Fundamental limitations of the McCumber relation applied to Er-doped silica and other amorphous-host lasers

The approximate McCumber procedure is often used to predict the emission cross-section spectrum of the 1.5-/spl mu/m transition of Er-doped glass fibers from the transition's measured absorption spectrum. By applying this procedure to a large number of published Er-doped fiber absorption spectra, we demonstrate that its accuracy is actually statistically quite low: it tends to overestimate the peak cross-section (by up to 75%) and predicts an emission spectrum that is erroneously depressed in the S band (below /spl sim/1530 nm) and inflated in the C and L bands. Error levels are substantial and yield unacceptably large errors when modeling Er-doped fiber devices. We provide analytic evidence that this failure is rooted in part in the approximations inherent to the procedure, and in part in a fundamental limitation of the underlying McCumber relation. Specifically, when applied to broad optical transitions, the McCumber relation yields poor predictions of the emission cross-section spectral shape, the error worsening in the L and S bands, with increasing homogeneous broadening, and with increasing bandwidth. The McCumber relation should be avoided for broad laser transitions, which includes most rare-earth transitions in many amorphous hosts.

[1]  Richard Ian Laming,et al.  Absorption and emission cross section of Er/sup 3+/ doped silica fibers , 1991 .

[2]  E. Desurvire,et al.  Study of spectral dependence of gain saturation and effect of inhomogeneous broadening in erbium-doped aluminosilicate fiber amplifiers , 1990, IEEE Photonics Technology Letters.

[3]  R. Laming,et al.  Operation of erbium-doped fiber amplifiers and lasers pumped with frequency-doubled Nd:YAG lasers , 1989 .

[4]  K. Dybdal,et al.  Detailed theoretical and experimental investigation of high-gain erbium-doped fiber amplifier , 1990, IEEE Photonics Technology Letters.

[5]  K. Dybdal,et al.  The design of erbium-doped fiber amplifiers , 1991 .

[6]  E. Desurvire,et al.  Amplification of spontaneous emission in erbium-doped single-mode fibers , 1989 .

[7]  C. R. Giles,et al.  Modeling erbium-doped fiber amplifiers , 1991 .

[8]  K. Rajnak,et al.  Energy Levels of Single‐Crystal Erbium Oxide , 1966 .

[9]  W. Barnes,et al.  High-quantum-efficiency Er(3+) fiber lasers pumped at 980 nm. , 1989, Optics letters.

[10]  D. Mccumber,et al.  Theory of Phonon-Terminated Optical Masers , 1964 .

[11]  J. N. Sandoe,et al.  Variation of Nd3+ cross section for stimulated emission with glass composition , 1971 .

[12]  J R Simpson,et al.  Evaluation of (4)I(15/2) and (4)I(13/2) Stark-level energies in erbium-doped aluminosilicate glass fibers. , 1990, Optics letters.

[13]  E. Desurvire,et al.  Spectral gain hole-burning at 1.53 mu m in erbium-doped fiber amplifiers , 1990, IEEE Photonics Technology Letters.

[14]  CHARACTERIZATION OF ER3+-DOPED GLASSES BY FLUORESCENCE LINE NARROWING , 1991 .

[15]  J. F. Massicott,et al.  High-gain broad spectral bandwidth erbium-doped fibre amplifier pumped near 1.5 mu m , 1989 .

[16]  E. Desurvire,et al.  Study of the complex atomic susceptibility of erbium-doped fiber amplifiers , 1990 .

[17]  M. Nakazawa,et al.  Lasing characteristics of Er3+‐doped silica fibers from 1553 up to 1603 nm , 1988 .

[18]  R. S. Quimby,et al.  General procedure for the analysis of Er(3+) cross sections. , 1991, Optics letters.

[19]  C. C. Robinson Multiple sites for Er3+ in alkali silicate glasses (I). The principal sixfold coordinated site of Er3+ in silicate glass , 1974 .

[20]  H. Shaw,et al.  Polarized superfluorescent fiber source. , 1997, Optics letters.

[21]  K. Dybdal,et al.  Spectroscopic Properties Of Er-Doped Silica Fibers And Preforms , 1990, Other Conferences.

[22]  R. Laming,et al.  Temperature dependent gain and noise characteristics of a 1480 nm-pumped erbium-doped fibre amplifier , 1990 .

[23]  W. Miniscalco,et al.  Optical and Electronic Properties of Rare Earth Ions in Glasses , 2001 .