Excited state dynamics of the Ho 3 + ions in holmium singly doped and holmium, praseodymium-codoped fluoride glasses André Felipe Henriques Librantz, Stuart D. Jackson, Fabio Henrique Jagosich, Laércio Gomes, Gaël Poirier, Sidney José Lima Ribeiro, and Younes Messaddeq Citation: Journal of Applied Physics 101, 123111 (2007); doi: 10.1063/1.2749285 View online: http://dx.doi.org/10.1063/1.2749285 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/101/12?ver=pdfcov Published by the AIP Publishing [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 186.217.234.225 On: Tue, 14 Jan 2014 12:48:27 http://scitation.aip.org/content/aip/journal/jap?ver=pdfcov http://oasc12039.247realmedia.com/RealMedia/ads/click_lx.ads/www.aip.org/pt/adcenter/pdfcover_test/L-37/1744363738/x01/AIP-PT/JAP_CoverPg_101613/aipToCAlerts_Large.png/5532386d4f314a53757a6b4144615953?x http://scitation.aip.org/search?value1=Andr�+Felipe+Henriques+Librantz&option1=author http://scitation.aip.org/search?value1=Stuart+D.+Jackson&option1=author http://scitation.aip.org/search?value1=Fabio+Henrique+Jagosich&option1=author http://scitation.aip.org/search?value1=La�rcio+Gomes&option1=author http://scitation.aip.org/search?value1=Ga�l+Poirier&option1=author http://scitation.aip.org/search?value1=Sidney+Jos�+Lima+Ribeiro&option1=author http://scitation.aip.org/search?value1=Younes+Messaddeq&option1=author http://scitation.aip.org/content/aip/journal/jap?ver=pdfcov http://dx.doi.org/10.1063/1.2749285 http://scitation.aip.org/content/aip/journal/jap/101/12?ver=pdfcov http://scitation.aip.org/content/aip?ver=pdfcov Excited state dynamics of the Ho3+ ions in holmium singly doped and holmium, praseodymium-codoped fluoride glasses André Felipe Henriques Librantz Center for Lasers and Applications, IPEN/CNEN-SP, P.O. Box 11049, São Paulo SP 05422-970, Brazil Stuart D. Jacksona� Optical Fibre Technology Centre, The University of Sydney, 206 National Innovation Centre, Australian Technology Park, Eveleigh 1430, Australia Fabio Henrique Jagosich and Laércio Gomes Center for Lasers and Applications, IPEN/CNEN-SP, P.O. Box 11049, São Paulo SP 05422-970, Brazil Gaël Poirier, Sidney José Lima Ribeiro, and Younes Messaddeq Institute of Chemistry, UNESP, P.O. Box 355, Araraquara, São Paulo 14801-970, Brazil �Received 29 September 2006; accepted 11 May 2007; published online 27 June 2007� The deactivation of the two lowest excited states of Ho3+ was investigated in Ho3+ singly doped and Ho3+, Pr3+-codoped fluoride �ZBLAN� glasses. We establish that 0.1–0.3 mol % Pr3+ can efficiently deactivate the first excited �5I7� state of Ho3+ while causing a small reduction of �40% of the initial population of the second excited �5I6� state. The net effect introduced by the Pr3+ ion deactivation of the Ho3+ ion is the fast recovery of the ground state of Ho3+. The Burshstein model parameters relevant to the Ho3+→Pr3+ energy transfer processes were determined using a least squares fit to the measured luminescence decay. The energy transfer upconversion and cross relaxation parameters for 1948, 1151, and 532 nm excitations of singly Ho3+-doped ZBLAN were determined. Using the energy transfer rate parameters we determine from the measured luminescence, a rate equation model for 650 nm excitation of Ho3+-doped and Ho3+, Pr3+-doped ZBLAN glasses was developed. The rate equations were solved numerically and the population inversion between the 5I6 and the 5I7 excited states of Ho3+ was calculated to examine the beneficial effects on the gain associated with Pr3+ codoping. © 2007 American Institute of Physics. �DOI: 10.1063/1.2749285� I. INTRODUCTION There has been a significant amount of interest for many decades in the use of sensitizing ions to transfer excitation energy from a pump source to an activator ion. There has been a similar amount of interest in the use of deactivator ions that receive excitation energy from the lower energy level of the luminescent transition of an activator ion; this interest has led to the improvement in several applications particularly in the area of material development for lasers and optical amplifiers. The luminescent 3F4 level of Tm3+, for example, can be efficiently depopulated by Ho3+ and Tb3+ ions in fluorozirconate �ZBLAN�, tellurite, Ge–Ga–As– S–CsBr and GeO2–Li2O–K2O–ZnO codoped glasses, mak- ing these materials suitable for use as optical amplifiers op- erating in 1.4–1.5 �m region of the spectrum.1–5 For applications requiring laser operation at 2.9 �m, Ho3+-doped LiYF4 �YLF� crystal6 operating on the 5I6→ 5I7 transition has the potential for pulsed laser operation despite the longer �16 ms lifetime of the lower laser �5I7� level when com- pared to the lifetime of the upper laser �5I6� level which is �3 ms.7 Many applications, however, require continuous wave �cw� operation in this spectral range. To achieve this end, a deactivator ion must be introduced in order to quench the excited state population in the 5I7 level. A 5I7 level life- time reduction to 2.2 ms in the presence of 1.2 mol % Nd3+ in codoped YLF crystal7 has shown some promise, but the population of the upper 5I6 laser level was reduced and the luminescence efficiency