of Nd-doped solid-state laser materials for 944-nm operation," IEEE J. Quantum Electron. 37, 469-480 (2001).
[CrossRef]

2000 (1)

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chan, S. T. Ho, E. W. Seelig, S. Liu, and R. P. H. Chang, "Spatial confinement of laser light in active random media," Phys. Rev. Lett. 84, 5584-5587 (2000).
[CrossRef] [PubMed]

1999 (2)

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, "Random laser action in semiconductor powder," Phys. Rev. Lett. 82, 2278-2281 (1999).
[CrossRef]

M. A. Noginov, N. Noginova, S. U. Egarievwe, J. C. Wang, and H. J. Caulfield, "New advances in solid state powder lasers: the effects of external seeding and external mirrors," http://spie.org/x648.xml?productlowbarid=340064 Proc. SPIE 3733, 223-227 (1999).
[CrossRef]

1998 (1)

H. Cao, Y. G. Zhao, C. H. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, "Ultraviolet lasing in resonators formed by scattering in semiconductor polycrystalline films," Appl. Phys. Lett. 73, 3656-3658 (1998).
[CrossRef]

1997 (2)

M. A. Días-García, F. Hide, B. J. Schwartz, M. R. Andersson, A. J. Heeger, and Q. Pei, "Plastic lasers: semiconducting polymers as a new class of solid-state laser materials," Synth. Met. 84, 455-462 (1997).
[CrossRef]

G. B. Loutts, C. Bonner, C. Meegoda, H. Ries, M. A. Noginov, N. Noginova, M. Curley, P. Venkateswarlu, A. Rapaport, and M. Bass, "Crystal growth, spectroscopic characterization, and laser performance of a new efficient laser material Nd:Ba5(PO4)3F," Appl. Phys. Lett. 71, 303-305 (1997).
[CrossRef]

1996 (5)

S. Kueck, K. Petermann, U. Pohlmann, and G. Huber, "Electronic and vibronic transitions of the Cr4+-doped garnets Lu3Al5O12, Y3Al5O12, Y3Ga5O12, and Gd3Ga5O12," J. Lumin. 68, 1-14 (1996).
[CrossRef]

F. Hide, B. J. Schwartz, M. A. Diaz-Garsia, and A. J. Heeger, "Laser emission from solutions and films containing semiconducting polymer and titanium dioxide nanocrystals," Chem. Phys. Lett. 256, 424-430 (1996).
[CrossRef]

F. Hide, M. A. Días-García, B. J. Schwartz, M. R. Andersson, Q. Pei, and A. J. Heeger, "Semiconducting polymers: a new class of solid-state laser materials," Science 273, 1833-1836 (1996).
[CrossRef]

Ch. M. Briskina, V. M. Markushev, and N. E. Ter-Gabrielyan, "Use of a model of coupled microcavities in the interpretation of experiments on powder lasers," Quantum Electron. 26, 923-927 (1996).
[CrossRef]

M. A. Noginov, N. E. Noginova, H. J. Caulfield, P. Venkateswarlu, T. Thompson, M. Mahdi, and V. Ostroumov, "Short-pulsed stimulated emission in the powders of NdAl3(BO3)4, NdSc3(BO3)4, and Nd:Sr5(PO4)3F laser crystals," J. Opt. Soc. Am. B 13, 2024-2033 (1996).
[CrossRef]

1995 (2)

M. A. Noginov, N. E. Noginova, H. J. Caulfield, P. Venkateswarlu, and M. Mahdi, "Line narrowing in the dye solution with scattering centers," Opt. Commun. 118, 430-437 (1995).
[CrossRef]

S. Kueck, K. Peterman, U. Pohlmann, and G. Huber, "Near-infrared emission of Cr4+-doped garnets: lifetimes, quantum efficiencies, and emission cross sections," Phys. Rev. B 51, 17323-17331 (1995).
[CrossRef]

1994 (3)

