J. Appl. Phys. 83 (3), 1 February /98/83(3)/1195/5/$ American Institute of Physics

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1 Temperature dependencies of linewidths, positions, and line shifts of spectral transitions of trivalent neodymium ions in barium magnesium yttrium germanate laser host Dhiraj K. Sardar a) and Steven C. Stubblefield Division of Earth and Physical Sciences, The University of Texas at San Antonio, San Antonio, Texas Received 17 July 1997; accepted for publication 27 October 1997 The spectral widths, positions, and shifts of the sharp emission lines for the R 1 X 5 and R 2 Y 3 inter-stark transitions within the respective intermanifold transitions of 4 F 3/2 4 I 9/2 and 4 F 3/2 4 I 11/2 of Nd 3 ions in Ba 0.25 Mg 2.75 Y 2 Ge 3 O 12 laser host have been investigated as a function of temperature. The linewidths of these transitions increased as the temperature of the host crystal was increased. The emission line for the R 1 X 5 transition shifted toward the shorter wavelength blue shift, while the emission line for the R 2 Y 3 transition shifted toward the longer wavelength red shift with increasing temperature. The experimental results of the temperature-dependent linewidths and line shifts of these transitions are explained in light of the existing theory of the phonon-ion interaction in crystalline solids American Institute of Physics. S I. INTRODUCTION A number of germanate laser hosts have been investigated by several researchers in the past, and these materials have been found to possess spectroscopic and laser characteristics which are superior to those of Nd:YAG. 1 5 Unfortunately, the UV radiation present in the flashlamp produces color centers during the pumping of these hosts. 1 These color centers have deleterious effects on the ultimate laser performance of these materials. However, the availability of efficient diode lasers operating at about 800 nm, which corresponds to a strong Nd 3 absorption band, can easily eliminate the shortcomings of the flashlamp pumping technology. When the germanate laser hosts are pumped with the narrow output bands from the appropriate diode lasers, it is possible to obtain high laser efficiencies and quality beams since the thermal stresses on the laser gain media are significantly reduced. Because of these favorable conditions, there has been a renewed interest in the germanate laser hosts in the recent years. A thorough spectroscopic investigation has been performed by the authors on the trivalent neodymium ions doped in barium magnesium yttrium germanate, Ba 0.25 Mg 2.75 Y 2 Ge 3 O 12 BAMGAR :Nd 3, a garnet structured host, and it has been shown that this material possesses many excellent spectroscopic and laser characteristics. 5,6 A detailed characterization of the lower-lying inter-stark energy levels of Nd 3 ions in BAMGAR has also been performed. 6 Laser action was achieved in Nd 3 :BAMGAR at nm at room temperature. 7 Although, for laser action, the thermal broadening and shift of the laser line profoundly affect the light amplification gain, output frequency stability, and thermal tunability of the laser, no studies have been performed yet on the thermal effects on the shift and width of the sharp emission lines of Nd 3 ions in BAMGAR host. a Electronic mail: dsardar@pclan.utsa.edu Therefore, owing to the potential of Nd 3 :BAMGAR as a laser material, the temperature dependencies of widths, positions, and shifts of the sharp lines at the R 1 X 5 and R 2 Y 3 inter-stark transitions within the 4 F 3/2 4 I 9/2 and 4 F 3/2 4 I 11/2 intermanifold transitions, respectively, of Nd 3 in BAMGAR have been investigated. The temperaturedependent linewidths and line shifts of these transitions have been verified with the existing theory of phonon-ion interaction based on the Debye model for phonons in the host lattice that leads to the phonon-relaxation processes. Recently, an excellent research work has been reported by Chen and Di Bartolo on the thermal effects on the sharp lines of Nd 3 in CaY 2 Mg 2 Ge 3 O 12, a garnet structured germanate crystal host. 8 The thermal effects on the sharp Nd 3 lines in other garnet hosts have also been reported by Chen and Di Bartolo 9 and Kushida. 