Abstract

We have applied the theory of McCumber to the 44I13/24I15/2 transition of Er3+-doped glasses and confirmed its ability to provide both spectra and accurate values of cross sections. For an Al/P–silica fiber, the exact McCumber treatment is within 3% of the measured emission cross section, whereas an Einstein analysis is off by >50%. An approximate treatment that eliminates the McCumber theory’s requirement of detailed electronic structure has been developed and found to usually provide more accurate values than an Einstein analysis.

© 1991 Optical Society of America

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References

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  1. R. J. Mears, L. Reekie, I. M. Jauncey, D. N. Payne, in Optical Fiber Communication, Vol. 3 of 1987 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1987), paper WI2.
  2. E. Desurvire, J. R. Simpson, IEEE J. Lightwave Technol. 7, 835 (1989).
    [CrossRef]
  3. W. J. Miniscalco, L. J. Andrews, B. A. Thompson, T. Wei, B. T. Hall, in Tunable Solid State Lasers, Vol. 5 of OSA Proceedings Series, M. L. Shand, H. P. Jenssen, eds. (Optical Society of America, Washington, D.C., 1989), p. 71.
  4. K. Dybdal, N. Bjerre, J. E. Pedersen, C. C. Larsen, Proc. Soc. Photo-Opt. Instrum. Eng. 1171, 209 (1990).
  5. P. R. Morkel, R. I. Laming, Opt. Lett. 14, 1062 (1989).
    [CrossRef] [PubMed]
  6. W. L. Barnes, R. I. Laming, P. R. Morkel, E. J. Tarbox, in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 50.
  7. D. E. McCumber, Phys. Rev. 134, A299 (1964).
    [CrossRef]
  8. B. DiBartolo, Optical Interactions in Solids (Wiley, New York, 1968), pp. 404–411.
  9. J. N. Sandoe, P. H. Sarkies, S. Parke, J. Phys. D 5, 1788 (1972).
    [CrossRef]
  10. N. E. Alekseev, V. P. Gapontsev, M. E. Zhabotinskii, V. B. Kravchenko, Yu. P. Rudnitskii, Laser Phosphate Glasses (Nauka, Moscow, 1983), pp. 6–25 (translation by Berkeley Scientific Translation Service).
  11. S. D. Zemon, G. M. Lambert, W. J. Miniscalco, L. J. Andrews, B. T. Hall, Proc. Soc. Photo-Opt. Instrum. Eng. 1171, 219 (1990).
  12. M. P. Singh, D. W. Oblas, J. O. Reese, W. J. Miniscalco, T. Wei, presented at Symposium on Optical Fiber Measurements, Boulder, Colo., September 11–12, 1990 (NIST special publ. no. 792, pp. 93–96).
  13. E. Desurvire, J. R. Simpson, Opt. Lett. 15, 547 (1990).
    [CrossRef] [PubMed]

1990

S. D. Zemon, G. M. Lambert, W. J. Miniscalco, L. J. Andrews, B. T. Hall, Proc. Soc. Photo-Opt. Instrum. Eng. 1171, 219 (1990).

K. Dybdal, N. Bjerre, J. E. Pedersen, C. C. Larsen, Proc. Soc. Photo-Opt. Instrum. Eng. 1171, 209 (1990).

E. Desurvire, J. R. Simpson, Opt. Lett. 15, 547 (1990).
[CrossRef] [PubMed]

1989

P. R. Morkel, R. I. Laming, Opt. Lett. 14, 1062 (1989).
[CrossRef] [PubMed]

E. Desurvire, J. R. Simpson, IEEE J. Lightwave Technol. 7, 835 (1989).
[CrossRef]

1972

J. N. Sandoe, P. H. Sarkies, S. Parke, J. Phys. D 5, 1788 (1972).
[CrossRef]

1964

D. E. McCumber, Phys. Rev. 134, A299 (1964).
[CrossRef]

Alekseev, N. E.

N. E. Alekseev, V. P. Gapontsev, M. E. Zhabotinskii, V. B. Kravchenko, Yu. P. Rudnitskii, Laser Phosphate Glasses (Nauka, Moscow, 1983), pp. 6–25 (translation by Berkeley Scientific Translation Service).