of the 2.9 �m emission decreased by approximately 50%. Recently,8 it has been shown that effective deactivation of the 5I7 level of Ho3+ using Pr3+ ions can lead to cw output from a ZBLAN-based fiber laser. With better choice of both the Ho3+ and Pr3+ ion concentrations, an unsaturated output power of 2.5 W was obtained from the fiber laser.9 This re- cent work extends past investigations10–12 into the successful use of the Pr3+ ion as a deactivator ion for the 4I13/2 level of the 4I11/2→ 4I13 laser transition of Er3+-doped ZBLAN; the current output power of �9 W from an Er3+, Pr3+-doped ZBLAN fiber laser demonstrates the power scaling potential of this particular rare-earth ion combination.13 In the present study we have carried out a detailed in- vestigation of the luminescence emitted from the excited states of the Ho3+ ion in ZBLAN glass and in the presence of Pr3+ ions. We have determined the Burshtein model param- eters for the luminescent decay and we have calculated the energy transfer rate parameters for the various energy trans- fer processes present in these glasses. We compare these re- sults with other fluorescent systems involving deactivation and estimate the improvement in the performance of ZBLAN-based lasers operating at 2.9 �m. In light of poten- tial directly diode pumped Ho3+-doped ZBLAN fiber lasers, we numerically solved the rate equations for singlya�Electronic mail: s.jackson@oftc.usyd.edu.au JOURNAL OF APPLIED PHYSICS 101, 123111 �2007� 0021-8979/2007/101�12�/123111/9/$23.00 © 2007 American Institute of Physics101, 123111-1 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 186.217.234.225 On: Tue, 14 Jan 2014 12:48:27 http://dx.doi.org/10.1063/1.2749285 http://dx.doi.org/10.1063/1.2749285 http://dx.doi.org/10.1063/1.2749285 Ho3+�4 mol % �-doped and Ho3+�4 mol % �, Pr3+�x mol % �-codoped ZBLAN glasses under cw pumping at 655 nm to determine the population inversion and its de- pendence on the Pr3+ concentration. II. EXPERIMENTAL PROCEDURE The ZBLAN glasses were prepared as either single �Ho3+� or double-doped �Ho3+, Pr3+� samples for the time-resolved luminescence spectroscopy experiments. The two sets of ZBLAN glasses were prepared from ultra- pure fluoride starting materials with the following compositions. �i� Ho3+-doped samples: �100−x� ��53 ZrF4–20 BaF2–4 LaF3–20 NaF�–x HoF3 �x =2,4 ,6 mol % �. �ii� Ho3+, Pr3+-codoped samples which have the Ho3+ concentration constant at 4 mol %: �96−y� ��53 ZrF4–20 BaF2–4 LaF3–20 NaF�–4 HoF3–y PrF3 �y =0.1,0.2,0.3 mol % �. The Ho3+-doped ZBLAN and Ho3+, Pr3+-codoped ZBLAN glasses were produced by melting the starting ma- terials at 850 °C for 120 min in a Pt–Au crucible. The liq- uids were poured into brass molds and annealed at 260 °C for 2 h to remove the mechanical stresses. The samples were cut and polished into 15�10�5 mm3 pieces. The absorption spectra of the glasses were measured us- ing a spectrophotometer �Cary/OLIS 17D� operating in the range of 300–2000 nm. The lifetimes of the Ho3+ excited states, i.e., the 5I6 and 5I7 levels, were measured after pulsed laser excitation from a tunable optical parametric oscillator �OPO� that was pumped by the second harmonic of a Q-switched Nd:YAG �yttrium aluminum garnet� laser �Bril- liant B from Quantel, France�. Optical pulse widths of 4 ns at 1151 and 1948 nm were used to directly excite the 5I6 and 5I7 energy levels of Ho3+, respectively. Selective optical ex- citation of the energy levels of Ho3+ was carried out in order to isolate the various components to the Ho3+ decay. The decay of the luminescence of the energy levels of Ho3+ was detected using an InSb infrared detector �Judson model J10D cooled to 77 K� in conjunction with a fast preamplifier �re- sponse time of �0.5 �s� and analyzed using a digital 200 MHz oscilloscope �Tektronix TDS 410�. All the fluores- cence decay times were measured at 300 K. To isolate the luminescence signals, bandpass filters with �80% transmis- sion at 1200 and 2000 nm �each with a half width of 15 nm and an extinction coefficient outside this band of �10−5� were used. III. EXPERIMENTAL RESULTS A. Luminescence from the 5I7 excited state of Ho3+ The absorption spectrum of Ho3+�4 mol % �, Pr3+�0.3 mol % �-doped ZBLAN glass is shown in Fig. 1. The spectrum was used to calculate the absorption cross sec- tion of the 5I8→ 5F5 absorption transition of Ho3+ at 650 nm in ZBLAN glass. The absorption spectrum of the Ho3+ and Pr3+ ions in ZBLAN codoped glass shows a strong overlap between the 5I8→ 5I7 absorption transition of Ho3+ �centered at 1950 nm� and the 3H4→ 3F2, 3H6 absorption transition of Pr3+ �centered at 2100 nm�; it is expected that efficient en- ergy transfer will occur from the 5I7 excited state of Ho3+ to the 3F2, 3H6 states of Pr3+. Figure 2 shows the luminescence decay of the 5I7-excited state in Ho3+�4 mol % �-doped ZBLAN and Ho3+�4 mol % �, Pr3+�x mol % �-codoped ZBLAN glasses. It can be observed that a strong decrease in the 5I7 excited state lifetime takes place for the Ho3+�4 mol % �, Pr3+�0.2 mol % � and Ho3+�4 mol % �, Pr3+�0.3 mol % �-codoped ZBLAN glasses in comparison with the decay of Ho3+�4 mol % �- doped ZBLAN glass. The