Erbium-doped fiber amplifiers are modeled using the propagation and rate equations of a homogeneous two-level laser medium. Numerical methods are used to analyze the effects of optical modes and erbium confinement on amplifier performance, and to calculate both the gain and amplified spontaneous emission (ASE) spectra. Fibers with confined erbium doping are completely characterized from easily measured parameters: the ratio of the linear ion density to fluorescence lifetime, and the absorption of gain spectra. Analytical techniques then allow accurate evaluation of gain, saturation, and noise in low-gain amplifiers (G >

Modeling erbium-doped fiber amplifiers

Tellurite glass: a new candidate for fiber devices

Fibre lasers in the mid-infrared regime are useful for a diverse range of fields, including chemical and biomedical sensing, military applications and materials processing. This Review summarizes the different rare-earth cations and host materials used in mid-infrared fibre laser technology, and discusses the future applications and challenges for the field.

Towards high-power mid-infrared emission from a fibre laser

Material-dependent properties influencing the performance of fiber amplifiers are reviewed together with the available data for Er/sup 3+/. The major glass types potentially useful in this application are considered and compared to silica. The topics addressed include quenching processes and the solubility of rare-earth ions, transition strengths and bandwidths at the 1500-nm gain transition, and the characteristics at the 800-, 980-, and 1480-nm pump bands. Aluminum is shown to be an extremely useful codopant for silica, improving its ability to dissolve rare-earth ions and providing desirable spectroscopic properties for Er/sup 3+/. For some of the attributes considered, other glasses have advantages over Al silica, but only with respect to gain bandwidth and pumping performance at 800 nm is significantly better than expected from other glass compositions. >

Erbium-doped glasses for fiber amplifiers at 1500 nm

Optical-absorption, -emission, and -excitation spectra are presented for ${\mathrm{Er}}^{3+}$ ions in fluorozirconate glass. Measured oscillator strengths of the transitions between $J$ manifolds at 300 and 15 K are compared with calculated electric and magnetic dipole oscillator strengths. Radiative rates for five luminescing states were calculated. The nonradiative rates from these excited states were determined by calculating the difference between the measured rates and the calculated radiative rates. The low-temperature nonradiative rates are in agreement with the phenomenological energy-gap law followed by rare-earth ions in a number of crystals and glasses. The temperature dependence of the lifetimes was analyzed using the Huang-Rhys theory of multiphonon emission. Values for the $^{4}I_{\frac{11}{2}}$ radiative and nonradiative rates obtained by the above methods are compared with those obtained applying the method Flaherty and DiBartolo used to study Mn${\mathrm{F}}_{2}$: ${\mathrm{Er}}^{3+}$. The multiphonon emission rates in fluorozirconate glass are much lower than the rates for the same levels of ${\mathrm{Er}}^{3+}$ in oxide glasses. Measurements of the bandwidths of the ground and excited states of ${\mathrm{Er}}^{3+}$ and the nearly exponential decay of the emissions indicate a relatively narrow distribution of site symmetries compared to oxide glasses.

Optical transitions of Er 3 + ions in fluorozirconate glass

Nonradiative decay of excited rare-earth ions by multiphonon emission has been investigated in a series of oxide glasses. Various rare-earth electronic levels were selectively excited by short-duration laser pulses and multiphonon relaxation rates were determined from measurements of fluorescence rise and decay times. Time resolution for fluorescence measurements was 3 nsec, so excited states were probed for which the decay was predominantly nonradiative. Excited states of ${\mathrm{Nd}}^{3+}$, ${\mathrm{Er}}^{3+}$, and ${\mathrm{Tm}}^{3+}$ with energy gaps to the next-lower $J$ state ranging from 1300 to 4700 ${\mathrm{cm}}^{\ensuremath{-}1}$ were studied. The multiphonon relaxation rates for each glass investigated exhibited an approximately exponential dependence on energy gap. Evidence of breakdown of this dependence was observed in the region of small energy gaps. The measured temperature dependences of the decay rates establish that the relaxation occurs predominantly by excitation of the highest-frequency vibrations associated with stretching modes of the glass network former. Borate, silicate, phosphate, germanate, and tellurite glasses were studied. From Raman spectra, the highest-frequency vibrations for these glasses ranged from 700 to 1400 ${\mathrm{cm}}^{\ensuremath{-}1}$. The corresponding multiphonon relaxation rates for a given energy gap differed by three orders of magnitude. The strength of the ion-phonon coupling was found to be approximately equal for all glasses.

Multiphonon relaxation of rare-earth ions in oxide glasses

Rates for nonradiative decay by multiphonon emission are measured for rare-earth ions in silicate laser glass and used to estimate quantum efficiencies.

C. B. Layne

Papers

Multiphonon relaxation of rare-earth ions in oxide glasses

Nonradiative relaxation of rare-earth ions in silicate laser glass

Measurement of nonradiative relaxation of rare earths in glasses using selective laser excitation