10 II. EXPERIMENTAL DETAILS The spectroscopic sample of BAMGAR:Nd 3 used in this study was mm 3. The single crystals of Nd 3 :BAMGAR with large sizes were grown by Linz at MIT using a top-seeded solution technique. 7,11 The optical quality of these large crystals were found to be quite good. The Nd 3 concentration in this host was determined 0.3 wt % by the inductively coupled plasma emission spectroscopy technique performed at Galbraith Laboratories, Knoxville, Tennessee. The corresponding Nd 3 concentration was determined cm 3. The sample was mounted at the cold finger of a CTI model 22, a closed-cycle helium cryogenic refrigerator, capable of controlling temperature from about 10 to 300 K. The temperatures were controlled by a Lake Shore model 320 temperature controller and measured by a silicon diode sensor attached to the sample holder. The fluorescence spectra were measured on Nd 3 :BAMGAR at temperatures ranging from 10 to 300 K, by exciting the sample with the J. Appl. Phys. 83 (3), 1 February /98/83(3)/1195/5/$ American Institute of Physics 1195

2 FIG. 1. Fluorescence spectrum of Nd 3 in BAMGAR for the 4 F 3/2 4 I 9/2 transition at 10 and 300 K. nm line from a Spectra Physics model 2005 argon ion laser. The spectral bandwidth, full width at half maximum FWHM, of the laser was 0.12 nm and the maximum laser power used in these measurements was kept at approximately 4 W. The laser beam with a Gaussian profile had a 1/e 2 radius of 0.63 mm and the beam divergence was 0.69 mrad. The fluorescence from the sample was collected at a right angle with respect to the direction of the excitation laser beam and focused onto the entrance slit of a SPEX model 340E scanning monochromator equipped with a reflection grating of 600 grooves/mm which blazes at 1 m. The signal was detected by a liquid nitrogen-cooled Ge detector attached to the exit slit of the monochromator and processed by a Spex model DS 1000 Datascan equipped with a RS-232 interface card. The spectral resolution was better than 0.2 nm in all measurements. An IBM personal computer was employed to control the monochromator and to acquire and analyze the data. III. RESULTS AND DISCUSSION The fluorescence spectra for the 4 F 3/2 4 I 9/2 and 4 F 3/2 4 I 11/2 transitions of Nd 3 in BAMGAR at 10 and 300 K are shown in Figs. 1 and 2, respectively. The solid lines in Figs. 1 and 2 represent the fluorescence data at 300 K and the dotted lines show the fluorescence data at 10 K. The temperature dependencies of widths, positions, and shifts of the FIG. 2. Fluorescence spectrum of Nd 3 in BAMGAR for the 4 F 3/2 4 I 11/2 transition at 10 and 300 K. FIG. 3. Energy level diagram of Nd 3 in BAMGAR for the R 1 X 5 and R 2 Y 3 inter-stark transitions within the 4 F 3/2, 4 I 9/2, and 4 I 11/2 manifolds of Nd 3 in BAMGAR at 300 K. sharp fluorescence lines are evident in Figs. 1 and 2. The spectral intensities are also found to be strongly dependent on temperature. Figures 1 and 2 show that several new emission lines appear as the crystal temperature is increased. It is important to note that the nm line in Fig. 1 and the nm line in Fig. 2 correspond to the R 2 X 1 and R 2 Y 1 inter-stark transition, respectively. These lines are nearly absent at 10 K, but both appear strongly at 300 K. These observations can be interpreted by the fact that at 10 K, the upper Stark level (R 2 ) of the 4 F 3/2 manifold is most likely not populated enough to render the desired emission line. At 300 K, however, the upper Stark level of the 4 F 3/2 manifold is sufficiently populated through the Boltzmann distribution of the Nd 3 ions. The upper Stark level populations give rise to additional lines which correspond to the inter-stark transitions between the components of the 4 F 3/2 and 4 I 9/2 manifolds in Fig. 1 and of the 4 F 3/2 and 4 I 11/2 manifolds in Fig. 2. The strong, well-resolved fluorescence lines for the inter-stark transitions identified as R 1 X 5 in Fig. 1 and identified as R 