Erbium Levels Research Articles

Theoretical analysis of the dynamic behavior of highly-efficient erbium/ytterbium codoped fiber lasers

A numerical study of the transient behavior of single-mode Er/sup 3+//Yb/sup 3+/ codoped fiber lasers is presented. The model, based on propagation-rate equations, includes both uniform up-conversion from the /sup 4/I/sub 15/2/ and /sup 4/I/sub 9/2/ erbium levels and the pair-induced energy transfer process from ytterbium to erbium. We show that neglecting the r dependence of the operating fiber laser parameters allows accurate simulation results at minimum numerical effort. Using this numerical model, we characterize the laser relaxation oscillations and the effect of ytterbium on the dynamic behavior and stability with respect to fluctuations of the pump power. Our results confirm that the presence of Yb/sup 3+/ enhances the efficiency of the laser and show that its stability is also significantly improved.

Modeling of highly-efficient grating-feedback and Fabry-Perot Er/sup 3+/-Yb/sup 3+/ co-doped fiber lasers

The continuous wave operations of highly-efficient Er/sup 3+//Yb/sup 3+/ co-doped fiber lasers pumped at 980 nm are numerically analyzed. The model, based on propagation-rate equations, includes uniform upconversion from the /sup 4/I/sub 13/2/ and /sup 4/I/sub 11/2/ erbium levels and a pair-induced energy transfer process from Yb/sup 3+/ to Er/sup 3+/; it allows the description of both single-mode and multimode laser operations. Numerical results show that slope efficiencies close to the quantum limit, with threshold pump powers of few mW, can be achieved in short single-frequency fiber lasers using grating Bragg reflectors. Moreover, we demonstrate the possibility of performing equispaced multiwavelength laser emissions in high-concentration Fabry-Perot fiber microlasers.

Excitation energy transfer between Er3+ and Tm3+ in LiNbO3

Nonradiative energy transfer between similar and different rare-earth ions in LiNbO3 has been evidenced for the first time. The contribution of nonradiative energy transfer to the decay of the1G4 and3H4 levels of thulium and the4S3/2 and4I13/2 levels of erbium is significant for activator concentrations of the order of several thousand ppm in LiNbO3. The excitation of higher-lying levels of both activators is transferred faster in codoped crystal to the lowest luminescent levels, from which the luminescence in the 1–2-μm spectral region occurs. This accelerated relaxation is advantageous for broadband optical pumping since the contribution of radiative transitions competing with the3F4−3H6 laser transition of thulium is reduced. On the other hand, it appears that erbium ions will influence adversely the efficiency of a laser-diode-pumped LiNbO3∶Er, Tm laser operating near 1.8 μm since the part of the3H4 excitation transferred to erbium ions is emitted from the long-lived4I11/2 level of Er3+. Furthermore, the4I13/2 excitation is not transferred fully to thulium ions and is lost in4I13/2−4I15/2 emission. Lithium niobate singly doped with thulium is more promising since the cross-relaxation process that transfers the excitation from the3H4 level to the3F4 level appears to be efficient in this host.

Population mechanisms of the green Er3+:LiYF4 laser

In computer simulations the mechanisms that lead to room-temperature continuous-wave green upconversion lasing in Er3+:LiYF4 are investigated. The rate-equation system considers the full erbium level scheme up to 2H9/2, ground-state depletion, excited-state absorption on the pump and laser wavelengths, three interionic processes, stimulated emission, and the crystal and resonator data of the experiments. Experimental results performed at the University of Hamburg, Germany, are reproduced in the simulation. The influence of different parameters as pump wavelength, absorption cross sections, interionic parameters, dopant concentration, and temperature is investigated. An avalanche effect which exploits the strong cross relaxation from the upper laser level and the upconversion from 4I13/2 leads to an efficient population of the upper laser level. At higher dopant concentrations the cross relaxation becomes detrimental to stimulated emission due to the depletion of the upper laser level. This concentration dependence can be considered as a general behavior of rare-earth-doped avalanche lasers.

