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Nonlinear theory of multiphonon relaxation of excited rare-earth ions in laser crystals
A general formula for the probability of multiphonon nonradiative transitions between J multiplets of 4 f N states of trivalent rare-earth ions in a crystal derived for a nonlinear mechanism is discussed. A technique is developed for calculating the quantities involved in this formula. Particular at...
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Published in: | Physics of the solid state 2008-09, Vol.50 (9), p.1597-1604 |
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Main Author: | |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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Summary: | A general formula for the probability of multiphonon nonradiative transitions between
J
multiplets of 4
f
N
states of trivalent rare-earth ions in a crystal derived for a nonlinear mechanism is discussed. A technique is developed for calculating the quantities involved in this formula. Particular attention is given to calculating the spectral density
J
(
p
)
(Ω), which is the Fourier transform (at the transition frequency) of the
p
th power of the correlation function
K
(
t
) of host ion displacements. Based on the central limit theorem from probability theory, an approximation is proposed for the spectral density
J
(
p
)
(Ω). The theoretical values of nonradiative multiphonon transition rates are compared with experimental ones. |
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ISSN: | 1063-7834 1090-6460 |
DOI: | 10.1134/S1063783408090011 |