Modeling the absorption spectra of Er 3 and Yb 3 in a phosphate glass

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1 JOURNAL OF APPLIED PHYSICS VOLUME 94, NUMBER 8 15 OCTOBER 2003 Modeling the absorption spectra of Er 3 and Yb 3 in a phosphate glass John B. Gruber a) Department of Physics, San José State University, San José, California Dhiraj K. Sardar Department of Physics and Astronomy, University of Texas at San Antonio, San Antonio, Texas Bahram Zandi ARL/Adelphi Laboratory Center, 2800 Powder Mill Road, Adelphi, Maryland J. Andrew Hutchinson and C. Ward Trussell Night Vision and Electronic Sensors Directorate, Burbeck Road, Suite 430, Ft. Belvoir, Virginia Received 16 January 2003; accepted 17 July 2003 Absorption spectra of Er 3 and Yb 3 ions, codopants in a phosphate glass, are reported at 8Kand at wavelengths between 350 and 1600 nm. Detailed structure appearing in the spectra, associated with individual multiplet states, 2S 1 L J, of Er 3 (4f 11 ) and Yb 3 (4f 13 ) is interpreted using a ligand-field coordination sphere model to characterize the microscopic environment surrounding the rare earth ions in multiple sites. Inhomogeneous broadening of the spectra is likely due to different configurations of PO 4 tetrahedra clustered about a caged rare earth ion in the amorphous host. Similarity between the Er 3 spectrum in the glass and in the spectrum of single-crystal LiErP 4 O 12, where Er 3 occupies sites of C 2 symmetry, suggests that an averaged site symmetry of C 2 is a reasonable approximation for Er 3 and Yb 3 ions in the phosphate glass. Calculated splitting of multiplet states by the ligand-field cluster model are compared with energy levels derived from the observed absorption peaks and well-defined shoulders. Inhomogeneous broadening of the spectra limit the precision in establishing the energy of the multiplet splittings, but the analysis is useful for modeling studies of the Er:Yb:phosphate glass as an eye-safe laser 1.53 m. The splitting of the Yb 3 (4f 13 ) 2 F J states is determined using parameters obtained from the Er 3 set by means of the three-parameter theory. No adjustments were made to the Yb 3 parameters that predict multiplet splittings in reasonable agreement with experimental data American Institute of Physics. DOI: / I. INTRODUCTION Phosphate glasses in bulk or clad fiber form with Er 3 as a dopant are popular materials for laser oscillators and amplifiers that operate at eye-safe wavelengths near 1.53 m. 1 5 For many applications Yb 3 ions are added as sensitizing codopants. 1 9 Modeling the performance and efficiency of devices using these materials has been underway for some years The optical spectra of Er 3 -doped phosphate glasses was first reported by Reisfeld and Eckstein some thirty years ago. 17 The optical and mechanical properties of these glasses have been improved considerably since that time due to technological advances in materials preparation. Recently, 18 an analysis of the absorption intensities of Er:Yb: phosphate glasses was reported on samples that are now available commercially. 19 As the need grows for improved photonic components in devices for applications, additional spectroscopic information becomes desirable, including a better understanding of the detailed microscopic environment surrounding the Er 3 and Yb 3 ions in the amorphous host. 1 3 For example, modeling the ligand-field splitting of the states of Er 3 and Yb 3 a Electronic mail: jbgruber@ .sjsu.edu ions in the glass leads to predictions of temperaturedependent changes in population distributions that may cause frequency shifts in stimulated emission and output power losses. 18 In the present study we have modeled the coordination environment of Er 3 /Yb 3 ions in the phosphate glass by assuming that the ion is surrounded by four phosphate tetrahedra arranged so that nonbridging oxygens complete the coordination. A second and third coordination sphere are also included, but appear to have minimal effect on the overall ligand-field splitting of the atomic states of the Er 3 /Yb 3 ions. However, because of interest in estimating energy transfer between Yb 3 ions and Er 3 ions found in substantial concentrations in the glass at a ratio of about 10/1, respectively, the model with multiple coordination spheres gives us a statistical value of the separation between these ions with intervening oxygens that suggests certain energytransfer mechanisms. 10,11,20 The calculated splitting is compared with 8 K absorption spectra obtained between 350 and 1600 nm in the phosphate glass and also in single-crystal LiErP 4 O 12, where Er 3 occupies sites of C 2 symmetry. 21,22 Similarity between the absorption spectra of Er 3 in the host glass and in the crystal further supports the modeled C 2 symmetry for the ion in the /2003/94(8)/4835/6/$ American Institute of Physics