2 Y 3 in Fig. 2, have been measured at ten different temperatures ranging from 10 to 300 K. Figure 3 portrays the R 1 X 5 and R 2 Y 3 inter-stark transitions within the 4 F 3/2, 4 I 9/2, and 4 I 11/2 intermanifolds of Nd 3 ions in BAMGAR at 300 K. 6 According to the ion-phonon interaction theory, 8 10,12 16 the linewidths of the R 1 X 5 and R 2 Y 3 inter-stark transitions arise from the crystal strain inhomogeneity, direct onephonon processes, multiphonon processes, and Raman phonon scattering processes. As the crystal temperature increases, the spectral line widths increase. Here, we will 1196 J. Appl. Phys., Vol. 83, No. 3, 1 February 1998 D. K. Sardar and S. C. Stubblefield

3 TABLE I. Some experimental linewidth and line shift data and fitting parameters for the R 1 X 5 and R 2 Y 3 transitions of Nd 3 in BAMGAR. Linewidth (cm 1 ) Experimental Fitting parameters Line Shift E (cm 1 ) Linewidth Line shift Transition 10 K 300 K K D K (cm 1 ) 0 (cm 1 ) D K (cm 1 ) E 0 (cm 1 ) R 1 X R 2 Y consider only the temperature-dependent line broadening mechanism which arises from the interaction between ion and the crystalline host lattice vibrations. The width in cm 1 of the ith energy level is, therefore, given by i i Strain i D i M i R. The first term i Strain in Eq. 1 is the width due to the strains present in the crystal lattice. Even at the lowest temperature, the measurable linewidth of a radiative transition is in general accounted for the random microscopic strains of the host crystal. These strains are purely statistical in nature and therefore give rise to a Gaussian line shape. The linewidth in impurity-doped crystalline solid is an intrinsic property and assumed to be essentially temperature independent. The second term i D represents the linewidth due to the direct or one-phonon process between the ith energy level and other nearby levels. The third term i M is the contribution due to the line broadening from the multiphonon emission processes which can take place between levels having an energy difference greater than the greatest available phonon energy, and the transition probability per unit time has been shown to be temperature independent. 15 Therefore, the multiphonon absorption processes are negligible in temperature ranges of interest. 13 The last term i R represents the line broadening due to the Raman multiphonon process associated with phonon scattering by the impurity ions. The Raman scattering process consists of the absorption of one phonon and the emission of another phonon without changing the electronic state of the ion and is given by the following expression: 8 1 R i T i T 7 D /T x 6 e x 0 e x 1 2 dx, where i is the coupling coefficient for the phonon-ion interaction, and D is the effective Debye temperature of the phonon distribution. The thermal broadening due to multiphonon, one-phonon, and Raman phonon scattering processes is homogeneous and gives rise to a Lorentzian lineshape. The shapes of the and nm line of Nd 3 in BAMGAR were found to be Lorentzian over the temperature range of 10 to 300 K. The width, in cm 1,oftheR 1 X nm line increased from cm 1 at 10 K to cm 1 at 300 K. The width, in cm 1, of the R 2 Y nm line increased from cm 1 at 10 K to cm 1 at 300 K. These values are provided in Table I. The total contribution to the linewidth due to microscopic strain, multiphonon, and direct one-phonon processes is assumed to be independent of temperature. The spectral width of the line is the sum of the energy spread of the two Stark energy levels involved in that particular transition, and can, therefore, be written in the following form: 8 T 0 T 7 D /T x 6 e x 0 e x 1 2 dx, 3 where 0 is the temperature-independent linewidth and is the simplified coupling coefficient. The simplified model described by Eq. 3 has been previously utilized by many researchers to explain the temperature-dependent linewidth data. 8 10,12 15 The measured linewidths for the R 1 X 5 and 2 FIG. 4. The linewidth of the R 1 X 5 transition of Nd 3 in BAMGAR as a function of temperature. The circles represent the experimental data and the solid curve shows the theoretical fit. FIG. 5. The linewidth of the R 2 Y 3 transition of Nd 3 in BAMGAR as a function of temperature. The circles represent experimental data and the solid curve is the theoretical fit. J. Appl. Phys., Vol. 83, No. 3, 1 February 1998 D. K. Sardar and S. C. Stubblefield 1197

