Abstract

Absorption and emission cross sections for the 4I9/24F3/2 transition in Nd:SrGdGa3O, have been measured as a function of temperature. A fluorescence branching ratio of 0.42 for this transition was calculated from a Judd–Ofelt analysis. Diode-pumped lasing was demonstrated at 0.911 μm at reduced temperature and 1.06 μm at room temperature. An optical slope efficiency of 9% was achieved at 1.06 μm with diode side pumping.

© 1991 Optical Society of America

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References

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  1. H. R. Verdun, L. R. Black, G. F. de la Fuente, and D. M. Andrauskas, “Growth and characterization of Nd-doped aluminates and gallates with the melilite structure,” in Digest of Topical Meeting on Tunable Solid State Lasers (Optical Society of America, Washington, D.C., 1989), pp. 166–168.
  2. A. A. Kaminskii, Laser Crystals (Springer-Verlag, Berlin, 1981).
  3. T. S. Lomheim and L. G. DeShazer, “Optical absorption intensities of trivalent neodymium in the uniaxial crystal yttrium vanadate,” J. Appl. Phys. 49, 5517–5522 (1978).
    [Crossref]
  4. W. T. Carnall, P. R. Fields, and K. Rajnak, “Electronic energy levels in the trivalent lanthanide aquo ions. I. Pr+3, Nd+3 Pm+3, Sm+3, Dy+3, Ho+3, Er+3, and Tm+3,” J. Chem. Phys. 49, 4424–4442 (1968).
    [Crossref]
  5. W. Krupke, “Induced-emission cross sections in neodymium laser glasses,” IEEE J. Quantum Electron. QE-10, 450–457 (1974).
    [Crossref]
  6. W. Ryba-Romanowski, B. Jezowska-Trzebiatowska, W. Piekarczyk, and M. Berkowski, “Optical properties and lasing of BaLaGa3O7 single crystals doped with neodymium,” J. Phys. Chem. Solids 49, 199–203 (1988).
    [Crossref]
  7. W. Ryba-Romanowski, M. U. Gutowska, W. Piekarczyk, M. Berkowski, Z. Mazurak, and B. Jezowska-Trzebiatowska, “Spectroscopic investigations of neodymium doped BaLaGa3O7 single crystals,” J. Lumin. 36, 369–372 (1987).
    [Crossref]
  8. P. F. Moulton, “Spectroscopic and laser characteristics of Ti:Al2O3,” J. Opt. Soc. Am. B 3, 125–133 (1986)
    [Crossref]
  9. F. Hanson, “Laser-diode side-pumped Nd:YAIO3 laser at 1.08 and 1.34 μm,” Opt. Lett. 14, 674–676 (1989).
    [Crossref] [PubMed]
  10. B. F. Aull and H. P. Jensen, “Vibronic interactions in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections,” IEEE J. Quantum Electron. QE-18, 925 (1982).
    [Crossref]
  11. E. V. Zharikov, V. A. Zhitnyuk, I. I. Kuratev, V. V. Laptev, V. A. Smirnov, A. V. Shestakov, and I. A. Shcherbakov, “Laser based on a GSGG:Cr+3,Nd+3 crystal which operates on the 4F3/2 → 4I9/2 transition at room temperature,” Bull. Acad. Sci. USSR Phys. Ser.98–100 (1984).
  12. J. M. Pellegrino, W. M. Yen, and M. J. Weber, “Composition dependence of Nd3+ homogeneous linewidths in glasses,” J. Appl. Phys. 51, 6332–6336 (1980).
    [Crossref]
  13. P. Nachman, J. Munch, and R. Yee, “Diode-pumped, frequency stable, tunable, continuous-wave Nd:glass laser,” IEEE J. Quantum Electron. QE-26, 317–322 (1990).
    [Crossref]
  14. G. B. Michelangeli, A. Landoni, M. Neri, G. Giuliani, and E. Palange, “Reliable single-mode operation and fine frequency tuning of a Nd-glass low-gain oscillator,” Opt. Commun. 65, 283–286 (1988).
    [Crossref]

1990 (1)

P. Nachman, J. Munch, and R. Yee, “Diode-pumped, frequency stable, tunable, continuous-wave Nd:glass laser,” IEEE J. Quantum Electron. QE-26, 317–322 (1990).
[Crossref]

1989 (1)

1988 (2)