Ho3+�5I7�→Pr3+�3F2 , 3H6� nonra- diative energy transfer �which we label ET1� is therefore very effective in Ho3+, Pr3+-codoped ZBLAN glass. The solid lines in Fig. 2 represent the best fit of the Ho3+�5I7� state luminescence decay using the Burshtein model,14 which FIG. 1. Absorption spectrum of Ho3+�4 mol % �, Pr3+�0.3 mol % �-doped ZBLAN glass measured at room temperature using the Cary 17D spectro- photometer. The sample thickness was equal to 5 mm. The Ho3+ ion con- centration of 4 mol % corresponds to 5.5�1020 ions cm−3. FIG. 2. Luminescence decay of the 5I7 level of Ho3+ in �a� singly Ho3+�4 mol % �-doped ZBLAN, �b� Ho3+�4 mol % �, Pr3+�0.2 mol % �-co doped ZBLAN, and �c� Ho3+�4 mol % �, Pr3+�0.3 mol % �-co doped ZBLAN induced by laser excitation at 1958 nm with a pulse duration of 4 ns and average energy of 5 mJ �and pulse repletion frequency of 10 Hz�. The solid lines represent the best fit using the Burshtein model, and �ET and �ET are the derived energy transfer parameters using a least squares fit. 123111-2 Librantz et al. J. Appl. Phys. 101, 123111 �2007� [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 186.217.234.225 On: Tue, 14 Jan 2014 12:48:27 includes donor migration in the energy transfer process. The expression we used to fit the luminescence decay for a dipole-dipole interaction is given by14 I�t� = I0 exp�− t �D − �ETt − �ET �t� , �1� where �D �=�D2� is equal to 31.8 ms and is the lifetime of 5I7 level measured for Ho3+�4 mol % �-doped ZBLAN. Note that this measured lifetime is longer than both the lifetime of the 5I7 state measured in a low concentration system �12 ms for 0.1 mol % Ho3+� and the radiative lifetime of 12.6 ms.15 This longer lifetime relates to the effects from excitation migra- tion of the 5I7 excited states at higher Ho3+ concentrations. �ET is the donor to acceptor �Pr3+� energy transfer parameter and �ET is the transfer parameter which is related to the donor to acceptor energy transfer which is assisted by dis- crete excitation migration �or hopping� among donor �5I7� states. The relative luminescence efficiency of the donor state �5I7� can be calculated by integrating I�t� for the entire decay. Integration of I�t� has been used to calculate the ef- fective lifetime of the 3H4�Tm3+� state due to Tm3+�3H6�, Tm3+�3H4�→Tm3+�3F4�, Tm3+ �3F4� cross relaxation �CR� among Tm3+ ions in Yb3+, Tm3+-codoped systems.16 The relative luminescence efficiency ���� has been calculated for the nonexponential decay of the donor state using the expression17 �� = 0 � I�t�dt 0 � exp�− t/�D�dt = 0 � I�t�dt �D . �2� In Eq. �2� we have used the normalized luminescence decay I�t� such that I�0�= I0=1, where I0 is the fluorescence inten- sity at t=0 and I�t→��=0. Using ��=WD / �WD+WET�, where WD=�D −1 is the donor intrinsic decay rate parameter and WET is the donor to acceptor energy transfer rate param- eter, one can obtain WET = 1 �D �1 − �� �� � . �3� In Eq. �3� WET=0 when ��=1 and WET→� for ��→0, as expected. The Ho3+→Pr3+ transfer rate parameter for ET1 �i.e., WET=WET1� was calculated using Eq. �3� that incorpo- rates the relative luminescence efficiency of the 5I7 �Ho3+� state and the intrinsic lifetime of this level ��D=�D2 =31.8 ms�. The values of WET1 are given in Table I. Based on this result, we can establish that the decay of the 5I7 state is practically totally radiative in ZBLAN glass and the nonradiative multiphonon decay rate to the ground state is negligible if these measurements are performed at room temperature. The relative luminescence efficiencies of the two lowest excited states of Ho3+ were obtained using the relation ��= 0 �Ii�t�dt /�Di, where i=2 refers to the 5I7 level and i=3 to the 5I6 state. Table I gives the energy transfer parameters ��ET, �ET� and the luminescence efficiency ���� of 5I7 state, which was diminished by ET1. One may obtain the microscopic transfer constant CDA�cm6 s−1� using the fol- lowing expression that relates this constant with the energy transfer parameter �ET�s−1/2�, CDA = 9�ET 2 16�3cA 2 , �4� where cA is the Pr3+ concentration. The calculated values of CDA varied from 3.1�10−38 to 4.8�10−38 cm6 s−1 as the Pr3+ concentration changed from 0.1 to 0.3 mol %, as shown in Table I. The average value of CDA for ET1 obtained in this work was equal to 3.9�10−38 cm6 s−1, which is higher than the microscopic rate constant found in the case of Ho3+ �5I7� deactivation by Nd3+ ions in Ho:Nd:YLF crystal in which case CDA was 8.6�10−41 cm6 s−1.7 If one assumes that �ET 2 relates to direct energy transfer, one can calculate the ratio R=�ET 2 /WET. which determines the relative contribution of direct energy transfer to the total energy transfer. Table I shows that the contribution of the direct energy transfer to the total energy transfer increases �i.e., R=0.15→0.55� and the influence of energy migration among donor ions decreases with increasing Pr3+ concentra- tion. This situation is expected because with increasing Pr3+ concentration each Ho3+ excitation finds a Pr3+ ion faster, i.e., less energy migration among Ho3+ ions is necessary be- fore direct energy transfer to a Pr3+ ion takes place. B. Luminescence from the 5I6 excited state of Ho3+ Figure 3 shows the luminescence decay of the 5I6 ex- cited state of Ho3+ observed at 1200 nm due to the Ho3+�5I6�→Pr3+�3F5 , 3F4�, energy transfer process �which we label ET2� in Ho3+, Pr3+-codoped ZBLAN glass. The solid line in Figs. 3�a� and 3�b� represents the best fit to the luminescence decay using the Burshtein model, i.e., Eq. �1�. The energy transfer rate parameter of ET2 with WET=WET2 was calculated using Eqs. �2� and �3�, where �� is now the relative luminescence efficiency of the 5I6 excited state and TABLE I. Energy transfer parameters relating to the 5I7 level The energy transfer parameters were obtained from the best fit to the 2000 nm lumines- cence of ZBLAN glasses double doped with 4 mol % Ho3+ and 0.1, 0.2, or 0.3 mol % Pr3. The energy transfer parameters �ET and �ET were obtained using a least squares fit and �D2=31.8 ms, which was measured indepen- dently from a Ho3+ �4 mol % �-doped ZBLAN sample. The relative lumi- nescence efficiency �� was calculated using the integration of the normal- ized luminescence decay of Ho3+ in Ho3+, Pr3+-codoped ZBLAN. Luminescence from the 5I7 level of Ho3+ Pr3+ �mol %� CDA �cm6 s−1� �10−38� �ET �s−1/2� �ET �s−1� �� 0.1 3.1±0.4 18.1±0.6 1455±3 1.428�10−2 0.2 3.9±0.7 40.3±0.8 3000±6 5.723�10−3 0.3 4.8±0.7 67.3±1.1 3393±27 3.773�10−3 Migration assisted Ho3+�5I7�→Pr3+ Pr3+ �mol %� WET1 �s−1� �ET 2 �s−1� R �=�ET 2 /WET1� 0.1 2171 328 0.15 0.2 5463 1624 0.30 0.3 8302 4529 0.55 123111-3 Librantz et al. J. Appl. Phys. 101, 123111 �2007� [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 186.217.234.225 On: Tue, 14 Jan 2014 12:48:27 �D=�D3=4.6 ms. The values of WET2 and �ET 2 are given in Table II. The values of R shown in Table II show that in a similar manner to ET1 the influence of direct energy transfer increases �i.e., R=0.009→0.15� and the influence of energy migration among donor ions decreases with increasing Pr3+ concentration. The ratio of direct energy transfer to the total energy transfer is smaller for ET2 compared to ET1, which suggests that more energy migration is required for ET2 compared to ET1. Table II gives the energy transfer parameters ��ET, �ET� and the relative luminescence efficiency ���� of the 5I6 state due to ET2. The microscopic transfer constant CDA varies from 0.18�10−41 to 3.51�10−41 cm6 s−1 in the case of the Ho3+ �5I6� deactivation by the Pr3+ �3F4 , 3F3� states, when the Pr3+ concentration changes from 0.1 to 0.3 mol %. The average value of CDA for ET2 is 2.05�10−41 cm6 s−1 is three order of magnitude smaller than the CDA value for ET1 and is approximately 36 times bigger than the corresponding pa- rameter determined for the case of Ho3+ �5I6� deactivation by Nd3+ in Ho:Nd:YLF crystal �CDA=5.6�10−42 cm6 s−1�.7 This indicates that the deactivation of the Ho3+ �5I6� state by energy transfer to Pr3+ ions will potentially have a larger impact on the population inversion of the 2.9 �m laser tran- sition compared to deactivation of the Ho3+�6I6� state that would be introduced by Nd3+ ions. C. Energy transfer upconversion „ETU… from the lowest excited states of Ho3+ Two emission bands centered at 1200 and 655 nm were observed in Ho3+ �4 mol % � -doped ZBLAN produced by pulsed laser excitations at 1958 and 1151 nm, respectively. The temporal characteristics of both upconversion emissions were observed to be dependent on the excitation energy den- sity up to the limit of �0.2 J /cm3. For larger energy densi- ties we observed a constant upconversion transient response. �The excitation energy densities were determined for con- stant energies of 3.1 mJ at 1958 nm and 8 and 12 mJ at 1151 nm. Four focus positions provided excitation volumes of 3.9�10−3, 7.6�10−3, 15.7�10−3, and 35.3�10−3 cm3.� This observation cannot be applied to the luminescence de- cay of the lower excited �or donor� level involved in the upconversion process because one finds that the initial part of the decay curve of the donor level changes its slope as the pulse energy is varied. When we measured the intrinsic 5I7 and 5I6 fluorescence decays, we used a 6 mJ pulse energy �i.e., 1.9 mJ absorbed� to minimize the effects from ETU. This is demonstrated by the fact that the best fit of the 5I7 �and 5I6� luminescence decay curve is purely exponential, as seen in Fig. 2�a�. The upconversion luminescence at 1200 nm was produced by a phonon-assisted ETU process, which we label ETU1 that can be represented by Ho3+�5I7 , 5I7�→Ho3+�5I6 , 5I8�. Figure. 