2 4836 J. Appl. Phys., Vol. 94, No. 8, 15 October 2003 Gruber et al. FIG. 1. Survey absorption spectra of Er 3 and Yb 3 in a phosphate glass; wavelength range nm; 8 K spectrum represented by solid line; 300 K spectrum represented by dashed line. FIG K absorption spectrum of 2 H 11/2 (Er 3 ) at 520 nm, 4 S 3/2 (Er 3 )at 540 nm, and 4 F 9/2 (Er 3 ) at 650 nm. glass. Although inhomogeneous broadening of the spectrum limits the precision in establishing an averaged value for the ligand-field split levels, 36 well-defined absorption peaks and shoulders in the 8 K spectrum are identified through a comparison with results obtained from the splitting calculations. The three-parameter theory 23 is used to predict the splitting of the 2 F J Yb 3 manifolds without adjustment of any parameters. The results give good agreement to the bands of Yb 3 spectra observed between 925 and 975 nm. II. SPECTROSCOPIC MEASUREMENTS Samples of phosphate glass codoped with Er 3 and Yb 3 were obtained from Kigre, Inc. 19 Concentrations of both ions were determined by chemical and spectroscopic means. In terms of wt % oxide, Er 2 O 3 and Yb 2 O 3, the amounts determined from spectroscopic analytical analysis 24 were within statistical agreement with the amounts of oxide used during the preparation of the glass, which indicates very little segregation was involved. Sample concentrations of Er and Yb were approximately and cm 3, respectively. For spectroscopic measurements, samples were polished to flat, parallel faces. Absorption spectra were obtained at 8 K and room temperature with an upgraded Cary Model 14 R spectrophotometer controlled by a desktop computer with data acquisition software from OLIS. Spectra were measured between 350 and 1600 nm. The spectral bandwidth was set at 0.2 nm for all measurements, and the spectrometer was internally calibrated to an accuracy of 0.3 nm. Survey spectra obtained at both temperatures are given in Fig. 1. To obtain the absorption spectrum at 8 K, the sample was mounted at the cold finger of a CTI Model-22 closedcycle helium cryogenic refrigerator. The sample temperature was monitored with a silicon-diode sensor attached to the base of the sample holder and maintained by using a Lake Shore temperature control unit. The 8 K absorption spectrum can be assigned with relative ease to transitions from the ground state to individual multiplet manifolds, 2S 1 L J, of Er 3 (4f 11 ) and Yb 3 (4f 13 ). Each manifold represented by an absorption band in Fig. 1 is characterized by structure consisting of peaks and well-defined shoulders. In Fig. 2 the 4 F 9/2 (Er 3 ) band 650 nm consists of four peaks and a shoulder; the 4 S 3/2 (Er 3 ) band 540 nm contains two peaks and a shoulder on the higher wavelength side of the band that shows temperature dependence when compared with the room temperature spectrum. The structure of the 2 H 11/2 (Er 3 ) band nm is enlarged in Fig. 3 to show three distinct peaks and a well-defined shoulder to the lower wavelength side of the band. In Fig. 4 the structure of the 2 F 5/2 (Yb 3 ) bands dominates the 4 I 11/2 (Er 3 ) spectrum due to the tenfold increase in concentration of Yb 3 over Er 3. Spectra of phosphate glasses with Er 3 only as the dopant reported earlier 17 allow us to separate the Yb 3 /Er 3 spectra shown in Fig. 4. The intense 2 F 5/2 (Yb 3 ) peak at 975 nm completely overlaps several weaker peaks due to 4 I 11/2 (Er 3 ). This match explains in part why Yb 3 is used as a sensitizing ion to populate the lasing manifold 4 I 13/2 (Er 3 ) through energy transfer to 4 I 11/2 (Er 3 ) followed by rapid decay to the 4 I 13/2 state. FIG K absorption spectrum of 2 H 11/2 (Er 3 ) showing the structure associated with the band observed near 520 nm.

