Marian E. Hills

Energy levels and crystal quantum states of trivalent holmium in yttrium aluminum garnet

Absorption spectra of Ho3+ ions in yttrium aluminum garnet (Ho3+:YAG) are reported between 2.16 and 0.23 μm at various temperatures between 4 K and room temperature. Laser‐excited excitation spectra and emission spectra from the 5F4 and 5S2 multiplet manifolds to the ground state manifold 5I8 were obtained at 4, 20, and 55 K. The majority of Ho3+ ions substitute for Y3+ ions in sites of D2 point‐group symmetry in the lattice. Over 1000 temperature‐dependent transitions (hot bands) establish 280 experimental Stark levels of the 4 f 10(2S+1LJ) multiplet manifolds. Symmetry labels Γ1, Γ2, Γ3, or Γ4, appropriate to D2 symmetry, have been assigned to Stark levels up to 43 000 cm−1. Experimental levels are compared with results obtained from a theoretical calculation. The model Hamiltonian includes Coulombic, spin‐orbit, and interconfiguration interaction terms for the 4 f 10 atomic configuration of Ho3+ and crystal‐field terms in D2 symmetry. The Hamiltonian was diagonalized within the 50 lowest 2S+1LJ manifol...

Symmetry, selection rules, and energy levels of Pr3+:Y3Al5O12

Abstract Absorption, fluorescence, and site-selective excitation spectra of Pr 3+ : Y 3 Al 5 O 12 are reported between 0.4 and 6.7 μm at several temperatures between 1.6 and 90 K. The complexity of the spectra indicates that Pr 3+ ions occupy several different sites. The most intense spectra, representing the majority of the Pr 3+ ions in dodecahedral lattice sites, are analyzed on the basis of electric-dipole selection rules for D 2 site symmetry. Weak spectra are reported but not analyzed due to the difficulty in assigning levels to a particular site. Analyses of intense spectra establish the symmetry of 17 Γ 1 , 12 Γ 2 , 10 Γ 3 , and 12 Γ 4 Stark levels. These 51 levels are compared with the results of a crystal-field splitting calculation. A Hamiltonian consisting of Coulombic, spin-orbit, and crystal-field (D 2 symmetry) terms was diagonalized for all manifolds of the Pr 3+ (4f 2 ) configuration. The rms deviation between calculated and experimental levels is 11 cm −1 .

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

Abstract 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.

Emission measurements and crystal‐field calculations for 4G5/2 to 6H7/2 transitions in Sm3+:YAG

A previously published analysis of the energy levels of Sm3+ in Y3Al5O12 (YAG) has been extended to include the 4G5/2 multiplet. New absorption and emission data are reported, and some previously reported levels have been reassigned. A theoretical calculation of intensities of emitted radiation originating at the 4G5/2 multiplet predicts that radiation emitted in transitions to the 6H7/2 multiplet is particularly strong. The strongest transitions originate at the lowest of the three levels in the 4G5/2 multiplet.

Energy levels and upconversion fluorescence in trivalent thulium‐doped yttrium scandium aluminum garnet

Absorption spectra of Tm3+ ions in yttrium scandium aluminum garnet are reported between 1.9 and 0.25 μm at 4 K. Laser‐excited fluorescence was observed at 4 K from Tm3+(4f12) multiplet manifolds 1D2, 1G4, 3F2, and 3H4 to the ground‐state manifold 3H6. Emission from 1D2 and 1G4 also includes transitions to Stark levels in manifolds 3F4 and 3H5. Upconversion excited fluorescence was observed between 1D2 and 3F4 at 10 K. Analysis of the fluorescence emission confirms assignments given to individual Stark levels based on an analysis of the absorption spectra. A crystal‐field splitting calculation was carried out in which a parameterized Hamiltonian (including Coulombic, spin‐orbit, and crystal‐field terms in D2 symmetry) was diagonalized for all multiplets of the Tm3+(4f12) configuration. The rms deviation between 42 experimental and calculated Stark levels was 8 cm−1.

Absorption spectra and energy levels of Sm3+:Y3Al5O12

Abstract Absorption spectra between 0.2 and 6.7 μm are reported for trivalent samarium in single-crystal yttrium aluminum garnet, Y 3 Al 5 O 12 , at liquid-helium, liquid-nitrogen, and room temperatures. Energy levels (4f 5 [ SL ] J μ) associated with sextet, quartet, and doublet states of Sm 3+ are established from data between 1500 and 46000 cm −1 . Most samarium ions occupy yttrium ion sites, which have D 2 point-group symmetry in the lattice. A free-ion wavefunction calculation predicts the assignment of 35 isolated [ SL ] J manifolds with an rms deviation of 32 cm −1 between calculated and observed centers of gravity. A hamiltonian consisting of coulombic, spin—orbit, and crystalline electric field (D 2 symmetry) terms is diagonalized for the two lowest sextet states [6H] J and [6F] J . The calculated Stark levels based on a single set of B km crystal field parameters are compared to the observed levels (54) yielding an rms deviation of 4.9 cm −1 .