A. G. Okhrimchuk and A. V. Shestakov, "Performance of YAG:Cr4+ laser crystal," Opt. Mater. 3, 1-13 (1994).
[CrossRef]

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, "Laser action in strongly scattering medium," Nature 368, 436-438 (1994).
[CrossRef]

W. L. Sha, C.-H. Liu, and R. R. Alfano, "Spectral and temporal measurements of laser action of rhodamine 640 dye in strongly scattering media," Opt. Lett. 19, 1922-1924 (1994).
[CrossRef] [PubMed]

1991 (1)

N. E. Ter-Gabrielyan, V. M. Markusev, V. R. Belan, Ch. M. Briskina, and V. F. Zolin, "Stimulated emission spectra of powders of double sodium and lanthanum tetramolybdate," IEEE J. Quantum Electron. 21, 32-33 (1991).
[CrossRef]

1986 (1)

V. M. Markushev, V. F. Zolin, and Ch. M. Briskina, "Luminescence and stimulated emission of neodymium in sodium lanthanum molybdate powders," Sov. J. Quantum Electron. 16, 281-283 (1986).
[CrossRef]

1982 (1)

B. F. Aull and H. P. Jenssen, "Vibronic interaction in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections," IEEE J. Quantum Electron. QE-18, 925-930 (1982).
[CrossRef]

1967 (1)

V. S. Letokhov, "Stimulated emission of an ensemble of scattering particles with negative absorption," JETP Lett. 5, 212-215 (1967).

Appl. Phys. B (1)

M. A. Noginov, G. Zhu, C. Small, and J. Novak, "Neodymium random laser with external mirrors," Appl. Phys. B 84, 269-273 (2006).
[CrossRef]

Appl. Phys. Lett. (2)

H. Cao, Y. G. Zhao, C. H. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, "Ultraviolet lasing in resonators formed by scattering in semiconductor polycrystalline films," Appl. Phys. Lett. 73, 3656-3658 (1998).
[CrossRef]

G. B. Loutts, C. Bonner, C. Meegoda, H. Ries, M. A. Noginov, N. Noginova, M. Curley, P. Venkateswarlu, A. Rapaport, and M. Bass, "Crystal growth, spectroscopic characterization, and laser performance of a new efficient laser material Nd:Ba5(PO4)3F," Appl. Phys. Lett. 71, 303-305 (1997).
[CrossRef]

Chem. Phys. Lett. (1)

F. Hide, B. J. Schwartz, M. A. Diaz-Garsia, and A. J. Heeger, "Laser emission from solutions and films containing semiconducting polymer and titanium dioxide nanocrystals," Chem. Phys. Lett. 256, 424-430 (1996).
[CrossRef]

IEEE J. Quantum Electron. (4)

N. E. Ter-Gabrielyan, V. M. Markusev, V. R. Belan, Ch. M. Briskina, and V. F. Zolin, "Stimulated emission spectra of powders of double sodium and lanthanum tetramolybdate," IEEE J. Quantum Electron. 21, 32-33 (1991).
[CrossRef]

B. F. Aull and H. P. Jenssen, "Vibronic interaction in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections," IEEE J. Quantum Electron. QE-18, 925-930 (1982).
[CrossRef]

M. A. Noginov, G. B. Loutts, B. D. Lucas, D. Fider, P. T. Higgins, A. Troung, N. Noginova, N. P. Barnes, and S. Kueck, "Development of Nd-doped solid-state laser materials for 944-nm operation," IEEE J. Quantum Electron. 37, 469-480 (2001).
[CrossRef]

M. Bahoura, K. J. Morris, G. Zhu, and M. A. Noginov, "Dependence of the neodymium random laser threshold on the diameter of the pumped spot," IEEE J. Quantum Electron. 41, 677-685 (2005).
[CrossRef]

J. Lumin. (2)

S. Kueck, K. Petermann, U. Pohlmann, and G. Huber, "Electronic and vibronic transitions of the Cr4+-doped garnets Lu3Al5O12, Y3Al5O12, Y3Ga5O12, and Gd3Ga5O12," J. Lumin. 68, 1-14 (1996).
[CrossRef]

A. Rapaport and M. Bass, "The role of stimulated emission in luminescence decay," J. Lumin. 97, 180-189 (2002).
[CrossRef]

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

JETP Lett. (1)

V. S. Letokhov, "Stimulated emission of an ensemble of scattering particles with negative absorption," JETP Lett. 5, 212-215 (1967).