3 J. Appl. Phys., Vol. 94, No. 8, 15 October 2003 Gruber et al FIG K absorption spectrum of 4 I 11/2 (Er 3 ) and 2 F 5/2 (Yb 3 ) between 918 and 975 nm; intense peaks of Yb 3 at 918, 932, and 975 nm mask details of the 4 I 11/2 (Er 3 ) that are identified from the spectrum reported in Ref. 17. FIG K absorption spectrum of 4 I 13/2 (Er 3 ). Bands at 918 and 932 nm are also associated with 2 F 5/2 (Yb 3 ) and can be diode pumped directly. Figure 5 shows the band structure associated with the absorption spectrum of 4 I 13/2 obtained at 8 K. A broad band is observed around 1490 nm and two distinct peaks with shoulders are found at 1533 and 1540 nm. The latter band with structure shows evidence of temperature dependence in the room temperature spectrum. The multiplet peak crosssection measured at room temperature is cm 2, using an index of refraction of Recently, 18 we calculated the radiative lifetime from 4 I 13/2 to 4 I 15/2, the ground state, and reported a value of 10 ms. The lifetime determined at room temperature has a measured value of 9 ms, which suggests that the decay process is largely radiative. Inhomogeneous broadening of the absorption bands limits the precision that can be assigned to the energy values cm 1 that are reported in Table I col. 4. In a detailed report on the spectroscopy of rare earth ions in different glasses, Zhabotinskii 25 estimated values of the inhomogeneous broadening, v (cm 1 ), of absorption and fluorescence bands for Er 3 in phosphate glasses. For samples containing Er 3 concentrations similar to ours, Zhabotinskii 25 indicates that inhomogeneous broadening, even for the sharpest peaks observed in Fig. 1, can affect values reported in Table I col. 4 by tens of wave numbers. These uncertainties, when introduced into the energy levels listed in Table I col. 4 limit our expectations for identifying the order of individual ligand-field split levels when the relative splittings are comparable to the calculated values given in col. 6. Nevertheless, results of the analysis, have proved to be very helpful to ongoing studies that model Er:Yb:phosphate glass as an eyesafe laser 1.53 m in a variety of applications. 6,13,25 The peaks and well-defined shoulders of the 8KEr 3 absorption spectrum are tabulated in Table I cols The energy of the reported wavelengths in vacuum wave numbers is given in col. 4 and can be compared col. 5 with the crystal-field Stark splitting of the same multiplet manifolds of Er 3 in single-crystal LiErP 4 O 12 reported by Mazurak and Gruber. 26 The similarity suggests that the coordination of the tetraphosphates around Er 3 in the glass and in the crystal is similar, and that choosing an averaged site symmetry of C 2 for Er 3 in the glass is reasonable, given that the point group symmetry of Er 3 in the crystal lattice of LiErP 4 O 12 is reported as C 2 based on x-ray crystallographic studies on single crystals. 21,22 III. MODELING THE COORDINATION ENVIRONMENT We assume that the RE 3 ion is surrounded by four phosphate tetrahedra, arranged so that nonbridging oxygens complete the eightfold coordination. Second and third coordination spheres are included as well in the model. A figure of the coordination spheres is given by Reisfeld and Eckstein Fig Different orientations of the phosphate tetrahedra produce somewhat different local symmetry sites for the RE 3 ions that is evident by the inhomogeneous broadening of the observed spectra. Some broadening is also observed in the single-crystal spectra of Er 3 in LiErP 4 O 12, where Er 3 ions occupy C 2 sites. 