Multiphonon relaxation of rare-earth ions in oxide glasses
TL;DR: In this paper, a series of oxide glasses were investigated for the nonradiative decay of excited rare-earth ions by multiphononon emission and the results showed that the strength of the ion-phonon coupling was approximately equal for all glasses.
Abstract: 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.
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TL;DR: Erbium-doped fiber amplifiers are modeled using the propagation and rate equations of a homogeneous two-level laser medium, and numerical methods are used to analyze the effects of optical modes and erbium confinement on amplifier performance.
Abstract: 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 >
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TL;DR: In this article, a review summarizes the different rare-earth cations and host materials used in mid-infrared fiber laser technology, and discusses the future applications and challenges for the field.
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TL;DR: In this paper, 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.
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871 citations
TL;DR: In this paper, the Huang-Rhys theory of multiphonon emission was used to calculate the radiative and non-radiative rates for five luminescing states in fluorozirconate glass.
Abstract: 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.
573 citations