4 displays the 1200 nm luminescence decay of 5I6 level when directly ex- cited at 1151 nm �Fig. 4�a�� and when indirectly excited at 1958 nm by the ETU1 process �Fig. 4�b��. A second upconversion luminescence at 655 nm was produced after two interacting 5I6 states promote excitation to the 5F5 level by way of a similar ETU process, labeled here as ETU2 and which can be represented by Ho3+�5I6 , 5I6�→Ho3+�5F5 , 5I8�. Figures 5�a� and 5�b� show the luminescence transient measured at 655 nm from the Ho3+ �5F5� excited state of Ho3+ �4 mol % �-doped ZBLAN. This 655 nm luminescence was produced by two distinct ways using �i� excitation at 532 nm to produce the 5I8 → 5S2 absorption transition which was followed by fast ��20 �s� decay to 5F5 state, see Fig. 5�a�; �ii� indirect exci- tation at 1151 nm to produce the 5I8→ 5I6 absorption transi- tion which was followed by ETU2, see Fig. 5�b�. Despite the fact that 655 nm upconversion luminescence has also been observed in Ho3+, Pr3+-codoped ZBLAN, we measured the ETU2 rate parameter using singly Ho3+-doped ZBLAN in FIG. 3. Luminescence decay of the 5I6 level of �a� Ho3+�4 mol % �, Pr3+�0.2 mol % �-co doped ZBLAN and �b� Ho3+�4 mol % �, Pr3+�0.3 mol % �-co doped ZBLAN. The 1200 nm luminescence was pro- duced by a pulsed laser excitation at 1151 nm with a pulse duration of 4 ns and mean energy of 6 mJ at 10 Hz. The solid lines represent the best fit using the Burshtein model, and �ET and �ET are the derived energy transfer parameters using a least squares fit. TABLE II. Energy transfer parameters relating to the 5I6 level. The energy transfer parameters were obtained from the best fit to the 1200 nm lumines- cence of ZBLAN glasses double doped with 4 mol % Ho3+ and 0.1, 0.2, or 0.3 mol %Pr3. The energy transfer parameters �ET and �ET were obtained using a least squares fit and �D2=4.6 ms, which was measured indepen- dently from a Ho3+�4 mol % �-doped ZBLAN sample. The relative lumines- cence efficiency �� was calculated using the integration of the normalized luminescence decay of Ho3+ in Ho3+, Pr3+-doped ZBLAN. Luminescence from the 5I6 level of Ho3+ Pr3+ �mol %� CDA �cm6 s−1� �10−40� �ET �s−1/2� �ET �s−1� �� 0.1 0.69±0.08 0.85±0.05 67.0±0.1 0.7285 0.2 0.76±0.06 1.78±0.06 118.0±0.3 0.5949 0.3 4.69±0.29 6.63±0.21 147.0±1.2 0.4433 Migration assisted Ho3+�5I6�→Pr3+ energy transfer Pr3+ �mol %� WET2 �s−1� �ET 2 �s−1� R �=�ET 2 /WET2� 0.1 81 0.73 0.009 0.2 148 3.2 0.021 0.3 273 44 0.161 123111-4 Librantz et al. J. Appl. Phys. 101, 123111 �2007� [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 186.217.234.225 On: Tue, 14 Jan 2014 12:48:27 order to eliminate the influence of ET2. The solid lines in Figs. 4�b� and 5�b� represent the best fit to the 1200 and 655 nm emissions using Eq. �5� that has been derived for the acceptor luminescence transient where the energy transfer involves the Burshtein �or Inokuti-Hirayama� model for a dipole-dipole energy transfer.18 The relation is given by I = I0�exp�− t �D − �ETUt − �ETU �t� − exp�− t �A �� , �5� where �A is the total lifetime of the acceptor excited state and �D is the intrinsic lifetime of the donor excited �Ho3+� ion. The first term in Eq. �5� gives the nonexponential decay of the donor excited state directly involved in the ETU process. The second term is the acceptor excited state decay. The adjustable transfer parameters ��ETU1 ,�ETU1� and ��ETU2 ,�ETU2� in Eq. �5� relate to ETU1 and ETU2 pro- cesses, respectively. The best fit to the upconversion lumi- nescence gave �a� �ETU1=66 s−1 and �ETU1 0.2 s−1/2 for 1200 nm emission; �b� �ETU2=33 s−1 and �ETU2=22 s−1/2 for 655 nm emission, measured for Ho3+�4 mol % �-doped ZBLAN. The luminescence efficiency of the donors in the lower state that are involved in the ETU process was ob- tained using the following expression: �� = 1 �D 0 � exp�− t �D − �ETUt − �ETU �t�dt , �6� in which I0=1 for t=0, according to Eq. �2�. The ETU rate parameter �WETU� was obtained using an expression similar to Eq. �3�. The relative luminescence efficiencies ���� due to ETU1 and ETU2 were obtained using �D�5I7�=31.8 ms and �D�5I6�=4.6 ms in Eq. �6�. The ETU rate parameters WETU1 and WETU2 were obtained for the Ho3+-doped ZBLAN sys- tem, using an equation similar to Eq. �3�. By observing the 655 nm luminescence transient shown in Fig. 5�b�, one ob- serves that the fluorescence decay is consistent with the mea- sured mean decay time ��� of the donor �5I6� state involved in the ETU2 process ��=1.33 ms�. On the other hand, the 655 nm luminescence has a short decay time of �41.8 �s when this level is directly excited at 532 nm by the short laser pulse of 4 ns duration and a pulse energy of 5 mJ, as shown in Fig. 5�a� for the Ho3+�4 mol % �-doped ZBLAN glass. The 655 nm emission exhibits the shortened decay time of 42 �s compared to the intrinsic 290 �s due to the phonon-assisted CR interaction Ho3+ �5F5 , 5I6� →Ho3+�5I8 , 5I7� that depopulates this state in a highly con- FIG. 4. �a� Luminescence decay of the 5I6 excited state at 1200 nm mea- sured after pulsed laser excitation at 1151 nm in singly Ho3+�4 mol % �-doped ZBLAN �density of excited 5I7 states of �5 �1017 cm−3� and �b� the upconversion luminescence at 1200 nm induced by pulsed laser excitation at a wavelength of 1958 nm �pulse energy=3.1 mJ in 4 ns� having a density of excited �5I7� states of 1.56�1018 cm−3. The solid line represents the best fit using the Burshtein model, and �ETU and �ETU are the ETU1 parameters using a least squares fit. FIG. 5. The 5F5 excited state luminescence of Ho3+ observed at 655 nm in singly Ho3+�4 mol % �-doped ZBLAN glass after �a� direct excitation at 532 nm and �b� exciting the 5I6 state at a wavelength of 1151 nm �pulse energy=8 mJ in 4 ns� having a density of excited �5I6� states of 1.17 �1018 cm−3. The solid line represents the best fit using the Burshtein model, and �ETU and �ETU are the ETU2 parameters using a least