Andrews, L. J.

S. D. Zemon, G. M. Lambert, W. J. Miniscalco, L. J. Andrews, B. T. Hall, Proc. Soc. Photo-Opt. Instrum. Eng. 1171, 219 (1990).

W. J. Miniscalco, L. J. Andrews, B. A. Thompson, T. Wei, B. T. Hall, in Tunable Solid State Lasers, Vol. 5 of OSA Proceedings Series, M. L. Shand, H. P. Jenssen, eds. (Optical Society of America, Washington, D.C., 1989), p. 71.

Barnes, W. L.

W. L. Barnes, R. I. Laming, P. R. Morkel, E. J. Tarbox, in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 50.

Bjerre, N.

K. Dybdal, N. Bjerre, J. E. Pedersen, C. C. Larsen, Proc. Soc. Photo-Opt. Instrum. Eng. 1171, 209 (1990).

Desurvire, E.

E. Desurvire, J. R. Simpson, Opt. Lett. 15, 547 (1990).
[CrossRef] [PubMed]

E. Desurvire, J. R. Simpson, IEEE J. Lightwave Technol. 7, 835 (1989).
[CrossRef]

DiBartolo, B.

B. DiBartolo, Optical Interactions in Solids (Wiley, New York, 1968), pp. 404–411.

Dybdal, K.

K. Dybdal, N. Bjerre, J. E. Pedersen, C. C. Larsen, Proc. Soc. Photo-Opt. Instrum. Eng. 1171, 209 (1990).

Gapontsev, V. P.

N. E. Alekseev, V. P. Gapontsev, M. E. Zhabotinskii, V. B. Kravchenko, Yu. P. Rudnitskii, Laser Phosphate Glasses (Nauka, Moscow, 1983), pp. 6–25 (translation by Berkeley Scientific Translation Service).

Hall, B. T.

S. D. Zemon, G. M. Lambert, W. J. Miniscalco, L. J. Andrews, B. T. Hall, Proc. Soc. Photo-Opt. Instrum. Eng. 1171, 219 (1990).

W. J. Miniscalco, L. J. Andrews, B. A. Thompson, T. Wei, B. T. Hall, in Tunable Solid State Lasers, Vol. 5 of OSA Proceedings Series, M. L. Shand, H. P. Jenssen, eds. (Optical Society of America, Washington, D.C., 1989), p. 71.

Jauncey, I. M.

R. J. Mears, L. Reekie, I. M. Jauncey, D. N. Payne, in Optical Fiber Communication, Vol. 3 of 1987 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1987), paper WI2.

Kravchenko, V. B.

N. E. Alekseev, V. P. Gapontsev, M. E. Zhabotinskii, V. B. Kravchenko, Yu. P. Rudnitskii, Laser Phosphate Glasses (Nauka, Moscow, 1983), pp. 6–25 (translation by Berkeley Scientific Translation Service).

Lambert, G. M.

S. D. Zemon, G. M. Lambert, W. J. Miniscalco, L. J. Andrews, B. T. Hall, Proc. Soc. Photo-Opt. Instrum. Eng. 1171, 219 (1990).

Laming, R. I.

P. R. Morkel, R. I. Laming, Opt. Lett. 14, 1062 (1989).
[CrossRef] [PubMed]

W. L. Barnes, R. I. Laming, P. R. Morkel, E. J. Tarbox, in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 50.

Larsen, C. C.

K. Dybdal, N. Bjerre, J. E. Pedersen, C. C. Larsen, Proc. Soc. Photo-Opt. Instrum. Eng. 1171, 209 (1990).

McCumber, D. E.

D. E. McCumber, Phys. Rev. 134, A299 (1964).
[CrossRef]

Mears, R. J.

R. J. Mears, L. Reekie, I. M. Jauncey, D. N. Payne, in Optical Fiber Communication, Vol. 3 of 1987 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1987), paper WI2.

Miniscalco, W. J.

S. D. Zemon, G. M. Lambert, W. J. Miniscalco, L. J. Andrews, B. T. Hall, Proc. Soc. Photo-Opt. Instrum. Eng. 1171, 219 (1990).

