Abstract

Data indicating energy transfer between erbium and neodymium in yttrium aluminum garnet have been analyzed. The observed rate of transfer cannot be explained by the standard model, which assumes that the transfer occurs through the dipole–dipole interaction between randomly distributed acceptors and donors. A new model for energy transfer is presented in which donors and acceptors affect each other's placement in the crystal. A much closer fit to the observed experimental data is obtained with this model and by assuming that the location of erbium ions in the nearest-neighbor sites to neodymium ions is not energetically favorable.

© 1990 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  8. M. Inokuti, F. Hirayama, J. Chem. Phys. 43, 1978 (1965).
    [CrossRef]
  9. S. R. Rotman, F. X. Hartmann, Chem. Phys. Lett. 152, 311 (1988).
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  10. S. R. Rotman, Appl. Phys. B 49, 59 (1989).
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    [CrossRef]
  12. S. Geller, Z. KristallogrKristallgeom. Kristallphys. Kristallchem. 125, 1 (1967).
  13. E. V. Zharikov, V. V. Laptov, A. A. Maier, V. V. Osiko, Inorg. Mater. 20, 857 (1984).

1989 (3)

W. Q. Shi, M. Bass, M. Birnbaum, J. Opt. Soc. Am. B 6, 23 (1989).
[CrossRef]

S. R. Rotman, Appl. Phys. B 49, 59 (1989).
[CrossRef]

S. R. Rotman, Appl. Phys. Lett. 54, 2053 (1989).
[CrossRef]

1988 (1)

S. R. Rotman, F. X. Hartmann, Chem. Phys. Lett. 152, 311 (1988).
[CrossRef]

1987 (1)

W. Q. Shi, R. Kurtz, J. Machan, M. Bass, M. Birnbaum, M. Kokta, Appl. Phys. Lett. 51, 1218 (1987).
[CrossRef]

1986 (3)

1984 (1)

E. V. Zharikov, V. V. Laptov, A. A. Maier, V. V. Osiko, Inorg. Mater. 20, 857 (1984).

1967 (1)

S. Geller, Z. KristallogrKristallgeom. Kristallphys. Kristallchem. 125, 1 (1967).

1965 (1)

M. Inokuti, F. Hirayama, J. Chem. Phys. 43, 1978 (1965).
[CrossRef]

1953 (1)

D. L. Dexter, J. Chem. Phys. 21, 836 (1953).
[CrossRef]

1948 (1)

T. Forster, Ann. Phys. 2, 55 (1948).
[CrossRef]

Bass, M.

W. Q. Shi, M. Bass, M. Birnbaum, J. Opt. Soc. Am. B 6, 23 (1989).
[CrossRef]

W. Q. Shi, R. Kurtz, J. Machan, M. Bass, M. Birnbaum, M. Kokta, Appl. Phys. Lett. 51, 1218 (1987).
[CrossRef]

Birnbaum, M.

W. Q. Shi, M. Bass, M. Birnbaum, J. Opt. Soc. Am. B 6, 23 (1989).
[CrossRef]

W. Q. Shi, R. Kurtz, J. Machan, M. Bass, M. Birnbaum, M. Kokta, Appl. Phys. Lett. 51, 1218 (1987).
[CrossRef]

Caird, J. A.

Denisov, A. L.

Dexter, D. L.

D. L. Dexter, J. Chem. Phys. 21, 836 (1953).
[CrossRef]

Forster, T.

T. Forster, Ann. Phys. 2, 55 (1948).
[CrossRef]

Geller, S.

S. Geller, Z. KristallogrKristallgeom. Kristallphys. Kristallchem. 125, 1 (1967).

Hartmann, F. X.

S. R. Rotman, F. X. Hartmann, Chem. Phys. Lett. 152, 311 (1988).
[CrossRef]

Hirayama, F.

M. Inokuti, F. Hirayama, J. Chem. Phys. 43, 1978 (1965).
[CrossRef]

Inokuti, M.

M. Inokuti, F. Hirayama, J. Chem. Phys. 43, 1978 (1965).
[CrossRef]

Kokta, M.

W. Q. Shi, R. Kurtz, J. Machan, M. Bass, M. Birnbaum, M. Kokta, Appl. Phys. Lett. 51, 1218 (1987).
[CrossRef]

Kristallogr, Z.

S. Geller, Z. KristallogrKristallgeom. Kristallphys. Kristallchem. 125, 1 (1967).

Krupke, W. F.

Kurtz, R.

W. Q. Shi, R. Kurtz, J. Machan, M. Bass, M. Birnbaum, M. Kokta, Appl. Phys. Lett. 51, 1218 (1987).
[CrossRef]

Laptov, V. V.

