Modeling of Er in ceramic YAG and comparison with single-crystal YAG Bahram Zandi a, John B. Gruber b, Dhiraj K. Sardar c, Toomas H. Allik d a ARL/Adelphi Laboratory Center, 2800 Powder Mill RoadAdelphi, MD 20783-1197 b Department of Physics, San José State University, San Jose, CA 95192 c Department of Physics and Astronomy, University of Texas at San Antonio,San Antonio, TX 78249-0697 d Science Applications International Corporation, P.O. Box 632, Fort Belvoir, VA 22060-5806 ABSTRACT Recent advances in the growth of rare earths doped into ceramic (poly-crystalline) materials have generated considerable interest for the next generation of tactical laser systems mainly because ceramics provide larger size, greater strength and lower cost factors in design than their single-crystalline counterparts. For many years, Nd:YAG has been the laser material choice for stability and high power Er has been an ion laser source of interest for defense due to its eye-safe emission at 1.5 µm and has applications in infrared counter-measures, illumination detection, remote sensing and communication technologies. A model Hamiltonian including atomic and crystal-field terms is diagonalized within the complete 4f 11 SLJM J basis set which includes 364 states. Within the standard deviation obtained between 117 comparable calculated-toobserved Stark levels, one set of atomic and crystal-field parameters describes the splitting of the Nd 3+ and Er 3+ energy levels in either the ceramic or single-crystal host. We report a detailed crystal-field splitting analysis for a number of multiplet manifolds of Nd 3+ and Er 3+ in both the ceramic and single-crystal form of YAG (Y 3 Al 5 O 12 ). With few exceptions, analysis shows that the energy-level structure of Nd 3+ and Er 3+ is similar in the ceramic and single-crystal laser rods. 1. INTRODUCTION Recent advances in the growth of rare earths doped into ceramic (poly-crystalline) materials have generated considerable interest for the next generation of tactical laser systems mainly because ceramics provide larger size, greater strength and lower cost factors in design than their single-crystalline counterparts. Er has been a laser source of interest for defense due to its eye-safe emission at 1.5 µm and has applications in infrared counter-measures, illumination detection, remote sensing and communication technologies. We report a detailed crystal-field splitting analysis for a number of multiplet manifolds of Er3+ in both the ceramic and single-crystal form of YAG (Y3Al5O12). With few exceptions, analysis shows that the energy-level structure of Er3+ is similar in the ceramic and single-crystal laser rods. Perhaps this is not surprising since the garnets are optically isotropic. Of comparable importance, especially in communication technologies, including infrared counter measures, remote sensing, rangfinding and illumination detection, are devices that depend on crystals of YAG that are doped with Er 3+ These crystals undergo laser oscillations around 1.64 and 2.94 µm. While the concentration of Nd 3+ is limited in the YAG host, such is not the case for Er 3+ since Y 3 Al 5 O 12 and Er 3 Al 5 O 12 form a solid solution over the entire concentration range. Mechanisms for upconversion in Er:YAG have been investigated as a means to optimize stimulated emission at either wavelength. Consequently, a comparative study of the spectroscopic properties of Er 3+ in ceramic and singlecrystal YAG would be of interest for similar reasons that have motivated the studies in Nd:YAG. 3 26 Laser Source and System Technology for Defense and Security, edited by Gary L. Wood, Proc. of SPIE Vol. 5792 (SPIE, Bellingham, WA, 2005) 0277-786X/05/$15 doi: 10.1117/12.602938
Absorption spectra obtained between 1550 nm and 440 nm and fluorescence spectra obtained between 1700 nm and 1500 nm are reported in a comparative spectroscopic study of ceramic YAG and single-crystal laser rod YAG, both containing 50 atomic percent Er3+ as a dopant in the garnet host. Spectra are observed in both samples at temperatures between 8 K and room temperature. A model Hamiltonian including atomic and crystal-field terms is diagonalized within the complete 4f11 SLJMJ basis set which includes 364 states. Within the standard deviation obtained between 117 comparable calculated-to-observed Stark levels, one set of atomic and crystal-field parameters describes the splitting of the Er3+ energy levels in either the ceramic or single-crystal host. Figure 1 shows how closely the single crystal and the ceramic absorption spectrum compare. Figure 2 shows the fluorescence from 4I13/2 to 4I15/2 obtained near 8 K in the ceramic sample. Proc. of SPIE Vol. 5792 27
2. THEORETICAL ENERGY LEVEL ANALYSIS A model Hamiltonian expressed in terms of free-ion or atomic parameters and the crystal-field splitting parameters is used to analyze the energy-level structure of the Er3+ ions that occupy Y3+ sites having D2 symmetry in the garnet structure. Table II shows the fluorescence spectrum and the theroretical energy levels fit. The model Hamiltonian was diagonalized within the complete 4f 3, SLJM J basis set which includes 364 states. In a crystal-field of D 2 symmetry each multiplet manifold of Er 3+ (4f 3 ) 2S+1 L J, splits into J + ½ Kramers doublets that can be assigned experimentally based on an energy-level scheme obtained from analyses of the absorption, fluorescence, and Zeeman data. Because the calculated splitting predict levels within the standard deviation reported earlier 9 for the same levels analyzed in single-crystal laser rods, there is no need to further refine the calculation for the Er 3+ levels in ceramic YAG by a least-squares fitting analysis. The calculated energy (Stark) levels are reported in column 7 in Table II. Columns 6-8 in Table II allow the reader to compare individual Stark levels observed in the ceramic, and crystal form with the calculated energy levels. The total Hamiltonian for Er 3+ includes Coulombic, spin-orbit, and interconfiguration interaction terms for SLJM J states of the electronic configuration (4f 9 ), and crystal electric-field terms that lift the degeneracy of the free-ion states in the lattice into a number of energy levels called Stark levels. The free-ion Hamiltonian, H F-I, used in our analysis is 9 k F I = k+ζ i i+α + +β 2 +γ 7 k i= 1 (1) H E e l s L(L 1) G(G ) G(R ), with values for electronic repulsion, E k, the spin orbit, ζ, and the generalized Trees interconfiguration interaction, α, β, and γ terms taken from earlier work reported by Carnall et al. 1 These parameters were used to obtain a set of freeion wave functions used in the calculation of the matrix elements of the crystal field for the lowest-energy 15 multiplets of the Er 3+ (4f 9 ) electronic configuration. In subsequent fitting we allow the centroids of the free-ion multiplets to vary to account for slight host dependence on the free-ion parameters. The crystal-field Hamiltonian is of the form, n 9 * CEF nm nm m= n i= 1 H B C (i), = (2) where the terms, B nm, represent the crystal-field parameters with n = 2, 4, and 6. In Eq. (2) the term C nm ( i ) is given as, C ( 1) C C (i) = [4 π /(2n+ 1)] Y ( θ, φ ), (3) 1/ 2 nm nm i i m * where n, m = nm and Y nm ( θ i, φ i ) represent spherical harmonics that can be written in operator form. An initial set of crystal-field parameters was obtained from a lattice-sum calculation based on a point charge model developed by Morrison. 2 The B nm are related to the lattice-sum components, A nm, through the expression B =ρ A, (4) nm n nm 28 Proc. of SPIE Vol. 5792
where ρ n (n = 2, 4, and 6) represent effective values of <r n > for the rare-earth ions in the lattice. The lattice-sum components are given as A = e qc (R ˆ )/R +, (5) 2 n 1 nm j nm j j j where q j is an adjustable effective charge on the ion at R j, e is the electron charge and the sum extends over all ions in the lattice. Lattice coordinates, ionic separations and effective ionic charges are obtained from several sources, including structural from x-ray crystallographic studies. Table I presents the absorption spectrum of Er 3+ in ceramic YAG between 1550 nm and 440 nm. A nominal sample temperature around 40 K allows us to identify the temperature-dependent (hot band) transitions from the four lowestenergy Stark levels (Z 1 -Z 4 ) in the ground-state multiplet manifold of Er 3+ (4f 11 ), 4 I 15/2. As a rare earth Kramers ions in D 2 symmetry (where Er 3+ substitutes for Y 3+ in the garnet lattice), we expect J+1/2 energy (Stark) levels for each multiplet manifold, 2S+1 L J, of Er 3+. In the fluorescence spectrum of Er 3+, we identify all eight (Z 1 -Z 8 ) of the expected Stark levels for 4 I 15/2. The hot bands are identified with an asterisk in column 2, and the transition assignments are given in column 5 of Table I. From the experimental energy differences (column 6), we establish the following: Z 1 = 0, Z 2 = 25, Z 3 = 59, and Z 4 = 79, all in cm -1. Within experimental error, these values agree with Z 1 -Z 4 values obtained from the fluorescence data obtained from the same (ceramic YAG) sample listed in Table II. To compare the excited manifold Stark levels observed in the ceramic sample based on Z 1 N n transitions (column 7) with similar levels in the single-crystal sample at approximately the same temperature and Er 3+ concentration, we list the levels from the single-crystal spectra in column 8 of Table I. Within the error analyses of the spectra of both heavilydoped samples, the Stark levels reported in columns 7 and 8 are similar. At shorter wavelengths, where the resolution of the absorption bands becomes increasingly problematic, the precision in the measurements becomes less. However, by making the measurements under similar conditions on both samples, we gain confidence in the comparable experimental results. Table III shows crystal-field splitting of 4I15/2 for Er in various concentrations of YAG. Proc. of SPIE Vol. 5792 29
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Figure 2. Fluorescence from 4I13/2 to 4I15/2 obtained near 8 K in the ceramic sample. 3. CONCLUSIONS In summary, we find that the crystal-field splitting of the energy levels of Er 3+ are similar in both the ceramic sample and in the laser rod sample containing Er 3+ in the garnet (YAG) host. The particle size in the ceramic host is sufficiently large so that the spectroscopic properties reflect the bulk phase of YAG. Stimulated Raman scattering measurements, as well as highly efficient CW laser oscillation at 1.064 µm in our ceramic sample indicate this new form of the garnet host is a very good alternative to Er 3+ :YAG single crystals. Perhaps this is not surprising since the garnets are optically isotropic. 32 Proc. of SPIE Vol. 5792
REFERENCES 1. W.T. Carnall, P.R. Fields, and D. Rajnak, J. Chem Phys. 49, 4424 (1968). 2. C.A. Morrison, Angular Momentum Theory Applied to Interactions in Solids (Springer, New York, 1988). 3. J.B. Gruber, D.K. Sardar, R.M. Yow, T.H. Allik, B. Zandi, J. Appl. Phys. 96, (2004). 4. J.B. Gruber, A.S. Nijjar, D.K. Sardar, R. Yow, C.C. Russell, T.H. Allik, B. Zandi, Spectral analysis and energy-level structure of Er3+(4f3) in polycrystalline ceramic garnet Y3Al5O12, J. of Applied Physics, Vol. 97, 11 Mar. 2005. Proc. of SPIE Vol. 5792 33