squares fit. 123111-5 Librantz et al. J. Appl. Phys. 101, 123111 �2007� [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 186.217.234.225 On: Tue, 14 Jan 2014 12:48:27 centrated system, i.e., for �Ho3+� 0.5 mol %. The lumines- cence decay of the 5F5-excited state was measured for three Ho3+-doped ZBLAN samples �2, 4, and 6 mol %� by direct excitation at 532 nm. The relative luminescence efficiency of the 5F5 state was obtained for the three Ho3+-doped ZBLAN samples using the integration of the luminescence decay curve previously described by Eq. �2�. The values obtained are given in Table III as well the corresponding CR rate parameter WCR that was calculated using a similar equation to Eq. �3� with �D=�D4=290 �s. The calculated values are given in Table III. D. Model for ETU in Ho3+-doped ZBLAN A detailed investigation of the time dependence of the ETU luminescence transient was carried out by monitoring the upconverted luminescence at 1200 and 655 nm as a func- tion of the absorbed excitation energy density and hence the density of excited Ho3+ ions. We made a fit to the lumines- cence transient using the Burshtein model given by Eq. �5� for a dipole-dipole interaction. The rate parameters for ETU were obtained using the integration method given by Eq. �6� and a similar equation to Eq. �3�. The results are presented in Table IV. Figures 6�a� and 6�b� display the ETU rate param- eters for ETU2 and ETU1 as a function of the density of excited Ho3+ ions. It can be observed that the rate parameter of both ETU processes reaches a constant rate when the ex- cited Ho3+ ion density reaches a value of 2�1018 cm−3; this behavior suggests that there exists a critical distance RC be- tween excited Ho3+ ions for both ETU processes. Based on a statistically random separation between the excited Ho3+ ions in the glass lattice, we can say that the fraction of excited Ho3+ ions fdR, which have another excited Ho3+ ion as the closest neighbor between distance R and R+dR, is given by,19 fdR = 4�R2NHo N* NHo �1 − N* NHo ���/3R3NHo−2� dR , �7� where N* is the concentration of Ho3+ excited ions �cm−3� and NC is the critical concentration of excited Ho3+ ions which is related to RC. Integrating Eq. �7� between Rm �the minimum distance between Ho3+ ions� and R=� yields the ETU efficiency as a function of N* according to �ETU = Rm RC fdR � 1 + Rc � fdR � 0 = 1 − exp�− NC/N*� , �8� where we use RC � fdR=exp�−NC /N*�, which has been deter- mined previously.19 The observation that the ETU rate pa- TABLE III. Parameters used in the rate equation modeling. Luminescence branching ratio and radiative lifetimes of Ho3+a Transition � �R � �expt� Wnr �s−1� 5F5→ 500 �s 290 �s 1448 5I6 0.05 5I7 0.18 5I8 0.77 5I6→ 5.9 ms 3.5 ms 116.2 5I7 0.09 5I8 0.91 5I7→ 5I8 1 12.6 ms 12 ms Ho3+→Ho3+ energy transfer rate parameters �expt�b Ho3+ �mol %� WCR �s−1� ���5F5� 2 107 76 0.2424 4 194 87 0.1503 6 251 23 0.1207 Ho3+→Pr3+ energy transfer rate parameters �expt�b Pr3+ �mol %� WET1 �s−1� WET2 �s−1� ���5I7� ���5I6� 0.1 2171 81 1.427�10−2 0.7285 0.2 5463 148 5.723�10−3 0.5949 0.3 8302 273 3.773�10−3 0.4433 aValues obtained from the literature �Ref. 15�. bExperimental relative luminescence efficiencies and calculated rate values �this work�. TABLE IV. Parameters relating to the proposed model for the ETU pro- cesses observed in Ho3+�4 mol % �-doped ZBLAN. Ho3+→Ho3+ ETU rate parameters �expt� ETU1 ETU2 K0 �s−1� 72 650 NC �cm−3� 3.6�1017 2.94�1017 RC �Å� 87 70 FIG. 6. ETU rate parameter as a function of the experimental excited Ho3+ ion density �N*� obtained by measuring the luminescence transient of �a� the 5F5 level after excitation at 1151 nm and �b� the 5I6 level after excitation at 1958 nm. The solid lines represent the best fit using the proposed model for ETU. 123111-6 Librantz et al. J. Appl. Phys. 101, 123111 �2007� [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 186.217.234.225 On: Tue, 14 Jan 2014 12:48:27 rameter dependence on N* in Figs. 6�a� and 6�b� displays a constant probability rate for higher excitation densities indi- cates that the ETU relative efficiency for large values of N* should be given by �ETU�N*�=WETU/K0, where K0 is the rate parameter constant. The solid lines in Figs. 6�a� and 6�b� represent the best fit using the model, which gave NC=2.94 �1017 cm−3 and K0=650 s−1 for ETU2 and NC=3.6 �1017 cm−3 and K0=72 s−1 for ETU1. These values for K0 should be used in a rate equation system simulating the op- eration of a laser because under these circumstances, higher excited Ho3+ ion densities �N*�1019 cm−3� are usually present. The luminescence intensities at 1200 and 655 nm pro- duced by the ETU1 and ETU2 processes, respectively as a function of the excited Ho3+ density are presented in Figs. 7�a� and 7�b�. It can be observed that the emissions are de- pendent on the square of N*, as represented by the solid and open squares in Figs. 7�a� and 7�b�. The proposed model for ETU predicts an ETU rate linearly dependent on the N* for N*�NC, i.e., WETU N*, as has been previously reported for ETU process between two Nd3+ ions in the 4F3/2 state.20 IV. DISCUSSION The rate parameters for ETU1 correspond to 11% of the rate parameters for ETU2, consequently ETU does not favor a population inversion between the 5I6 and 5I7 energy levels in singly Ho3+-doped ZBLAN glass. The opposite situation has been observed in the case of Er3+-doped ZBLAN glass, where the corresponding rate parameter values for ETU1 are three times larger than the corresponding rate parameter val- ues for ETU2 and ETU contributes positively to a population inversion.21 �The ETU processes in Er3+ involve similarly positioned energy levels as in Ho3+.