The effect of pair-induced energy transfer on the performance of silica waveguide amplifiers with high Er/sup 3+//Yb/sup 3+/ concentrations

High-concentration Er/sup 3+//Yb/sup 3+/ co-doped silica waveguide amplifiers are numerically analyzed. With optimized rare-earth concentrations the effect of Er/sup 3+//Er/sup 3+/ ion-pairs can be neglected and each Er/sup 3+/ ion can be assumed to be paired only to the surrounding Yb/sup 3+/ ions. The rate-equations model includes uniform upconversion mechanisms from /sup 4/I/sub 13/2/ and /sup 4/I/sub 11/2/ erbium levels and an Yb/sup 3+/ to Er/sup 3+/ pair-induced energy transfer process. Numerical results demonstrate the possibility of fabricating short- and high-gain integrated optical amplifiers; it is shown that net gain as high as 3 dB/cm can be obtained. >

Site-selective spectra and energy levels of trivalent erbium in calcium fluorophosphate

Site-selective excitation and fluorescence spectra, and conventional polarized transverse and axial absorption spectra of trivalent erbium-doped single crystals of calcium fluorophosphate (Ca 5 (PO 4 ) 3 F), a fluorapatie mineral known as FAP, have been analyzed over the wavelength range 1.60 μm to 0.34 μm at temperatures between 4 K and room temperature. There was no spectroscopic evidence to indicate a phase transition from the hexagonal phase at room temperature to the monoclinic phase around 133 K as reported earlier. Most spectra are interpreted in terms of Er 3+ ions replacing Ca 2+ ions in Ca(I) sites and Ca(II) sites. A majority of the Er 3+ ions prefer the Ca(II) sites, where charge compensation is possible, by replacing F - with O 2- during the growth process. Measured room temperature fluorescence lifetimes are reported for Er:FAP, YbEr:FAB, and Yb:FAP. Absorption cross-sections are reported for Er:FAP. The absorption cross-sections for Er 3+ ( 4 I 15/2 → 4 I 13/2 ) are larger than the emission cross-sections for the lasing transition in Er:phosphate glass. Overlap of the two spectra makes Er:FAP a passive Q -switch for the Er:phosphate glass laser operating at 1.53 μm. A crystal-field splitting calculation for Er 3+ ions in both Ca 2+ sites is described. The initial crystal-field parameters were obtained from a lattice-sum calculation. By varying the initial set of crystal-field splitting parameters, B nm (cm -1 ), by only a small amount, we obtained good agreement between calculated and observed Stark levels.

Investigation of effects of gamma radiation on erbium doped fibre amplifiers

A series of irradiation tests on erbium fibre amplifiers using fibres with different erbium and codopant levels show the range of gain losses induced and permit some conclusions about the relative roles of the fibre constituents.

Muon spin relaxation in ErRh4B4

Data on zero-field μSR in ErRh4B4 are presented for temperatures from 4 to 300 K. Due to the large erbium moment, most of the muons have a relaxation time of less than 10 ns for temperatures below about 50 K. The data have been analyzed in terms of two distinct muon sites in the material. The deduced erbium relative fluctuation rate versus temperature is related to the crystalline electric field levels of erbium in the RERh4B4 structure.

Isotope shift studies and electronic configuration assignments to the energy levels of neutral erbium

Isotope shifts Δ T (170-166) have been evaluated for 54 even and 94 odd energy levels covering almost all the known configurations of the neutral erbium. These Δ T values have been derived from the isotope shift measurements carried out in 159 lines in the region 3900–4605 A using a Fabry-Perot spectrometer and liquid-air-cooled hollow cathode source with highly enriched 170Er and 166Er isotopic samples. Electronic configurations assigned to energy levels of Er I by earlier workers have been mostly confirmed and in few cases revisions have been suggested on the basis of observed Δ T values. Probable configurations have been also suggested for unassigned levels of Er I, and a large number of even levels could be assigned to 4 f 11 5 d 6 s 6 p configuration.

Radiative lifetimes of optical levels of neutral erbium, gadolinium and neodymium

Lifetimes of 47 atomic levels (energy range between 16,000 and 27,000 cm−1) of ErI, GdI and NdI have been determined using the selective pulsed laser excitation of the atoms in an atomic beam and applying the delay coincidence method for registration.

Optical and magnetic properties of Er 3+ in LiYF 4

High-resolution, polarized fluorescence spectroscopy has been used to study magnetically split energy levels of triply ionized erbium in the scheelite host lithium yttrium fluoride. Primary attention focused upon characterizing the Stark components of JLS manifolds involved in the material's several lasing transitions. Measurements at 2K yield energies and signed g factors which differ considerably from previously published zero-field studies and corresponding theoretical predictions of magnetic splittings. Polarization data allow definitive assignment of S 4 irreducible representations similar to those reported for erbium levels in the isomorphic host CaWO 4. Summation of g∥'s for the three Γ 7,8 levels of the 4I 13 2 multiplet yields a value of 3.16 ± 0.23, whereas the recently developed partial g-sum rule predicts 3.32.