21 From these observations we conclude that a modeled C 2 symmetry site is a reasonable choice for the RE 3 ion in the glass. We assume that the PO 4 tetrahedra are undistorted having P O and O O bond distances of 1.57 and 2.56 Å, respectively. 17 By assuming a radius of 1.2 Å for the nonbridging oxygens and a radius of 0.85 Å for Er 3, values obtained from the literature, 27,28 we obtain an Er O bond distance of about 2.05 Å. Atomic polarizabilities and effective ionic charges are also included in parameterized form in the modeling calculations. 28 The model Hamiltonian proposed by McClure 29 and later by Morrison 23 for the coordination spheres for Er 3 /Yb 3 in the phosphate glass is given by H e j V r j, j, j e n m A nm j r j n Y n m j, j. 1 Equation 1 is expanded in parametric form, where ligandfield components associated with the first, second, and third coordination spheres (A m n ) and averaged expectation values r n for the 4 f electrons, are treated as phenomenological m parameters. The product of these parameters is given as B n

4 4838 J. Appl. Phys., Vol. 94, No. 8, 15 October 2003 Gruber et al. TABLE I. Absorption spectra of Er 3 in a phosphate glass and in the LiErP 4 O 12 crystal. a 2S 1 LJ b nm c cm 1 c glass E (cm 1 d ) obs E (cm 1 ) obs e crystal E (cm 1 ) calc f % free-ion states 4 I13/ I 13/ I 11/ I 9/ I 13/ I 11/ I 9/ sh I 13/ I 11/ I 15/ sh I 13/ I 11/ I 15/ I 13/ I 11/ I 15/ b I 13/ I 15/ I 15/ I 13/ I 11/ I 15/2 4 I11/ I 11/ I 9/ F 9/ I 11/ I 9/ F 9/ sh I 11/ I 9/ I 13/2 970 sh I 11/ I 13/ F 9/ I 11/ I 13/ F 9/ I 11/ I 13/ I 9/2 4 I9/ I 9/ I 11/ I 13/ I 9/ I 11/ S 3/ I 9/ I 11/ H 11/ I 9/ I 11/ F 9/ I 9/ I 11/ H 11/2 4 F9/ F 9/ I 11/ I 9/ F 9/ I 11/ F 5/ F 9/ I 11/ H 11/ F 9/ I 11/ F 5/ F 9/ F 5/ I 11/2 4 S3/ S 3/ H 11/ G 9/ S 3/ H 11/ I 9/2 2 H11/ H 11/ S 3/ F 7/ H 11/ S 3/ F 7/ H 11/ S 3/ F 7/ H 11/ S 3/ F 7/ H 11/ S 3/ F 7/ H 11/ S 3/ F 7/2 4 F7/ F 7/ H 11/ F 5/ F 7/ H 11/ F 5/ F 7/ H 11/ F 5/ F 7/ F 5/ H 11/2 4 F5/ F 5/ F 3/ H 11/ F 5/ F 3/ F 7/ F 5/ F 3/ F 7/2 4 F3/ F 3/ F 5/ F 7/ F 3/ F 5/ F 7/2 2 G9/ G 9/ K 15/ G 11/ G 9/ K 15/ G 11/ G 9/ K 15/ G 11/ G 9/ K 15/ G 11/ G 9/ G 11/ K 15/2 4 G11/ G 11/ K 15/ G 9/2 379 sh G 11/ G 9/ K 15/ G 11/ G 9/ K 15/ G 11/ G 9/ K 15/ G 11/ G 9/ K 15/ G 11/ G 9/ K 15/2 a The absorption spectrum of the glass was obtained at 8 K; the spectrum of Er 3 in LiErP 4 O 12 was obtained at 4 K Ref. 26. b The multiplet states of Er 3 4 f 11 ( 2S 1 L J ); the number listed in the column is the centroid for that state. c The wavelength in nm for well-defined absorption peaks and shoulders; sh corresponds to a shoulder; b indicates a broad band. d Energy in vacuum wave numbers. e Stark levels of Er 3 in LiErP 4 O 12 (cm 1 ) from Ref. 26. f Calculated splitting based on the following parameters: B , B , B , B , IB , B , IB , B , B 6 162, IB , B , IB , B , IB ; units are in cm 1 ; imaginary terms are given as IB n m.