W. J. Miniscalco, L. J. Andrews, B. A. Thompson, T. Wei, B. T. Hall, in Tunable Solid State Lasers, Vol. 5 of OSA Proceedings Series, M. L. Shand, H. P. Jenssen, eds. (Optical Society of America, Washington, D.C., 1989), p. 71.

M. P. Singh, D. W. Oblas, J. O. Reese, W. J. Miniscalco, T. Wei, presented at Symposium on Optical Fiber Measurements, Boulder, Colo., September 11–12, 1990 (NIST special publ. no. 792, pp. 93–96).

Morkel, P. R.

P. R. Morkel, R. I. Laming, Opt. Lett. 14, 1062 (1989).
[CrossRef] [PubMed]

W. L. Barnes, R. I. Laming, P. R. Morkel, E. J. Tarbox, in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 50.

Oblas, D. W.

M. P. Singh, D. W. Oblas, J. O. Reese, W. J. Miniscalco, T. Wei, presented at Symposium on Optical Fiber Measurements, Boulder, Colo., September 11–12, 1990 (NIST special publ. no. 792, pp. 93–96).

Parke, S.

J. N. Sandoe, P. H. Sarkies, S. Parke, J. Phys. D 5, 1788 (1972).
[CrossRef]

Payne, D. N.

R. J. Mears, L. Reekie, I. M. Jauncey, D. N. Payne, in Optical Fiber Communication, Vol. 3 of 1987 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1987), paper WI2.

Pedersen, J. E.

K. Dybdal, N. Bjerre, J. E. Pedersen, C. C. Larsen, Proc. Soc. Photo-Opt. Instrum. Eng. 1171, 209 (1990).

Reekie, L.

R. J. Mears, L. Reekie, I. M. Jauncey, D. N. Payne, in Optical Fiber Communication, Vol. 3 of 1987 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1987), paper WI2.

Reese, J. O.

M. P. Singh, D. W. Oblas, J. O. Reese, W. J. Miniscalco, T. Wei, presented at Symposium on Optical Fiber Measurements, Boulder, Colo., September 11–12, 1990 (NIST special publ. no. 792, pp. 93–96).

Rudnitskii, Yu. P.

N. E. Alekseev, V. P. Gapontsev, M. E. Zhabotinskii, V. B. Kravchenko, Yu. P. Rudnitskii, Laser Phosphate Glasses (Nauka, Moscow, 1983), pp. 6–25 (translation by Berkeley Scientific Translation Service).

Sandoe, J. N.

J. N. Sandoe, P. H. Sarkies, S. Parke, J. Phys. D 5, 1788 (1972).
[CrossRef]

Sarkies, P. H.

J. N. Sandoe, P. H. Sarkies, S. Parke, J. Phys. D 5, 1788 (1972).
[CrossRef]

Simpson, J. R.

E. Desurvire, J. R. Simpson, Opt. Lett. 15, 547 (1990).
[CrossRef] [PubMed]

E. Desurvire, J. R. Simpson, IEEE J. Lightwave Technol. 7, 835 (1989).
[CrossRef]

Singh, M. P.

M. P. Singh, D. W. Oblas, J. O. Reese, W. J. Miniscalco, T. Wei, presented at Symposium on Optical Fiber Measurements, Boulder, Colo., September 11–12, 1990 (NIST special publ. no. 792, pp. 93–96).

Tarbox, E. J.

W. L. Barnes, R. I. Laming, P. R. Morkel, E. J. Tarbox, in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 50.

Thompson, B. A.

W. J. Miniscalco, L. J. Andrews, B. A. Thompson, T. Wei, B. T. Hall, in Tunable Solid State Lasers, Vol. 5 of OSA Proceedings Series, M. L. Shand, H. P. Jenssen, eds. (Optical Society of America, Washington, D.C., 1989), p. 71.

Wei, T.

W. J. Miniscalco, L. J. Andrews, B. A. Thompson, T. Wei, B. T. Hall, in Tunable Solid State Lasers, Vol. 5 of OSA Proceedings Series, M. L. Shand, H. P. Jenssen, eds. (Optical Society of America, Washington, D.C., 1989), p. 71.

