1f:T414,A simple dielectric theory is used to describe the operating properties of phonon-terminated masers of the type reported by Johnson, Dietz, and Guggenheim. Basic to this model is a broadband gain characteristic which describes the frequency-dependent gain of the active maser material as a function of the populations of metastable electronic levels and of the temperature or temperatures describing lattice vibrations. The power levels required to produce phonon saturation are estimated to be extremely high (typically, \ensuremath{\sim}${10}^{10}$ W/${\mathrm{cm}}^{2}$ power output). Because phonon saturation does not ordinarily occur, a single-lattice temperature is generally sufficient. In that case, details of the electron-phonon coupling are unimportant, and the gain can be related by detailed balance to fluorescence and absorption spectra. Effects of phonon saturation are briefly discussed in the event that they might pertain to exceptional systems and because they give insight into the principles of operation of these masers.20:T4f5,Systematic studies of spectral intensities using the Judd-Ofelt (J-O) theory for crystal-field-induced electric-dipole transitions demonstrate that Nd-doped glasses can be tailored for specific laser applications by proper selection of the glass constituents. Variations with glass composition are reported for the following properties: induced-emission cross section, peak fluorescence wavelength, effective fluorescence bandwidth, radiative lifetime, transition probabilities, and fluorescence branching ratios. Both glass network formers and network-modifier ions were changed. In these studies the induced-emission cross section for the Nd ³⁺ , ⁴ F_{3/2} \rightarrow ⁴ I_{11/2} laser transition was varied by more than a factor of 4 by changing the glass host.21:T53d,A method for estimating the microscopic probability rate of phonon-assisted energy transfer between rare-earth $(3+)$ ions in solids was developed based on Dexter's theory for phonon-assisted energy transfer. The proposed method in this paper enables one to calculate the overlap integral from fundamental cross-section spectra of nonresonant energy transfer involving a multiphonon generation in both donor and acceptor sites. A translation of the donor emission spectrum towards the acceptor absorption scaled with the $N$-phonon emission probability represents the $m$-phonon emission band which performs the energy transfer to the acceptor. A nonvanishing overlap integral ${10}^{\ensuremath{-}2}--{10}^{\ensuremath{-}3}$ times smaller than for the resonant case is found. A multiphonon generation probability assisting the energy transfer was considered due to a combined mechanism of creation and annihilation of phonons. The participation of each phonon in the process was determined. This method was used to investigate the ${\mathrm{Tm}}^{3+}{(}^{3}{F}_{4})\ensuremath{\rightarrow}{\mathrm{Ho}}^{3+}{(}^{5}{I}_{7}),{\mathrm{Er}}^{3+}{(}^{4}{I}_{13/2})\ensuremath{\rightarrow}[{\mathrm{Ho}}^{3+}{(}^{5}{I}_{7}),{\mathrm{Tm}}^{3+}{(}^{3}{F}_{4})]$ direct energy transfers in ${\mathrm{LiYF}}_{4}$ crystals, as well the back transfers.

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