5 J. Appl. Phys., Vol. 94, No. 8, 15 October 2003 Gruber et al TABLE II. Splitting of 4 I 15/2 in a phosphate glass and in LiErP 4 O 12 crystal. 2S 1 LJ a Z n b E (cm 1 ) c glass E (cm 1 ) d crystal E (cm 1 ) e calc. % free-ion states 4 I15/ I 15/ I 13/ H 11/ I 15/ I 13/ F 9/ I 15/ I 13/ H 11/ I 15/ I 13/ F 9/ I 15/ I 13/ F 9/ I 15/ I 13/ F 9/ I 15/ F 9/ I 13/ I 15/ I 13/ F 9/2 a Number under the multiplet state is the calculated centroid. b Split level number within the manifold. c Splitting reported in Ref. 25. d Splitting reported in Ref. 26. e Calculated splitting based on analysis of levels given in Table I. A n m r n. These parameters, B n m, should not be confused with the B nm parameters associated with crystal-field parameters for RE 3 in a crystalline solid. 23 The Y n m ( j, j ) in Eq. 1 are normalized spherical harmonics that can be written in tensor operator form as introduced by Judd. 30 Equation 1 is diagonalized together with an effective free-ion Hamiltonian for the ligand field energy levels and wave functions written in a SLJM J basis set for the 14 lowest states of the Er 3 (4f 11 ) electronic configuration. The center of gravity for each manifold was varied to give the best overall agreement for J-mixing between states. The free-ion wave functions were obtained from Carnall et al. 31 for Er 3. For Yb 3 the simplicity of the electronic structure (4 f 13 ) allows us to diagonalize Eq. 1 directly and to adjust the separation between the excited state, 2 F 5/2, and the ground state, 2 F 7/2 based on experimental data. The C 2 axis was chosen as the quantization axis. In this symmetry both real and imaginary terms appear in the expansion of the ligand-field potential. The coordinate system is rotated about the C 2 axis so that B 2 2 is real, and B 2 0, B 4 0, and B 6 0 are real. For C 2 symmetry, a total set of 14 parameters obtains. An initial set of B n m was calculated based on the bond distances, angles, and charges on the atoms given earlier. As a first step, we carried out a least-squares fitting analysis of the Er 3 centroids, 4 I 15/2, 4 I 13/2, 4 I 11/2, 4 I 9/2, 4 F 9/2, 4 S 3/2, 2 H(2) 11/2, 4 F 7/2, 4 F 5/2, 4 F 3/2, 2 G 9/2, 4 G 11/2, 2 K 15/2, 4 G 9/2, and 2 G 7/2. The 8 K absorption bands representing these multiplet manifolds were identified from an earlier investigation in which the entire energy matrix for the 4 f 11 electronic configuration was diagonalized. 32 The 4 I 11/2 multiplet centroid was determined from the data of Reisfeld and Eckstein. 17 Next, we allowed the initial set of B n m to vary in order to match calculated multiplet splittings with the observed structure in the bands appearing in the 8 K absorption spectrum. Energy values from 36 well-defined peaks and shoulders listed in Table I col. 4 were selected for a least-squares fitting analysis. The final calculation is given in Table I col. 6. This same calculation also predicts multiplet splittings in reasonable agreement with the Stark level splitting of Er 3 multiplet manifolds in single-crystal LiErP 4 O 12, where Er 3 ions occupy sites of C 2 symmetry in the lattice. 26 The agreement between the glass and crystal spectra, and the calculated splitting supports the choice of C 2 symmetry for the averaged Er 3 sites in the phosphate glass. It is of interest to compare the calculated splitting of the ground-state, 4 I 15/2, with experimental values as well. Not having our own fluorescence data, we list in Table II the splitting reported by Zhabotinskii 25 from an analysis of the 4 K fluorescence spectrum of Er 3 in a Ba Al phosphate glass. The calculated splitting does not involve any adjustment to the parameters obtained from our analysis of the excited multiplets reported in Table I. Not knowing the detailed composition of Zhabotinskii s samples, we decided not to combine his data with ours for a least-squares fitting analysis. Table II also includes the splitting of 4 I 15/2 of Er 3 in single-crystal LiErP 4 O 12 obtained from an analysis of the 4 K fluorescence spectrum 4 S 3/2 4 I 15/2 obtained by Mazurak and Gruber. 26 The agreement between calculated values and experimental values, having the uncertainties described earlier, provides further indication that the results of modeling the phosphate glass spectra are encouraging enough for us to use the wave functions generated in the present study to explore energy transfer mechanisms in a study currently underway. The calculated splitting of the 2 F 5/2 manifold of Yb 3 was carried out by using the three-parameter theory 23 to determine a set of splitting parameters from the final set for Er 3 listed in Table I footnote e. Because the Yb 3 (4f 13 ) configuration involves fewer levels than parameters, no least-squares fitting was done. Bands 918 nm cm 1, 932 nm cm 1, and 975 nm cm 1 represent the averaged splitting of the multiplet. Relative to the experimental centroid of cm 1, a calculated splitting of , , and cm 1 is obtained. The agreement suggests consistency in the method used to interpret the bands and structure observed in the absorption spectra of Er:Yb:phosphate glass. 1 W. Koechner, Solid State Laser Engineering Springer, New York, P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers: Fundamentals and Technology Academic, New York, 1999.

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