W. Ryba-Romanowski, B. Jezowska-Trzebiatowska, W. Piekarczyk, and M. Berkowski, “Optical properties and lasing of BaLaGa3O7 single crystals doped with neodymium,” J. Phys. Chem. Solids 49, 199–203 (1988).
[Crossref]

G. B. Michelangeli, A. Landoni, M. Neri, G. Giuliani, and E. Palange, “Reliable single-mode operation and fine frequency tuning of a Nd-glass low-gain oscillator,” Opt. Commun. 65, 283–286 (1988).
[Crossref]

1987 (1)

W. Ryba-Romanowski, M. U. Gutowska, W. Piekarczyk, M. Berkowski, Z. Mazurak, and B. Jezowska-Trzebiatowska, “Spectroscopic investigations of neodymium doped BaLaGa3O7 single crystals,” J. Lumin. 36, 369–372 (1987).
[Crossref]

1986 (1)

1984 (1)

E. V. Zharikov, V. A. Zhitnyuk, I. I. Kuratev, V. V. Laptev, V. A. Smirnov, A. V. Shestakov, and I. A. Shcherbakov, “Laser based on a GSGG:Cr+3,Nd+3 crystal which operates on the 4F3/2 → 4I9/2 transition at room temperature,” Bull. Acad. Sci. USSR Phys. Ser.98–100 (1984).

1982 (1)

B. F. Aull and H. P. Jensen, “Vibronic interactions in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections,” IEEE J. Quantum Electron. QE-18, 925 (1982).
[Crossref]

1980 (1)

J. M. Pellegrino, W. M. Yen, and M. J. Weber, “Composition dependence of Nd3+ homogeneous linewidths in glasses,” J. Appl. Phys. 51, 6332–6336 (1980).
[Crossref]

1978 (1)

T. S. Lomheim and L. G. DeShazer, “Optical absorption intensities of trivalent neodymium in the uniaxial crystal yttrium vanadate,” J. Appl. Phys. 49, 5517–5522 (1978).
[Crossref]

1974 (1)

W. Krupke, “Induced-emission cross sections in neodymium laser glasses,” IEEE J. Quantum Electron. QE-10, 450–457 (1974).
[Crossref]

1968 (1)

W. T. Carnall, P. R. Fields, and K. Rajnak, “Electronic energy levels in the trivalent lanthanide aquo ions. I. Pr+3, Nd+3 Pm+3, Sm+3, Dy+3, Ho+3, Er+3, and Tm+3,” J. Chem. Phys. 49, 4424–4442 (1968).
[Crossref]

Andrauskas, D. M.

H. R. Verdun, L. R. Black, G. F. de la Fuente, and D. M. Andrauskas, “Growth and characterization of Nd-doped aluminates and gallates with the melilite structure,” in Digest of Topical Meeting on Tunable Solid State Lasers (Optical Society of America, Washington, D.C., 1989), pp. 166–168.

Aull, B. F.

B. F. Aull and H. P. Jensen, “Vibronic interactions in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections,” IEEE J. Quantum Electron. QE-18, 925 (1982).
[Crossref]

Berkowski, M.

W. Ryba-Romanowski, B. Jezowska-Trzebiatowska, W. Piekarczyk, and M. Berkowski, “Optical properties and lasing of BaLaGa3O7 single crystals doped with neodymium,” J. Phys. Chem. Solids 49, 199–203 (1988).
[Crossref]

W. Ryba-Romanowski, M. U. Gutowska, W. Piekarczyk, M. Berkowski, Z. Mazurak, and B. Jezowska-Trzebiatowska, “Spectroscopic investigations of neodymium doped BaLaGa3O7 single crystals,” J. Lumin. 36, 369–372 (1987).
[Crossref]

Black, L. R.

H. R. Verdun, L. R. Black, G. F. de la Fuente, and D. M. Andrauskas, “Growth and characterization of Nd-doped aluminates and gallates with the melilite structure,” in Digest of Topical Meeting on Tunable Solid State Lasers (Optical Society of America, Washington, D.C., 1989), pp. 166–168.

Carnall, W. T.

W. T. Carnall, P. R. Fields, and K. Rajnak, “Electronic energy levels in the trivalent lanthanide aquo ions. I. Pr+3, Nd+3 Pm+3, Sm+3, Dy+3, Ho+3, Er+3, and Tm+3,” J. Chem. Phys. 49, 4424–4442 (1968).
[Crossref]

de la Fuente, G. F.

