The relation between absorption and emission spectra in a rare-earth doped solid is explored analytically and through numerical simulations on a model system. It is found that the widely used theory of McCumber [D. E. McCumber, Phys. Rev. 136, A954 (1964)] is strictly valid only when the linewidth of each individual transition between Stark levels is ≪kBT. When this assumption is relaxed, deviations between actual simulated spectra and McCumber-calculated spectra are found for both homogeneous and inhomogeneous broadening. The McCumber transform introduces a characteristic distortion of each component transition, in which the low-energy side of the spectrum is increased, and the high-energy side is decreased. The average degree of distortion for the model system is calculated to be 5% for a homogeneous width of 50 cm−1 at room temperature, but only 1% for a purely inhomogeneous width of 50 cm−1. For both homogeneous and inhomogeneous spectra, the distortion varies with the linewidth Δν as (Δν)3/2. The dependence of the distortion on temperature is different for the two types of line shapes, however: ∼T2 for homogeneous and ∼T−1 for inhomogeneous broadening. For most rare-earth doped glasses and crystals at room temperature, the average degree of distortion is expected to be on the order of 5% or less, although the actual discrepancy in the spectral wings can be much larger. The effects described here are likely to be of importance when using McCumber’s theory to obtain accurate cross section values in the spectral wings of rare-earth transitions.
The validity of the theory of McCumber [Phys. Rev.136, A954-A957 (1964)] has been tested by applying it to a number of ground-state transition in various rare-earth-doped glasses. Special attention was given to those aspects of the experimental procedure that can lead to systematic errors, such as reabsorption of fluorescence and baseline subtraction uncertainties in the absorption measurements. To ensure consistency between absorption and fluorescence measurements, we used the same geometry for light collection and measurement. With these experimental procedures properly implemented, we find that in all cases there is excellent agreement between the spectral shape of calculated and measured cross-section spectra at room temperature. This is true even for the thermally coupled (2H9/2,4F5/2) and 4F3/2 levels of Nd, which span an energy range of ∼2000 cm−1, much larger than the typical width of a single Stark level manifold. The results suggest that, at room temperature, the McCumber theory is not restricted to crystalline hosts but remains valid for the broader transitions characteristic of rare-earth-doped glass.
In this paper, we present a low-temperature study of rare earth doped glasses, which are important for creating compact, efficient gain media. We resolved effective Stark components of erbium doped glasses by analyzing their absorption cross sections at T=293K and T=110K. Using these Stark energy levels and the McCumber theory, we calculated the radiative lifetime of the I/-I/ transition in erbium. Our calculated lifetime agrees with the measured lifetime for this transition better than previously accepted methods.
Homogeneous and inhomogeneous spectral linewidths of the ${(}^{2}{F}_{5/2}{)}_{1}\ensuremath{-}{(}^{2}{F}_{7/2}{)}_{1}$ transition in
Yb3+-doped fluorozirconate glasses are determined by fitting Voigt profiles to the inhomogeneously broadened emission and absorption spectra between 10 and 300 K. The homogeneous linewidth varied as $(12\ifmmode\pm\else\textpm\fi{}2)\ifmmode\times\else\texttimes\fi{}{T}^{(1.9\ifmmode\pm\else\textpm\fi{}0.1)}\mathrm{MHz}$ for emission and $(10\ifmmode\pm\else\textpm\fi{}1)\ifmmode\times\else\texttimes\fi{}{T}^{1.9\ifmmode\pm\else\textpm\fi{}0.1}$ for absorption over the entire temperature range, similar to that of other rare-earth-doped systems previously studied by fluorescence line narrowing and photon echoes. The inhomogeneous linewidths were nearly independent of temperature, but different by $\ensuremath{\sim}30%$ between emission and absorption. The structural and dynamic properties in this disordered system are discussed.
We present optical linewidth and line-shape studies of transitions of
4f impurity ions in doubly doped systems and show that interactions which involve excitation transfer between the impurity systems produce homogeneous broadening and line-shape changes in the optical transitions. In particular, we have studied the behavior of the 5985-\AA{} line of
Pr3+ in doubly doped La
F3:
Pr3+,
Nd3+ as a function of
Nd3+ concentration. The 5985-\AA{}
Pr3+ transition at 4.2\ifmmode^\circ\else\textdegree\fi{}K involves two long-lived electronic states of the
Pr3+ ion; it follows that in the singly doped La
F3:
Pr3+ the transition shows a Gaussian shape which is characteristic of inhomogeneous strain and imperfection broadening. As
Nd3+ is added to the system, a broader Lorentzian component begins to appear in the 5985-\AA{}
Pr3+ transition and eventually (at
Nd3+ concentrations of \ensuremath{\sim}1% or above) completely dominates the width and shape of the transition. The Lorentzian component of the transition line shape was successfully separated using a Fourier-transform technique and the width of this component was studied as a function of the
Nd3+ concentration. The width is found to increase linearly with increasing
Nd3+ concentration up to concentrations of 2%; at higher concentrations, the linewidth saturates and approaches an asymptotic value of \ensuremath{\sim}2 ${\mathrm{cm}}^{\ensuremath{-}1}$. We construe this homogeneous component to be evidence of a rapid short-range energy transfer mechanism between the
Pr3+ and
Nd3+ systems at the terminating
(3H6)1 level of the 5985-\AA{}
Pr3+ transition. Various mechanisms are investigated as causes of the energy transfer process; it is concluded that the spin-exchange interaction is the most probable cause for the transfer. Results of other spectroscopic measurements on the doubly doped La
F3:
Pr3+,
Nd3+ system are also presented.
The reciprocity relation of McCumber which states that the emission and absorption spectra of broad solid-state laser transitions are related by the classical Boltzmann factor is critically examined. It is argued that it should be treated as an exact property of homogeneously broadened amorphous host gain media at room temperature. The contradiction between these conclusions and those of recent literature arguing against the applicability of the McCumber relation for erbium doped silica is resolved. Experimental support for the McCumber relationship in erbium doped silica fiber is provided.
The nature of inhomogeneous broadening in rare earth systems plays an important role in the dynamical optical properties of ions in crystals. For this reason much of the work on the nature of the inhomogeneous broadening in rare earth doped systems has concentrated on the investigation of ion-ion interactions such as spectral transfer and up conversion processes.1,3 Variations in homogeneous optical dephasing times across the inhomogeneous optical line have also been reported.4 These studies concentrate on the variations of collective effects of ion- ion interactions at different positions in the inhomogeneous optical line in relatively heavily doped rare earth systems. We report variations in optically detected NQR (ODNQR) linewidths and shifts of Pr3+ hyperfme transitions in the optical ground state as a function of position in the inhomogeneous optical line and for satellite transitions of the 1D2-3H4 transition in lightly doped (0.5 at. %) Pr3+:LaF3.