4 TABLE II. Experimental and theoretical temperature-dependent linewidths of the R 1 X 5 and R 2 Y 3 transitions of Nd 3 in BAMGAR and their deviations. Temperature K (R 1 X 5 ) (R 2 Y 3 ) cm 1 cm 1 Exp Theo Exp Theo R 2 Y 3 transitions of Nd 3 in BAMGAR are plotted as a function of temperature in Figs. 4 and 5, respectively. The circles in these figures represent the experimental data, and the solid curves are the theoretical fits. The experimental data were best fitted to Eq. 3 with the fitting parameters of D K, cm 1, and cm 1 for the R 1 X 5 transition, and D K, cm 1, and cm 1 for the R 2 Y 3 transition. These values are given in Table I. The values of these parameters, along with Eq. 3, can then be used to recalculate the linewidths for the R 1 X 5 and R 2 Y 3 transitions, which are given in Table II. A measure of the accuracy of the fit is given by the rms deviation: 17 1 rms, 4 2 1/2 q p where q is the number of analyzed temperature-dependent linewidths, p is the number of fitting parameters sought, which in this case is three, and Exp Theo is the deviation of the theoretically predicted linewidth from the experimentally measured one. Here, the sum is taken over all the temperature-dependent linewidths observed. Using the values provided in Table II, the rms deviations of 0.13 and 0.67 cm 1 for the R 1 X 5 and R 2 Y 3 transitions, respectively, have been obtained. The rms linewidths of the respective transitions are and cm 1. The ratios of the rms deviations and the rms linewidths yield the rms errors of only 0.16% for the R 1 X 5 transition and 2.65% for the R 2 Y 3 transition, respectively, which represent the relative errors of the theoretical fits. The phonon theory suggests that the thermal shift of a given transition is due to stationary effects of the phononion interaction. It is assumed that the thermal shift of a sharp spectral line is the algebraic sum of the shifts of the two levels involved in the transitions. Therefore, the simplified theoretical expression for the line shift can be given in the following form: 8 E T E 0 T 4 0 D /T x 3 e x 1 dx, 5 where E 0 (in cm 1 ) E(at0K) E(at10K), and E at 0 K was obtained by extrapolating the experimental line positions to absolute zero temperature. For the R 1 X 5 and R 2 Y 3 transitions, the line shifts ( E 0 ) were estimated to be 0.30 and 0.10 cm 1. In contrast to the R 2 Y nm line which shifted toward the longer wavelength red shift, the R 1 X 5 (940.4 nm) line shifted toward the shorter wavelength blue shift with increasing temperature. The qualitative discussion on the so-called blue shift is provided in the next section. The line positions of the R 1 X 5 and R 2 Y 3 transitions are shown in Fig. 6. The temperature-dependent line shifts for the R 2 Y 3 transition are plotted as a function of temperature in Fig. 7. The circles represent the experimental data and the solid curve is the theoretical fit. The measured line shifts have been fitted to Eq. 5 with the fitting parameters of D K, cm 1, and E 0 FIG. 6. The line positions for the R 1 X 5 and R 2 Y 3 transitions of Nd 3 in BAMGAR as a function of temperature J. Appl. Phys., Vol. 83, No. 3, 1 February 1998 D. K. Sardar and S. C. Stubblefield