H. R. Verdun, L. R. Black, G. F. de la Fuente, and D. M. Andrauskas, “Growth and characterization of Nd-doped aluminates and gallates with the melilite structure,” in Digest of Topical Meeting on Tunable Solid State Lasers (Optical Society of America, Washington, D.C., 1989), pp. 166–168.

DeShazer, L. G.

T. S. Lomheim and L. G. DeShazer, “Optical absorption intensities of trivalent neodymium in the uniaxial crystal yttrium vanadate,” J. Appl. Phys. 49, 5517–5522 (1978).
[Crossref]

Fields, P. R.

W. T. Carnall, P. R. Fields, and K. Rajnak, “Electronic energy levels in the trivalent lanthanide aquo ions. I. Pr+3, Nd+3 Pm+3, Sm+3, Dy+3, Ho+3, Er+3, and Tm+3,” J. Chem. Phys. 49, 4424–4442 (1968).
[Crossref]

Giuliani, G.

G. B. Michelangeli, A. Landoni, M. Neri, G. Giuliani, and E. Palange, “Reliable single-mode operation and fine frequency tuning of a Nd-glass low-gain oscillator,” Opt. Commun. 65, 283–286 (1988).
[Crossref]

Gutowska, M. U.

W. Ryba-Romanowski, M. U. Gutowska, W. Piekarczyk, M. Berkowski, Z. Mazurak, and B. Jezowska-Trzebiatowska, “Spectroscopic investigations of neodymium doped BaLaGa3O7 single crystals,” J. Lumin. 36, 369–372 (1987).
[Crossref]

Hanson, F.

Jensen, H. P.

B. F. Aull and H. P. Jensen, “Vibronic interactions in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections,” IEEE J. Quantum Electron. QE-18, 925 (1982).
[Crossref]

Jezowska-Trzebiatowska, B.

W. Ryba-Romanowski, B. Jezowska-Trzebiatowska, W. Piekarczyk, and M. Berkowski, “Optical properties and lasing of BaLaGa3O7 single crystals doped with neodymium,” J. Phys. Chem. Solids 49, 199–203 (1988).
[Crossref]

W. Ryba-Romanowski, M. U. Gutowska, W. Piekarczyk, M. Berkowski, Z. Mazurak, and B. Jezowska-Trzebiatowska, “Spectroscopic investigations of neodymium doped BaLaGa3O7 single crystals,” J. Lumin. 36, 369–372 (1987).
[Crossref]

Kaminskii, A. A.

A. A. Kaminskii, Laser Crystals (Springer-Verlag, Berlin, 1981).

Krupke, W.

W. Krupke, “Induced-emission cross sections in neodymium laser glasses,” IEEE J. Quantum Electron. QE-10, 450–457 (1974).
[Crossref]

Kuratev, I. I.

E. V. Zharikov, V. A. Zhitnyuk, I. I. Kuratev, V. V. Laptev, V. A. Smirnov, A. V. Shestakov, and I. A. Shcherbakov, “Laser based on a GSGG:Cr+3,Nd+3 crystal which operates on the 4F3/2 → 4I9/2 transition at room temperature,” Bull. Acad. Sci. USSR Phys. Ser.98–100 (1984).

Landoni, A.

G. B. Michelangeli, A. Landoni, M. Neri, G. Giuliani, and E. Palange, “Reliable single-mode operation and fine frequency tuning of a Nd-glass low-gain oscillator,” Opt. Commun. 65, 283–286 (1988).
[Crossref]

Laptev, V. V.

E. V. Zharikov, V. A. Zhitnyuk, I. I. Kuratev, V. V. Laptev, V. A. Smirnov, A. V. Shestakov, and I. A. Shcherbakov, “Laser based on a GSGG:Cr+3,Nd+3 crystal which operates on the 4F3/2 → 4I9/2 transition at room temperature,” Bull. Acad. Sci. USSR Phys. Ser.98–100 (1984).

Lomheim, T. S.

T. S. Lomheim and L. G. DeShazer, “Optical absorption intensities of trivalent neodymium in the uniaxial crystal yttrium vanadate,” J. Appl. Phys. 49, 5517–5522 (1978).
[Crossref]

Mazurak, Z.