Nature (1)

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, "Laser action in strongly scattering medium," Nature 368, 436-438 (1994).
[CrossRef]

Opt. Commun. (1)

M. A. Noginov, N. E. Noginova, H. J. Caulfield, P. Venkateswarlu, and M. Mahdi, "Line narrowing in the dye solution with scattering centers," Opt. Commun. 118, 430-437 (1995).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Opt. Mater. (1)

A. G. Okhrimchuk and A. V. Shestakov, "Performance of YAG:Cr4+ laser crystal," Opt. Mater. 3, 1-13 (1994).
[CrossRef]

Phys. Rev. A (1)

M. A. Noginov, I. N. Fowlkes, G. Zhu, and J. Novak, "Random laser thresholds in cw and pulsed regimes," Phys. Rev. A 70, 043811 (2004).
[CrossRef]

Phys. Rev. B (1)

S. Kueck, K. Peterman, U. Pohlmann, and G. Huber, "Near-infrared emission of Cr4+-doped garnets: lifetimes, quantum efficiencies, and emission cross sections," Phys. Rev. B 51, 17323-17331 (1995).
[CrossRef]

Phys. Rev. Lett. (2)

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, "Random laser action in semiconductor powder," Phys. Rev. Lett. 82, 2278-2281 (1999).
[CrossRef]

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chan, S. T. Ho, E. W. Seelig, S. Liu, and R. P. H. Chang, "Spatial confinement of laser light in active random media," Phys. Rev. Lett. 84, 5584-5587 (2000).
[CrossRef] [PubMed]

Proc. SPIE (1)

M. A. Noginov, N. Noginova, S. U. Egarievwe, J. C. Wang, and H. J. Caulfield, "New advances in solid state powder lasers: the effects of external seeding and external mirrors," http://spie.org/x648.xml?productlowbarid=340064 Proc. SPIE 3733, 223-227 (1999).
[CrossRef]

Quantum Electron. (1)

Ch. M. Briskina, V. M. Markushev, and N. E. Ter-Gabrielyan, "Use of a model of coupled microcavities in the interpretation of experiments on powder lasers," Quantum Electron. 26, 923-927 (1996).
[CrossRef]

Science (1)

F. Hide, M. A. Días-García, B. J. Schwartz, M. R. Andersson, Q. Pei, and A. J. Heeger, "Semiconducting polymers: a new class of solid-state laser materials," Science 273, 1833-1836 (1996).
[CrossRef]

Sov. J. Quantum Electron. (1)

V. M. Markushev, V. F. Zolin, and Ch. M. Briskina, "Luminescence and stimulated emission of neodymium in sodium lanthanum molybdate powders," Sov. J. Quantum Electron. 16, 281-283 (1986).
[CrossRef]

Synth. Met. (1)

M. A. Días-García, F. Hide, B. J. Schwartz, M. R. Andersson, A. J. Heeger, and Q. Pei, "Plastic lasers: semiconducting polymers as a new class of solid-state laser materials," Synth. Met. 84, 455-462 (1997).
[CrossRef]

Other (3)

R. M. Balachandran, A. Pacheco, and N. M. Lawandy, "Photonic textile fibers," in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, 1995), pp. 114-115.

O. Svelto, Principles of Lasers, 4th ed. (Plenum, 1998).

M. A. Noginov, Solid-State Random Lasers (Springer, 2005).

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 (6)

Fig. 1
Fig. 1

(1) Decay rate of population inversion ( d n n d t ) 1 , (2) decay rate of emission decay ( d E E d t ) 1 , and (3) emission photon density E as a function of population inversion n.