� The ET1 energy trans- fer process has a larger rate parameter than the ETU2 process in Ho3+ �4 mol % �, Pr3+ �0.3 mol % �-doped ZBLAN, which will minimize the negative effect of ETU on the laser gain. ET1 effectively quenches the 5I7 intrinsic lifetime of 31.8 ms to such an extent that the mean decay time is only 120 �s for Ho3+ �4 mol % �, Pr3+ �0.3 mol % �-codoped ZBLAN glass. Similar effects have been observed on the lower laser level of Er3+ �8.75 mol % �, Pr3+ �1.55 mol % �-codoped ZBLAN glass, where the Er3+ �4I13/2� intrinsic lifetime of 9 ms is reduced to 20 �s due an efficient Er3+�4I13/2� →Pr3+�3F3 , 3F4� energy transfer process.21 A. Rate equations for the Ho3+, Pr3+-codoped ZBLAN system Figure 8 shows a simplified energy level scheme of the Ho3+, Pr3+ system considered for cw diode laser pumping at 650 nm. n1, n2, n3, and n4 are the 5I8, 5I7, 5I6, and 5F5 popu- lations of Ho3+, respectively. For the Pr3+ ion, only the ground state 3H4 �n5� population was considered because the 3F4, 3F3, 3F2, 3H6, and 3H5 excited state populations of Pr3+ are strongly depopulated by fast multiphonon decay to the ground state and consequently they were neglected in the FIG. 7. Measured dependence of �a� 650 nm and �b� 1200 nm emission as a function of the excited Ho3+ ion density. The solid line represents I=aN*b, where b=2 for both ETU processes. FIG. 8. Simplified energy level diagram for the Ho3+, Pr3+ system used for the rate equations modeling. The diagram shows the optical pumping at 650 nm, the 2900 nm laser emission from the 5I6 excited state of Ho3+, and the Ho3+→Pr3+ energy transfer processes. 123111-7 Librantz et al. J. Appl. Phys. 101, 123111 �2007� [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 186.217.234.225 On: Tue, 14 Jan 2014 12:48:27 model. The rate equations comprising the model using the fact that n1+n2+n3+n4=0.04 for a Ho3+ concentration of 4 mol % are dn1 dt = − �14n1 IP h� + n2 �2 + B31 �R3 n3 − WCRn1n4 + WET1n2n5 + WET2n3n5 + WETU1n2 2 + WETU2n3 2 + �41 �R4 n4, �9� dn2 dt = WCRn1n4 + �B32 �R3 + WnR�32��n3 − n2 �2 − WET1n2n5 + �42 �R4 n4 − 2WETU1n2 2, �10� dn3 dt = WCRn1n4 − n3 �3 − WET2n3n5 − 2WETU2n3 2 + ��43 �R4 + WnR�43��n4 + WETU1n2 2, �11� dn4 dt = �14n1 IP h� + WETU2n3 2 − WCRn1n4 − n4 �4 , �12� where IP is the pump intensity given in W cm−2 and h� is the photon energy at 650 nm. �ij represents the luminescence branching ratio and �Ri is the radiative lifetime of 5F5, 5I6 and 5I7 excited states of Ho3+ labeled as i=4, 3, and 2, re- spectively. B. Numerical simulation of the rate equation system Calculations were performed for the singly Ho3+- and the Ho3+, Pr3+-codoped ZBLAN glasses containing 4 mol % Ho3+ and 0.1, 0.2, and 0.3 mol % Pr3+ using a computer program incorporating the Runge-Kutta numerical method. Figure 9 shows the time evolutions of n2�t�, n3�t�, and �n�t�=n3�t�−n2�t�, the population inversion of Ho3+ after switching the pump laser on at t=0 �using a pump rate of 80 s−1 at 650 nm�. Equilibrium in the populations was ob- tained after 10 ms in the Ho3+ �4 mol % �, Pr3+ �0.3 mol % �-doped ZBLAN system, see Fig. 9�b�. At that stage, the value for �n was obtained. On the other hand, equilibrium in the value for �n in the singly Ho3+-doped ZBLAN system is established at a comparatively longer time, see Fig. 9�a�. In addition, n3 n2 and �n 0 for most of the calculation for the singly Ho3+-doped ZBLAN system. Figure 10 shows �n obtained for 2.92 �m laser emis- sion from Ho3+ in both singly Ho3+-doped and Ho3+, Pr3+-codoped ZBLAN systems as a function of the pump rate �RP� for the three Pr3+ concentrations used in this work. The pump rates can be converted to pump intensities IP �W/cm2� using IP= �h�RP� /�abs, where �abs� 5I8→ 5F5�=8.56 �10−20 cm2 at 650 nm. The results presented in Fig. 10 show that 0.3 mol % Pr3+, which produces a strong quench- ing of the 5I7 level decay time, leads to �n 0. The similar Ho3+ �3 mol % �, Pr3+ �0.3 mol % �-codoped ZBLAN glass has been shown experimentally to provide efficient 2.92 �m laser emission.9 Thus we have shown both experimentally and theoretically that the Pr3+ ion is a very effective deacti- vator for the 2.92 �m 5I6→ 5I7 laser transition of Ho3+. It is important to clarify that we have dealt with the total population inversion between the 5I6 and 5I7 multiplet levels without considering Stark splitting. We can, however, sketch out how the 5I7 multiplet splitting will affect the calculated population inversion. The 5I7 multiplet has three main sub- levels localized at 4835, 5049, and 5243 cm−1 �Ref. 15� hav- ing Boltzmann occupation factors f i equal to 0.676, 0.234, and 0.090, respectively. For the purposes of calculating the population