E. V. Zharikov, V. V. Laptov, A. A. Maier, V. V. Osiko, Inorg. Mater. 20, 857 (1984).

Machan, J.

W. Q. Shi, R. Kurtz, J. Machan, M. Bass, M. Birnbaum, M. Kokta, Appl. Phys. Lett. 51, 1218 (1987).
[CrossRef]

Maier, A. A.

E. V. Zharikov, V. V. Laptov, A. A. Maier, V. V. Osiko, Inorg. Mater. 20, 857 (1984).

Marion, J. E.

Osiko, V. V.

E. V. Zharikov, V. V. Laptov, A. A. Maier, V. V. Osiko, Inorg. Mater. 20, 857 (1984).

Ostroumov, G. G.

Ostroumov, V. G.

Privis, Y. S.

Rotman, S. R.

S. R. Rotman, Appl. Phys. B 49, 59 (1989).
[CrossRef]

S. R. Rotman, Appl. Phys. Lett. 54, 2053 (1989).
[CrossRef]

S. R. Rotman, F. X. Hartmann, Chem. Phys. Lett. 152, 311 (1988).
[CrossRef]

Saidov, Z. S.

Shcherbakov, I. A.

Shi, W. Q.

W. Q. Shi, M. Bass, M. Birnbaum, J. Opt. Soc. Am. B 6, 23 (1989).
[CrossRef]

W. Q. Shi, R. Kurtz, J. Machan, M. Bass, M. Birnbaum, M. Kokta, Appl. Phys. Lett. 51, 1218 (1987).
[CrossRef]

Shinn, M. D.

Smirnov, V. A.

Stokowski, S. E.

Zharikov, E. V.

E. V. Zharikov, V. V. Laptov, A. A. Maier, V. V. Osiko, Inorg. Mater. 20, 857 (1984).

Ann. Phys. (1)

T. Forster, Ann. Phys. 2, 55 (1948).
[CrossRef]

Appl. Phys. B (1)

S. R. Rotman, Appl. Phys. B 49, 59 (1989).
[CrossRef]

Appl. Phys. Lett. (2)

S. R. Rotman, Appl. Phys. Lett. 54, 2053 (1989).
[CrossRef]

W. Q. Shi, R. Kurtz, J. Machan, M. Bass, M. Birnbaum, M. Kokta, Appl. Phys. Lett. 51, 1218 (1987).
[CrossRef]

Chem. Phys. Lett. (1)

S. R. Rotman, F. X. Hartmann, Chem. Phys. Lett. 152, 311 (1988).
[CrossRef]

Inorg. Mater. (1)

E. V. Zharikov, V. V. Laptov, A. A. Maier, V. V. Osiko, Inorg. Mater. 20, 857 (1984).

J. Chem. Phys. (2)

D. L. Dexter, J. Chem. Phys. 21, 836 (1953).
[CrossRef]

M. Inokuti, F. Hirayama, J. Chem. Phys. 43, 1978 (1965).
[CrossRef]

J. Opt. Soc. Am. B (4)

Kristallgeom. Kristallphys. Kristallchem. (1)

S. Geller, Z. KristallogrKristallgeom. Kristallphys. Kristallchem. 125, 1 (1967).

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Figures (2)

Fig. 1
Fig. 1

Donor–acceptor radial-distance probability distribution. r1 is the radius of the inner volume, rD is one half the average distance between donors, A is the magnitude of the radial probability in the inner volume, and B is determined by Eq. (2).

Fig. 2
Fig. 2

Experimental and theoretical (correlated and uncorrelated) plots of fluorescence intensity (decay of 4F3/2 level of Nd+3) as a function of time.

Tables (1)

Tables Icon

Table 1 Parameters for Fit to Er,Nd:YAG Dataa

Equations (6)

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N D ( t ) = N D ( 0 ) exp [ t / τ D Γ ( 1 3 / s ) c / c 0 ( t / τ D ) 3 / s ] ,
B = r D 3 A r 1 3 r D 3 r 1 3 ,
N D ( t ) = N D ( 0 ) exp [ t / τ D A π c / c 0 ( t / τ D ) 1 / 2 ( B A ) Φ ( z 1 ) / exp ( z 1 ) ( 1 B ) Φ ( z D ) / exp ( z D ) ] ,
Φ ( z ) = i = 0 ( 2 z ) i ( 2 i 1 ) ! ! ,
z i = ( r 0 / r i ) 6 ( t / τ 0 ) .
F 4 3 / 2 ( Nd 3 + ) + I 4 15 / 2 ( Er 3 + ) I 4 15 / 2 ( Nd 3 + ) + I 4 13 / 2 ( Er 3 + ) .

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