M. P. Singh, D. W. Oblas, J. O. Reese, W. J. Miniscalco, T. Wei, presented at Symposium on Optical Fiber Measurements, Boulder, Colo., September 11–12, 1990 (NIST special publ. no. 792, pp. 93–96).

Zemon, S. D.

S. D. Zemon, G. M. Lambert, W. J. Miniscalco, L. J. Andrews, B. T. Hall, Proc. Soc. Photo-Opt. Instrum. Eng. 1171, 219 (1990).

Zhabotinskii, M. E.

N. E. Alekseev, V. P. Gapontsev, M. E. Zhabotinskii, V. B. Kravchenko, Yu. P. Rudnitskii, Laser Phosphate Glasses (Nauka, Moscow, 1983), pp. 6–25 (translation by Berkeley Scientific Translation Service).

IEEE J. Lightwave Technol.

E. Desurvire, J. R. Simpson, IEEE J. Lightwave Technol. 7, 835 (1989).
[CrossRef]

J. Phys. D

J. N. Sandoe, P. H. Sarkies, S. Parke, J. Phys. D 5, 1788 (1972).
[CrossRef]

Opt. Lett.

Phys. Rev.

D. E. McCumber, Phys. Rev. 134, A299 (1964).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng.

S. D. Zemon, G. M. Lambert, W. J. Miniscalco, L. J. Andrews, B. T. Hall, Proc. Soc. Photo-Opt. Instrum. Eng. 1171, 219 (1990).

K. Dybdal, N. Bjerre, J. E. Pedersen, C. C. Larsen, Proc. Soc. Photo-Opt. Instrum. Eng. 1171, 209 (1990).

Other

W. L. Barnes, R. I. Laming, P. R. Morkel, E. J. Tarbox, in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 50.

M. P. Singh, D. W. Oblas, J. O. Reese, W. J. Miniscalco, T. Wei, presented at Symposium on Optical Fiber Measurements, Boulder, Colo., September 11–12, 1990 (NIST special publ. no. 792, pp. 93–96).

R. J. Mears, L. Reekie, I. M. Jauncey, D. N. Payne, in Optical Fiber Communication, Vol. 3 of 1987 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1987), paper WI2.

W. J. Miniscalco, L. J. Andrews, B. A. Thompson, T. Wei, B. T. Hall, in Tunable Solid State Lasers, Vol. 5 of OSA Proceedings Series, M. L. Shand, H. P. Jenssen, eds. (Optical Society of America, Washington, D.C., 1989), p. 71.

B. DiBartolo, Optical Interactions in Solids (Wiley, New York, 1968), pp. 404–411.

N. E. Alekseev, V. P. Gapontsev, M. E. Zhabotinskii, V. B. Kravchenko, Yu. P. Rudnitskii, Laser Phosphate Glasses (Nauka, Moscow, 1983), pp. 6–25 (translation by Berkeley Scientific Translation Service).

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Figures (2)

Fig. 1
Fig. 1

Comparison of the shape of the measured stimulated-emission cross section with that calculated from the absorption cross section using the McCumber theory. The absorption spectrum used is also included. The glass is low-fluorine fluorophosphate composition L11.

Fig. 2
Fig. 2

Comparison of stimulated-emission cross sections scaled using the radiative lifetime (measured), the Einstein relation (Einstein), and the McCumber theory with an estimated (McCumber). The glass is fluorophosphate L11.

Tables (1)

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Table 1 Comparison of Procedures for Determining σe

Equations (5)

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g 1 ν 2 σ a ( ν ) d ν = g 2 ν 2 σ e ( ν ) d ν ,
σ e ( ν ) = σ a ( ν ) exp [ ( - h ν ) / k T ] ,
1 τ = 8 π n 2 c 2 ν 2 σ e ( ν ) d ν ,
N 1 N 2 = exp ( / k T ) ,
N 1 N 2 = 1 + j = 2 8 exp ( - E 1 j / k T ) exp ( - E 0 / k T ) [ 1 + j = 2 7 exp ( - E 2 j / k T ) ] .

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