inversion, the 5I6 multiplet is located at 8544 cm−1 with f =1. Three main emission lines are ob- served at 2.8 �m �1�, 2.94 �m �2�, and 3.11 �m �3�. The population inversion for each 5I6→ 5I7�i� transition will be given by �ni=n3−n2f i=n2��n3 /n2�− f i�. In the case of Ho3+ �4 mol % �-doped ZBLAN, we have seen that n3 /n2� f3 =0.09, so �ni 0 for all the emission lines involved in the 5I6→ 5I7 transition. A positive but smaller population inver- sion can be obtained for the 2.94 and 3.11 �m emission lines in Ho3+ �4 mol % �, Pr3+ �0.2 mol % �-codoped ZBLAN compared to Ho3+ �4 mol % �, Pr3+ �0.3 mol % �-codoped ZBLAN. V. CONCLUSIONS We have investigated in detail the deactivation of the 5I7 excited state level of Ho3+ in the presence of Pr3+ ions in ZBLAN glasses. Two energy transfer upconversion pro- FIG. 9. Calculated evolution of the excited state populations �in mol %� of Ho3+ obtained by numerical simulation of the rate equations for �a� Ho3+�4 mol % �-doped ZBLAN and �b� Ho3+�4 mol % �, Pr3+�0.3 mol % �-codoped ZBLAN. The simulations were obtained under a continuous pump rate of 80 s−1 at 650 nm. 123111-8 Librantz et al. J. Appl. Phys. 101, 123111 �2007� [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 186.217.234.225 On: Tue, 14 Jan 2014 12:48:27 cesses ETU1 and ETU2 which lead to the excitation of the 5I6 and 5F5 states were shown to occur in singly Ho3+-doped ZBLAN glass. The rate parameters for these ETU processes were determined and it was established that the rate param- eters for ETU2 were higher than those for ETU1. The rate parameter of the CR process involving the excited 5F5 level and the 5I8 ground state of Ho3+ was determined from a best fit to the 655 nm luminescence. With all the relevant energy transfer rate parameters available, we numerically solved the rate equations for the ZBLAN system under cw laser pump- ing at 650 nm. The results established that the Ho3+ �4 mol % �-doped ZBLAN glass that was codoped with 0.3 mol % Pr3+ showed considerable improvement in the value of �n as compared to the corresponding singly Ho3+-doped ZBLAN glass because of strong depopulation of the 5I7 level of Ho3+ by ET1. As a consequence, the doubly doped glass exhibited a maximum population inversion equal to �3.3% of total Ho3+ population for a cw pump rate of 80 s−1. These facts indicate that Ho3+, Pr3+-codoped ZBLAN glass is a promising candidate for high power laser operation at 2.9 �m using diode laser pumping at 650 nm. The effect of 5I7 deactivation by Pr3+ ions on the population inversion of the 5I6→ 5I7 transition in Ho3+, Pr3+-codoped ZBLAN glass is comparable to the gain improvement reported for Er3+, Pr3+-codoped ZBLAN glass. ACKNOWLEDGMENTS The authors thank financial support from FAPESP �Grant Nos.1995/4166-0 and 2000/10986-0�, CNPq, and the Australian Research Council. 1L. D. da Vila, L. Gomes, L. V. G. Tarelho, S. J. L. Ribeiro, and Y. Mes- saddeq, J. Appl. Phys. 95, 5451 �2004�. 2L. D. da Vila, L. Gomes, C. R. Eyzaguirre, E. Rodriguez, C. L. César, and L. C. Barbosa, Opt. Mater. �Amsterdam, Neth.� 27, 1333 �2005�. 3J. H. Song, J. Heo, and S. H. Park, J. Appl. Phys. 97, 083542 �2005�. 4A. F. H. Librantz, L. Gomes, S. J. L. Ribeiro, and Y. Messaddeq, J. Lu- min., http://dx.doi.org/10.1016/j.jlumin.2007.05.010. 5A. F. H. Librantz, L. Gomes, S. J. L. Ribeiro, and Y. Messaddeq, Proc. SPIE 6190, 6190G �2006�. 6N. Karayianis, D. E. Wortman, and H. P. Jenssen, J. Phys. Chem. Solids 37, 675 �1976�. 7F. H. Jagosich, L. Gomes, L. V. G. Tarelho, L. C. Courrol, and I. M. Ranieri, J. Appl. Phys. 91, 624 �2002�. 8S. D. Jackson, Electron. Lett. 39, 772 �2003�. 9S. D. Jackson, Opt. Lett. 29, 334 �2004�. 10M. Pollnau, IEEE J. Quantum Electron. 33, 1982 �1997�. 11S. D. Jackson, T. A. King, and M. Pollnau, Opt. Lett. 24, 1133 �1999�. 12B. Srinivasan, J. Tafoya, and R. K. Jain, Opt. Express 4, U10 �1999�. 13X. Zhu and R. Jain, Opt. Lett. 32, 26 �2007�. 14A. I. Burshtein, JETP Lett. 35, 885 �1972�. 15L. Wetenkamp, G. F. West, and H. Többen, J. Non-Cryst. Solids 140, 25 �1992�. 16A. Braud, S. Girard, J. L. Doualan, M. Thuau, R. Moncorgé, and A. M. Tkachuk, Phys. Rev. B 61, 5280 �2000�. 17R. K. Watts, in Optical Properties of Ions in Solids, Energy Transfer Phenomena, edited by B. Di Bartolo �Plenum, New York, 1975�, pp. 307– 336. 18L. D. da Vila, L. Gomes, L. V. G. Tarelho, S. J. L. Ribeiro, and Y. Mes- saddeq, J. Appl. Phys. 93, 3873 �2003�. 19L. Gomes and F. Luty, Phys. Rev. B 30, 7194 �1984�. 20J. Fernandez, R. Balda, M. L. M. Lacha, A. Oleaga, and J. L. Adam, J. Lumin. 94–95, 325 �2001�. 21P. S. Golding, S. D. Jackson, T. A. King, and M. Pollnau, Phys. Rev. B 62, 856 �2000�. FIG. 10. Calculated population inversion �in mol %� for the laser emission at 2.9 �m obtained for a simulation with continuous laser pumping at 650 nm for �a� Ho3+�4 mol % �-doped ZBLAN and �b� Ho3+�4 mol % �, Pr3+�x mol % �-codoped ZBLAN glasses, where x=0.1, 0.2, and 0.3 mol %. Note that the Ho3+ ion concentration of 1 mol % corresponds to 1.375 �1020 ions cm−3. 123111-9 Librantz et al. J. Appl. Phys. 101, 123111 �2007� [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 186.217.234.225 On: Tue, 14 Jan 2014 12:48:27