W. Ryba-Romanowski, M. U. Gutowska, W. Piekarczyk, M. Berkowski, Z. Mazurak, and B. Jezowska-Trzebiatowska, “Spectroscopic investigations of neodymium doped BaLaGa3O7 single crystals,” J. Lumin. 36, 369–372 (1987).
[Crossref]

Michelangeli, G. B.

G. B. Michelangeli, A. Landoni, M. Neri, G. Giuliani, and E. Palange, “Reliable single-mode operation and fine frequency tuning of a Nd-glass low-gain oscillator,” Opt. Commun. 65, 283–286 (1988).
[Crossref]

Moulton, P. F.

Munch, J.

P. Nachman, J. Munch, and R. Yee, “Diode-pumped, frequency stable, tunable, continuous-wave Nd:glass laser,” IEEE J. Quantum Electron. QE-26, 317–322 (1990).
[Crossref]

Nachman, P.

P. Nachman, J. Munch, and R. Yee, “Diode-pumped, frequency stable, tunable, continuous-wave Nd:glass laser,” IEEE J. Quantum Electron. QE-26, 317–322 (1990).
[Crossref]

Neri, M.

G. B. Michelangeli, A. Landoni, M. Neri, G. Giuliani, and E. Palange, “Reliable single-mode operation and fine frequency tuning of a Nd-glass low-gain oscillator,” Opt. Commun. 65, 283–286 (1988).
[Crossref]

Palange, E.

G. B. Michelangeli, A. Landoni, M. Neri, G. Giuliani, and E. Palange, “Reliable single-mode operation and fine frequency tuning of a Nd-glass low-gain oscillator,” Opt. Commun. 65, 283–286 (1988).
[Crossref]

Pellegrino, J. M.

J. M. Pellegrino, W. M. Yen, and M. J. Weber, “Composition dependence of Nd3+ homogeneous linewidths in glasses,” J. Appl. Phys. 51, 6332–6336 (1980).
[Crossref]

Piekarczyk, W.

W. Ryba-Romanowski, B. Jezowska-Trzebiatowska, W. Piekarczyk, and M. Berkowski, “Optical properties and lasing of BaLaGa3O7 single crystals doped with neodymium,” J. Phys. Chem. Solids 49, 199–203 (1988).
[Crossref]

W. Ryba-Romanowski, M. U. Gutowska, W. Piekarczyk, M. Berkowski, Z. Mazurak, and B. Jezowska-Trzebiatowska, “Spectroscopic investigations of neodymium doped BaLaGa3O7 single crystals,” J. Lumin. 36, 369–372 (1987).
[Crossref]

Rajnak, K.

W. T. Carnall, P. R. Fields, and K. Rajnak, “Electronic energy levels in the trivalent lanthanide aquo ions. I. Pr+3, Nd+3 Pm+3, Sm+3, Dy+3, Ho+3, Er+3, and Tm+3,” J. Chem. Phys. 49, 4424–4442 (1968).
[Crossref]

Ryba-Romanowski, W.

W. Ryba-Romanowski, B. Jezowska-Trzebiatowska, W. Piekarczyk, and M. Berkowski, “Optical properties and lasing of BaLaGa3O7 single crystals doped with neodymium,” J. Phys. Chem. Solids 49, 199–203 (1988).
[Crossref]

W. Ryba-Romanowski, M. U. Gutowska, W. Piekarczyk, M. Berkowski, Z. Mazurak, and B. Jezowska-Trzebiatowska, “Spectroscopic investigations of neodymium doped BaLaGa3O7 single crystals,” J. Lumin. 36, 369–372 (1987).
[Crossref]

Shcherbakov, I. A.

E. V. Zharikov, V. A. Zhitnyuk, I. I. Kuratev, V. V. Laptev, V. A. Smirnov, A. V. Shestakov, and I. A. Shcherbakov, “Laser based on a GSGG:Cr+3,Nd+3 crystal which operates on the 4F3/2 → 4I9/2 transition at room temperature,” Bull. Acad. Sci. USSR Phys. Ser.98–100 (1984).

Shestakov, A. V.

E. V. Zharikov, V. A. Zhitnyuk, I. I. Kuratev, V. V. Laptev, V. A. Smirnov, A. V. Shestakov, and I. A. Shcherbakov, “Laser based on a GSGG:Cr+3,Nd+3 crystal which operates on the 4F3/2 → 4I9/2 transition at room temperature,” Bull. Acad. Sci. USSR Phys. Ser.98–100 (1984).

