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Optics Letters

General procedure for the analysis of Er^3+ cross sections

William J. Miniscalco, Richard S. Quimby

Published Feb 15, 1991• 586 citations
Publisher

Abstract

We have applied the theory of McCumber to the (4)4I(13/2) ? (4)I(15/2) transition of Er(3+) -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.

DOI
10.1364/ol.16.000258

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We have applied the theory of McCumber to the (4)4I(13/2) ? (4)I(15/2) transition of Er(3+) -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.
A detailed set of measurements is presented on determining the emission and absorption cross sections of Er/sup 3+/ doped fibers for the /sup 4/I/sub 13/2/ to /sup 4/I/sub 15/2/ transition. Two techniques are employed: the Fuchtbauer-Ladenberg analysis, based on spectroscopic data, and a more direct technique involving optical saturation of the transition. The cross sections, and in particular their ratio, are significantly different for the two techniques. Possible reasons for this are discussed, and it is concluded that the Fuchtbauer-Ladenberg approach is inappropriate in this situation.>
An application to transitions involving thermalized states of a procedure based on the McCumber theory to determine emission and absorption cross sections in waveguides from transversal fluorescence spectra is presented. The procedure is tested in Er-doped Ti:LiNbO/sub 3/ waveguides to provide accurate cross-section values for the recently attractive 550-nm band. We also study the excited-state absorption transition around 860 nm and present, to our knowledge, the first published cross-section values for this transition.
The polarization-dependent absorption and emission spectra of the 4113/2-4115/2 transition (A - 1.5 pm) in single crystal bulk Er:LiNbOs have been measured. Low-temperature (10 K) measurements of the Stark split energy levels of these two manifolds indicate at least two Er3+ sites. McCumber theory is applied to determine the Er:LiNb03 absorption and emission cross sections. These values are used to calculate the gain charac- teristics of Er:LiNbOs channel waveguides. Calculations indicate that a gain of 10 dB is achievable in a waveguide of several centimeters using -20-mW pump power.
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.
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.
Based on the transmission spectra of Er3+-doped LiNbO3 optical waveguides in this paper we report some experimental and theoretical results concerning the evaluation of some spectroscopic parameters which characterize the above mentioned waveguides. The absorption experimental spectra were used to determine the homogeneous absorption and emission cross sections (utilising the density matrix formalism and the McCumber's theory and taking into account the Stark splitting of the levels), the oscillator strength of the absorption transition, the spontaneous emission probabilities, the radiative lifetime and the excitation energy in three regions of the optical spectrum: around 1550 nm, 980 nm and 550 nm, respectively. Also, we measured the rising and falling times and we calculated the homogeneous upconversion factor corresponding to the transition 4I15/2->4F7/2.