Multisite optical spectra and energy levels of trivalent thulium ions in yttrium scandium gallium garnet

Intrinsic structural disorder in scandium‐substituted garnets, attributed to mixed occupancy of certain sites in the crystal lattice by different cations, has direct consequences for the optical spectra of rare‐earth activator ions dispersed over multiple sites. In trivalent thulium‐doped yttrium scandium gallium garnet (Tm3+:YSGG), site‐selective laser excitation spectra reveal the presence of Tm3+ ions in regular D2 sites, disturbed regular sites, and in octahedral C3i sites. Absorption spectra obtained at 4 K between 0.26 and 1.85 μm are broader than those observed in more‐ordered crystal hosts and include structure attributed to Tm3+ ions in sites of other than D2 symmetry. A crystal‐field splitting calculation was carried out in which a parametrized Hamiltonian (including Coulombic, spin‐orbit, and crystal‐field terms for Tm3+ ions in D2 symmetry) was diagonalized for all manifolds of the Tm3+ (4f12) configuration. The rms deviation between 52 experimental and calculated Stark levels of Tm3+ in regul...

Energy levels of Cr3+ ions in C3i sites of Y3Al5O12

Abstract From an analysis of the ultraviolet absorption spectrum of Cr 3+ ions in Y 3 Al 5 O 12 we have obtained a sufficient number of energy levels to perform a crystal-field splitting calculation for Cr 3+ ions in sites of C 3i symmetry in the lattice. The Hamiltonian used included Coulombic, crystal-field (C 3i symmetry), spin-orbit interaction, and effective interconfiguration interaction terms and was diagonalized within the complete basis for 3d 3 atomic configuration. The calculated energy levels were compared with experimental levels up to 40000 cm −1 . From the data, we have assigned 29 Stark levels to Cr 3+ ions in C 3+ sites which agree with calculated levels to within an rms deviation of 18 cm −1 . The values of the parameters that give the best agreement are F (2) = 52724, F (4) = 38380, ξ = 252, α = 132, γ = −124, B 20 = 1091, B 40 = −21574, and B 43 = 27224 cm −1 (Dq= 1605, ν = 891, and ν′= −104.8 cm −1 ). The crystal-field splitting of Cr 3+ levels in S 4 lattice sites is also predicted with the use of the free-ion parameters obtained in this paper and a point-charge lattice-sum model.

Analysis of the optical spectra of trivalent holmium in yttrium scandium gallium garnet

The absorption spectrum of Ho3+ ions in yttrium scandium gallium garnet (Ho3+:YSGG) is reported at 4 K between 1.93 and 0.28 μm. Laser excitation spectra and laser‐excited fluorescence spectra from Ho3+(4f10)2S+1LJ multiplet manifolds 5F4, 5S2, and 5F3 to the ground‐state manifold 5I8 were obtained at 4, 8, and 70 K. Unresolved emission is observed from Ho3+ ions in slightly disturbed cation (Y3+) sites along with emission coming from Ho3+ ions occupying the regular cation (Y3+) sites having D2 symmetry. Temperature‐dependent transitions (hot bands) observed in absorption at 8 and 70 K establish experimental crystal‐field split (Stark) levels in 24 excited manifolds and the seven lowest energy Stark levels in 5I8 (Z1=0, Z2=6, Z3=17, Z4=29, Z5=87, Z6=95, and Z7=102, all in cm−1). An algorithm is used to establish D2 symmetry labels Γ1, Γ2, Γ3, or Γ4 of individual experimental Stark levels. These levels are compared with results obtained from a calculation in which a parameterized Hamiltonian was diagonaliz...

Spectroscopic analysis of Er3+(4f11) in Y3Sc2Al3O12

Abstract Absorption spectra of Er 3+ (4f 11 ) in single crystal Y 3 Sc 2 Al 3 O 12 (YSAG) are reported between 1.54 and 0.20 μm at 15 and 90 K. Laser-excited emission and excitation spectra obtained at 77 K are presented involving transitions between the 4 S 3 2 manifold and the 4 I 15 2 ground state manifold and between the 2 P 3 2 manifold and the 4 I 15 2 , 4 I 13 2 , 4 I 11 2 , and 4 I 9 2 manifolds. The individual Stark levels of twenty-nine 2 S +1 L j manifolds up to 43700 cm −1 were analyzed. Levels above 28000 cm −1 are analyzed for the first time in a garnet crystal. Temperature-dependent spectra were used to establish 120 Stark levels. The spectra indicate that most Er 3+ ions substitute for Y 3+ ions in dodecahedral sites in the lattice. Spectroscopic evidence for Er 3+ ions in octahedral sites is found in the spectrum of the 4 I 13 2 manifold. The 74 experimental Stark levels lowest in energy are compared with the results of a crystal-field splitting calculation. The Hamiltonian used includes Coulombic, spin-orbit, and interconfigurational interaction terms for the 4f 11 atomic configuration of Er 3+ and crystal-field terms appropriate for D 2 symmetry. The entire Hamiltonian was diagonalized within a 4f 11 SLJM J basis set which included the lowest fifteen 2 S +1 Lj manifolds. The rms deviation between 74 calculated and experimental Stark levels was 8 cm −1 .