Smirnov, V. A.

E. V. Zharikov, V. A. Zhitnyuk, I. I. Kuratev, V. V. Laptev, V. A. Smirnov, A. V. Shestakov, and I. A. Shcherbakov, “Laser based on a GSGG:Cr+3,Nd+3 crystal which operates on the 4F3/2 → 4I9/2 transition at room temperature,” Bull. Acad. Sci. USSR Phys. Ser.98–100 (1984).

Verdun, H. R.

H. R. Verdun, L. R. Black, G. F. de la Fuente, and D. M. Andrauskas, “Growth and characterization of Nd-doped aluminates and gallates with the melilite structure,” in Digest of Topical Meeting on Tunable Solid State Lasers (Optical Society of America, Washington, D.C., 1989), pp. 166–168.

Weber, M. J.

J. M. Pellegrino, W. M. Yen, and M. J. Weber, “Composition dependence of Nd3+ homogeneous linewidths in glasses,” J. Appl. Phys. 51, 6332–6336 (1980).
[Crossref]

Yee, R.

P. Nachman, J. Munch, and R. Yee, “Diode-pumped, frequency stable, tunable, continuous-wave Nd:glass laser,” IEEE J. Quantum Electron. QE-26, 317–322 (1990).
[Crossref]

Yen, W. M.

J. M. Pellegrino, W. M. Yen, and M. J. Weber, “Composition dependence of Nd3+ homogeneous linewidths in glasses,” J. Appl. Phys. 51, 6332–6336 (1980).
[Crossref]

Zharikov, E. V.

E. V. Zharikov, V. A. Zhitnyuk, I. I. Kuratev, V. V. Laptev, V. A. Smirnov, A. V. Shestakov, and I. A. Shcherbakov, “Laser based on a GSGG:Cr+3,Nd+3 crystal which operates on the 4F3/2 → 4I9/2 transition at room temperature,” Bull. Acad. Sci. USSR Phys. Ser.98–100 (1984).

Zhitnyuk, V. A.

E. V. Zharikov, V. A. Zhitnyuk, I. I. Kuratev, V. V. Laptev, V. A. Smirnov, A. V. Shestakov, and I. A. Shcherbakov, “Laser based on a GSGG:Cr+3,Nd+3 crystal which operates on the 4F3/2 → 4I9/2 transition at room temperature,” Bull. Acad. Sci. USSR Phys. Ser.98–100 (1984).

Bull. Acad. Sci. USSR Phys. Ser. (1)

E. V. Zharikov, V. A. Zhitnyuk, I. I. Kuratev, V. V. Laptev, V. A. Smirnov, A. V. Shestakov, and I. A. Shcherbakov, “Laser based on a GSGG:Cr+3,Nd+3 crystal which operates on the 4F3/2 → 4I9/2 transition at room temperature,” Bull. Acad. Sci. USSR Phys. Ser.98–100 (1984).

IEEE J. Quantum Electron. (3)

P. Nachman, J. Munch, and R. Yee, “Diode-pumped, frequency stable, tunable, continuous-wave Nd:glass laser,” IEEE J. Quantum Electron. QE-26, 317–322 (1990).
[Crossref]

B. F. Aull and H. P. Jensen, “Vibronic interactions in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections,” IEEE J. Quantum Electron. QE-18, 925 (1982).
[Crossref]

W. Krupke, “Induced-emission cross sections in neodymium laser glasses,” IEEE J. Quantum Electron. QE-10, 450–457 (1974).
[Crossref]

J. Appl. Phys. (2)

T. S. Lomheim and L. G. DeShazer, “Optical absorption intensities of trivalent neodymium in the uniaxial crystal yttrium vanadate,” J. Appl. Phys. 49, 5517–5522 (1978).
[Crossref]

J. M. Pellegrino, W. M. Yen, and M. J. Weber, “Composition dependence of Nd3+ homogeneous linewidths in glasses,” J. Appl. Phys. 51, 6332–6336 (1980).
[Crossref]

J. Chem. Phys. (1)

W. T. Carnall, P. R. Fields, and K. Rajnak, “Electronic energy levels in the trivalent lanthanide aquo ions. I. Pr+3, Nd+3 Pm+3, Sm+3, Dy+3, Ho+3, Er+3, and Tm+3,” J. Chem. Phys. 49, 4424–4442 (1968).
[Crossref]