5 FIG. 7. The line shift for the R 2 Y 3 transition of Nd 3 in BAMGAR as a function of temperature. The circles represent experimental data and solid curve represents the theoretical fit cm 1 for the R 2 Y 3 line. These values are given in Table I. IV. SUMMARY AND CONCLUSION The fluorescence spectra of the 4 F 3/2 4 I 9/2 and 4 F 3/2 4 I 11/2 intermanifold transitions of Nd 3 in BAMGAR have been used to investigate the temperature dependencies of the linewidths, positions, and line shifts of the R 1 X 5 and R 2 Y 3 inter-stark transitions. In the temperature range of K, the linewidths increased by 2.66 and cm 1 for the R 1 X 5 and R 2 Y 3 transitions, respectively. The temperature-dependent linewidths and line shifts of these transitions are verified with the analytical expressions of the existing phonon-ion interaction theory, which assumes the Debye model for phonons in solids and gives rise to phonon relaxation processes. The different Debye temperatures for the Nd:BAMGAR system would give slightly better fittings in Figs. 4, 5, and 7. Nevertheless, a reasonable compromise is made to fit all the data with a single Debye temperature of K for this system and good fittings of the linewidth and line shift data with the existing theory are obtained. The accuracies of the fittings of the experimental linewidths with the available theoretical expressions have been given by the rms errors which are significantly small in both the R 1 X 5 and R 2 Y 3 transitions. The fluorescence linewidth of the R 1 X 5 transition is about three times larger than that of the R 2 Y 3 transition in the temperature range of K. The larger residual width for the R 1 X 5 transition appears to be mainly due to spontaneous one-phonon and multiphonon emission processes of the R 1 X 5,...,X 1 transitions. 9 The fluorescence linewidths for the R 2 Y 3 transition are about 20 and 33 cm 1 at 10 and 300 K, respectively. Since the threshold pumping power for laser oscillation is directly proportional to the width of the laser line, it is important that the laser line has narrow width at the operating temperature. Because of the narrow fluorescence width of the nm line, the Nd 3 : BAMGAR has the potential for the well-known 1.06 laser system. In crystalline solids, the sharp spectral lines are usually observed to shift toward the longer wavelengths as the crystal temperature increases, and the red shift can be verified with the existing theory. The observed red shift for the R 2 Y 3 transition of Nd 3 in BAMGAR was found to agree well with the theoretical expression given by Eq. 5. However, the observed blue shift for the R 1 X 5 transition with increasing temperature could not be fitted with the available theoretical expressions. Although the red shifts of the sharp spectral lines are commonly observed in solids due to the increase in temperature, the blue shifts have been also observed in several other crystals The observed blue shift of the R 1 X 5 transition of Nd 3 in BAMGAR may be explained by exceptionally fast lowering of the terminal Stark level X 5. The blue shift of the nm line for the R 1 X 5 transition within the 4 F 3/2 4 I 9/2 intermanifold transition may also be accounted for by the so-called pushing effect due to the thermal broadening of the Stark levels of the 4 I 11/2 manifold. 10,13 Therefore, owing to the pushing effect of the Stark levels of the immediate upper manifold 4 I 11/2, the terminal level X 5, the highest level of the lower manifold 4 I 9/2, is likely to move downward. Therefore, the 940 nm line for the R 1 X 5 transition is expected to shift toward the shorter wavelength. It is, however, not yet clear as to why the X 5 level was pushed downward so consistently as temperature of the BAMGAR:Nd 3 crystal was increased. Further studies on the thermal shifts of other inter-stark transitions of Nd 3 ions will help better understand the seemingly anomalous blue shift. ACKNOWLEDGMENTS The authors would like to thank Dr. Tom Allik of Science Applications International Corporations for supplying us with the sample used in this study. We would also like to thank Dr. Greg Quarles of Lightning Optical Corporation for numerous fruitful discussions. This research was supported by the National Science Foundation Grant No. DMR D. K. Sardar, S. Vizcarra, M. A. Islam, T. H. Allik, E. J. Sharp, and A. A. Pinto, J. Lumin. 60/61, ; Opt. Mater. 3, M. Alam, K. H. Gooen, B. Di Bartolo, A. Linz, A. Sharp, L. Gillespie, and G. Janney, J. Appl. Phys. 39, M. J. Ferry, M. L. Kliewer, R. J. Reeves, R. C. Powell, and T. H. Allik, J. Appl. Phys. 68, T. H. Allik, M. J. Ferry, R. J. 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