Energy transfer between Tm 3+ and Er 3+ in borate and phosphate glasses

A study of the energy transfer process between thulium and erbium is presented. From our measurements of fluorescence emissions and decay times the energy transfer efficiencies and probabilities were calculated. In this work the energy transfer which occurs between the upper levels in the UV and VIS regions of the two ions was especially studied. In the Tm-Er system, a mutual migration of energy occurs. The energy transfer from thulium to erbium is a multichannel process in which the energy is transferred from all the metastable levels of thulium to the matching energy levels of erbium. In addition, backtransfer of energy from erbium to thulium occurs by crossrelaxation of respective erbium transitions. The efficiency of energy transfer from thulium to erbium is independent of the levels between which the transfer occurs, but is dependent on the matrix. It is concluded that the energy is transferred via the phonons of the host glass.

Isotope Shifts in the Spectra of Dy i and Er i†

Atomic isotope shifts in the visible region of the spectra of dysprosium and erbium have been measured using separated isotopes and a Fabry–Perot interferometer. Results include data on 165 lines for the shift Δν(164–160) in Dy i and on 146 lines for the shift Δν(170–166) of Er i. Isotope shifts for 68 low-lying odd levels of dysprosium have been obtained relative to the 5I term of the 4f106s2 configuration. In the spectra of both dysprosium and erbium it has been determined that fn−1ds2–fns2 transitions exhibit positive isotope shifts and fnsp–fns2 transitions have negative isotope shifts. The observed isotope shifts in certain low-lying 4f126s6p levels of erbium indicate strong configuration interaction.

4f^12(^3H_6)6s6p Levels of Neutral Erbium (Er i)†

The twelve 4f12(3H6)6s6p levels of neutral erbium are reported and interpreted in the JIJII coupling scheme. Intensity relations of the lines connecting 10 of them to the ground level are discussed. The values of G1(6s6p)=3373 cm−1 and ζp=1870 cm−1 for the interaction parameters are obtained directly from these levels.

Low Odd Levels of Erbium i*

Low Odd Levels of Erbium i*

Atomic Energy Levels of Neutral Erbium*

The wavenumbers of nearly 8000 transitions in Er i and Er ii lying in the visible and near ultraviolet have been measured to an estimated accuracy of ±0.015 cm−1. Of these lines, 385 are observed to show self-reversal at extreme excitation conditions. The high precision of the line list, along with these reversal data, have led to the identification of the seven lowest levels of the ground configuration of neutral erbium, 4f126s2. Furthermore, the classification of the eight lowest levels in singly ionized erbium, as reported by McNally and Vandersluis, has been well corroborated, and two more levels have been found.

Studies of Low-Lying Levels of Erbium and Tungsten Isotopes with (d,p) Reactions

Natural metal targets of erbium and tungsten and separated isotope targets of ${\mathrm{W}}^{182}$ and ${\mathrm{W}}^{183}$ were bombarded with an energy-analyzed 15-MeV deuteron beam and energy spectra of outgoing protons from the stripping reaction were taken using a precision magnetic analyzer and photographic plates. Ground-state rotational bands of even-even nuclei ${\mathrm{Er}}^{168}$ and ${\mathrm{W}}^{184}$ were observed in the highest energy region of the respective spectra. Relative intensities and angular distributions for different rotational levels agreed reasonably well with the predictions from the stripping reaction theory using the Nilsson eigenfunction for the captured neutron orbit. The next highest energy proton groups were assigned to the intrinsic two-quasi-particle or phonon excitation levels of the above even-even nuclei, on the basis of peak positions, yields, and angular distributions. Transition rates to the so-called $\ensuremath{\gamma}$-vibrational states were found quite high. Several prominent peaks with smaller $Q$ values were interpreted as due to those levels of the odd-$A$ isotopes which were associated with the Nilsson eigenstates involving low orbital angular momenta. The absolute cross sections for almost all transitions studied agreed with the predicted ones, using the distorted-wave Born approximation and the pairing interaction theory, within an accuracy of a factor of two or three.

Crystal Field Parameters for Erbium in Er (C2H5SO4)3·9H2O

Intermediate coupling wave functions and eigenvalues for f11 were used to compute the effective operator equivalent factors for the free-ion levels of erbium. The Stark splitting of the ground level 4I15/2 was used in a first-order perturbation calculation on the ground state to determine the crystal field parameters. The parameters that fit the experimental data best are; 〈r2〉A2=125.80, 〈r4〉A4=—31.06, 〈r6〉A6=—81.19, 〈r6〉A66=387.19. The parameters were used to calculate the Stark splitting of the free-ion levels and the results compared with experimentally observed values for ten levels. For the 46 Stark levels involved the calculation predicts the splitting with an average deviation of 3.4 cm—1.