J. Lumin. (1)

W. Ryba-Romanowski, M. U. Gutowska, W. Piekarczyk, M. Berkowski, Z. Mazurak, and B. Jezowska-Trzebiatowska, “Spectroscopic investigations of neodymium doped BaLaGa3O7 single crystals,” J. Lumin. 36, 369–372 (1987).
[Crossref]

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

J. Phys. Chem. Solids (1)

W. Ryba-Romanowski, B. Jezowska-Trzebiatowska, W. Piekarczyk, and M. Berkowski, “Optical properties and lasing of BaLaGa3O7 single crystals doped with neodymium,” J. Phys. Chem. Solids 49, 199–203 (1988).
[Crossref]

Opt. Commun. (1)

G. B. Michelangeli, A. Landoni, M. Neri, G. Giuliani, and E. Palange, “Reliable single-mode operation and fine frequency tuning of a Nd-glass low-gain oscillator,” Opt. Commun. 65, 283–286 (1988).
[Crossref]

Opt. Lett. (1)

Other (2)

H. R. Verdun, L. R. Black, G. F. de la Fuente, and D. M. Andrauskas, “Growth and characterization of Nd-doped aluminates and gallates with the melilite structure,” in Digest of Topical Meeting on Tunable Solid State Lasers (Optical Society of America, Washington, D.C., 1989), pp. 166–168.

A. A. Kaminskii, Laser Crystals (Springer-Verlag, Berlin, 1981).

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Figures (8)

Fig. 1
Fig. 1

The 4I9/24F3/2 absorption spectrum of Nd:SrGdGa3O7 from 300 to 100 K for E perpendicular to the crystal c axis.

Fig. 2
Fig. 2

The 4I9/24F3/2 absorption spectrum of Nd:SrGdGa3O7 from 300 to 100 K for E parallel to the crystal c axis.

Fig. 3
Fig. 3

The absorption at 911 and 918.6 nm as a function of temperature.

Fig. 4
Fig. 4

The 4F3/24I1/2, 4I9/2 emission cross sections of Nd:SrGdGa3O7 for E perpendicular to the crystal c axis at 300 K (solid curve) and 100 K (dashed curved). The data at 100 K assume the same fluorescence branching as at 300 K.

Fig. 5
Fig. 5

The emission cross section as in Fig. 4 for E parallel to the crystal c axis.

Fig. 6
Fig. 6

Polarized absorption spectra of the diode pump bands at room temperature.

Fig. 7
Fig. 7

Laser performance with diode array side pumping. Mirror transmissions are 0.03 (●), 0.076 (■), 0.174 (▲) at 1.06 μm and ~0.003 (○) at ~0.9 μm.

Fig. 8
Fig. 8

Laser emission spectra for different cold-tip temperatures. Crystal temperature was somewhat warmer.

Tables (4)

Tables Icon

Table 1 Refractive-Index Measurements and Fitted Sellmeier Coefficients for Nd:SrGdGa3O7

Tables Icon

Table 2 Measured and Calculated Absorption Line Strengths for Nd:SrGdGa3O7

Tables Icon

Table 3 Calculated Radiative Decay Rates and Branching Ratios from the 4F3/2 Level

Tables Icon

Table 4 Stimulated Emission Cross Sections from the 4F3/2 Level Calculated from the Measured Spectra

Equations (7)

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

S ( I 4 9 / 2 , J ) = 9 ch ( 2 J + 1 ) 8 π 3 N λ e 2 [ n e ( n e 2 + 2 ) 2 J k π ( λ ) d λ + 2 n 0 ( n 0 2 + 2 ) 2 J k σ ( λ ) d λ ] .
n 2 = 1 + a λ 2 b λ 2 - 1 .
I ( I 4 J ) = 1 3 I 4 J g π ( λ ) λ d λ + 2 3 I 4 J g σ ( λ ) λ d λ .
σ σ ( λ ) = g s ( λ ) λ 5 η β 9 / 2 8 π c n 0 2 τ I 9 / 2 ,
S = S 0 ln ( R ) ln ( 1 + x ) + ln ( R ) ,
1 S = 1 S 0 + ln ( 1 - x ) S 0 ln ( R ) ,
P 0 = - h ν p ln ( 1 - x ) + ln ( R ) 2 σ τ η α ,

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