Fig. 2
Fig. 2

(a) Absorption spectrum of Cr : YAG ( k 1.06 a b s = 5.6 cm 1 ) ; (b) effective emission cross-section spectrum of Nd : BFAP powder. The ratio of the emission cross sections at 1.06 and 1.32 μ m is equal to 1.8.

Fig. 3
Fig. 3

Random lasing threshold in ( Nd : BFAP ) x ( Cr : YAG ) 1 x as a function of the diameter of the pumped spot; (1) x = 1 , (2) x = 0.75 , (3) x = 0.54 ; Inset, input–output curves in ( Nd : BFAP ) x ( Cr : YAG ) 1 x random lasers recorded in setup 1. The diameter of the pumped spot was approximately equal to 0.5 mm .

Fig. 4
Fig. 4

Ratio of the absorption loss to the radiation loss in ( Nd : BFAP ) x ( Cr : YAG ) 1 x random laser as a function of Cr : YAG concentration, 1 x .

Fig. 5
Fig. 5

Effective pre-lasing emission decay times measured in pure Nd : BFAP powder in a glass cuvette (setup 1a), traces 1 and 2, and in a cuvette with a front 1.32 mirror (setup 3), traces 3 and 4. Traces 1 and 3 correspond to a 1.06 μ m emission and traces 2 and 4 correspond to a 1.32 μ m emission. The diameter of the pumped spot is 0.8 mm .

Fig. 6
Fig. 6

Input–output curves obtained in pure Nd : BFAP random laser (at λ = 1.06 μ m ) in setup 1a (trace 1) and setup 3 (trace 2). The diameter of the pumped spot was approximately equal to 0.38 mm .

Equations (18)

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

n t h = 2 α l ln ( R 1 R 2 ) 2 l σ e m ,
ln ( R 1 R 2 ) = 2 l c c τ c = 2 l c τ p .
n t h = α + ( c τ p ) 1 σ e m = α l + l c ( c τ c ) 1 l σ e m .
n t h = E t h h ν p u m p η o η ,
α x 1.06 l + l c c τ c α x = 1 1.06 l + l c c τ c = E t h ( x ) 1.06 η x E t h ( x = 1 ) 1.06 η x = 1 ,
α x 1.06 ( c τ p ) 1 = l α x 1.06 l c ( c τ c ) 1 = E t h ( x ) 1.06 η x E t h ( x = 1 ) 1.06 η x = 1 1 .
E t h ( x ) 1.32 E t h ( x ) 1.06 = ( l c c τ c 1.32 α x 1.06 l + l c c τ c 1.06 ) ( σ e m 1.06 σ e m 1.32 ) .
d n d t = P ( t ) h v p u m p S l p n τ E h v e c σ e m n ,
d E d t = E τ p + ζ n τ h v e m + E c σ e m n ,
E ζ n τ h ν e m τ p 1 c σ e m n .
d n n d t = τ 1 ζ n τ c σ e m n τ p 1 c σ e m n .
d E E d t = d n n d t τ p 1 τ p 1 c σ e m n .
σ e m = 1 τ I ( λ ) λ 5 8 π c n r e f r 2 I ( λ ) λ d λ ,
E t h 1.32 E t h 1.06 = 1.8 1.29 = 1.4 .
E t h 1.32 E t h 1.06 = 1.8 2.3 = 0.78 .
E t h 1.32 E t h 1.06 = 1.8 2.3 × 1 1.29 = 0.61 .
[ 1.8 2.3 = ] 0.78 < E t h 1.32 E t h 1.06 < 1.42 [ = 1.8 2.3 × 1.3 × 1.4 ]
[ 1.8 2.3 × 1 1.29 = ] 0.61 < E t h 1.32 E t h 1.06 < 1.10 [ 1.8 2.3 × 1 1.29 × 1.3 × 1.4 ]

Metrics