Energy level decay and excited state absorption processes in dysprosium-doped fluoride glassLaércio Gomes, André Felipe Henriques Librantz, and Stuart D. Jackson Citation: J. Appl. Phys. 107, 053103 (2010); doi: 10.1063/1.3311561 View online: http://dx.doi.org/10.1063/1.3311561 View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v107/i5 Published by the AIP Publishing LLC. Additional information on J. Appl. Phys.Journal Homepage: http://jap.aip.org/ Journal Information: http://jap.aip.org/about/about_the_journal Top downloads: http://jap.aip.org/features/most_downloaded Information for Authors: http://jap.aip.org/authors

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Energy level decay and excited state absorption processesin dysprosium-doped fluoride glass

Laércio Gomes,1 André Felipe Henriques Librantz,1,2 and Stuart D. Jackson3,a�

1Center for Lasers and Applications, IPEN/CNEN-SP, P.O. Box 11049, São Paulo, SP 05422-970, Brazil2Department of Sciences, UNINOVE, São Paulo, SP 01156-050, Brazil3Institute of Photonics and Optical Science, School of Physics, University of Sydney, Camperdown 2006,Australia

�Received 3 November 2009; accepted 15 January 2010; published online 2 March 2010�

The primary excited state decay processes relating to the 6H13/2→ 6H15/2�3 �m laser transition insingly Dy3+-doped fluoride �ZBLAN� glass have been investigated in detail using time-resolvedfluorescence spectroscopy. Selective laser excitation of the 6F9/2, 6H7/2 energy levels at 1125 nm and6F11/2, 6H9/2 energy levels at 1358 nm established that the energy levels above the 6H11/2 level,excluding the 4F9/2 level, are entirely quenched by multiphonon emission in ZBLAN glass. The6H11/2 and 6H13/2 energy levels emit luminescence with peaks at �1700 and �2880 nm,respectively, but at low quantum �luminescence� efficiencies. The quantum efficiency of the 6H11/2level and 6H13/2 level is �9�10−5 and �1.3�10−2, respectively, for �Dy3+�=0.5 mol % based oncalculations of the radiative lifetimes using the Judd–Ofelt theory. Excited state absorption �ESA�was detected by monitoring the rise time of the 1700 nm luminescence after tuning the probewavelength across the spectral range from 1100 to 1400 nm. As a result of nonradiative decay of thehigher excited states, ESA contributes to the heating of �3 �m fiber lasers based on Dy3+-dopedfluoride glass. For �Dy3+� up to 4 mol %, we found no evidence of energy transfer processesbetween Dy3+ ions that influence the decay characteristics of the 6H11/2 and 6H13/2 energy levels.© 2010 American Institute of Physics. �doi:10.1063/1.3311561�

I. INTRODUCTION

The moderately spaced energy levels of the rare earthions Pr3+, Nd3+, and Dy3+ that exist above the ground state ofeach ion allow the possibility for a number of electron tran-sitions to fluoresce at midinfrared wavelengths after excita-tion with moderate ��10 000 cm−1� photon energies. Themajority of midinfrared laser research has consequently cen-tered on these ions when they are doped into low phononenergy crystals such as LaCl3 �Ref. 1� and KPb2Cl5 �Ref. 2�and low phonon energy glasses, e.g., the chalcogenides.3 Re-cently there have been a number of demonstrations ofDy3+-doped fluoride �ZBLAN� glass fiber lasers operatingcontinuous wave on the quasi-three-level 6H13/2→ 6H15/2�3 �m transition after optical excitation at 1.1 �m �Ref. 4�and 1.3 �m.5 The use of the fiber geometry for the genera-tion of midinfrared laser radiation provides good thermalmanagement and a comparatively lower threshold because ofthe extended longitudinal dimension and small transversecross section relevant to optical fibers.

The 6H13/2→ 6H15/2 transition of Dy3+ is a phonon termi-nated transition that offers broadband fluorescence but it hasbeen shown experimentally, however, that fiber lasers oper-ating on this Dy3+ transition in ZBLAN glass require rela-tively large pump intensities for the creation of a thresholdpopulation inversion. To examine the potential of this transi-tion for the creation of highly efficient 3 �m lasers, detailedspectroscopic studies are required that will reveal the impor-tant energy transfer and energy level decay processes that

relate to the 6H13/2→ 6H15/2 transition. To fulfill this objec-tive, we prepared a number of Dy3+-doped fluorozirconateglasses of varying Dy3+ concentration and measured the lu-minescence decay characteristics after selective energy levelexcitation. The luminescence efficiencies of these levelswere determined when the experimental decay times werecompared with the radiative lifetimes calculated using theJudd–Ofelt theory. Absorption cross sections for pump ex-cited state absorption �ESA� from the 6H11/2 level at�1300 nm have been obtained.

II. EXPERIMENTAL PROCEDURE

The Dy3+-doped fluorozirconate �ZBLAN� glass samplesused for the time-resolved luminescence spectroscopy mea-surements were prepared from ultra-pure fluoride startingmaterials and made with the composition: �100−x��53 ZrF4–20 BaF2–4 LaF3–20 NaF�–x�DyF3� with x=0.5,1, 2, and 4 mol %. The starting powder materials weremelted at 850 °C for 120 min in a Pt–Au crucible. The liq-uids were poured into brass molds and annealed at 260 °Cfor 2 h to remove the mechanical stresses. The samples werecut and polished into 15�10�5 mm3 rectangular prisms.

Absorption spectra in the range of 2000–10000 nm weremeasured using a Fourier transform infrared spectrophotom-eter �Nicolet 6700�. The decay characteristics of the excitedstates of Dy3+ were measured using pulsed 12 mJ 4 ns laserexcitation from a tunable optical parametric oscillator �OPO�pumped by the second harmonic of a Q-switched Nd-YAGlaser �Brilliant B from Quantel�. Tunable laser excitationfrom the OPO was used to excite the 6F9/2, 6H7/2 energya�Electronic mail: s.jackson@usyd.edu.au.

JOURNAL OF APPLIED PHYSICS 107, 053103 �2010�

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levels at 1125 nm and 6F11/2, 6H9/2 energy levels at 1358 nmenergy levels directly; see simplified energy level diagram inFig. 1. The fluorescence spectrum was measured using abox-car integrator in conjunction with a 0.25 m monochro-mator �Kratos� containing a diffraction grating blazed at2600 nm. A Germanium filter was used to filter out the probelight and an infrared detector InSb �J-10D Judson� cooled to77 K was used for detecting the luminescence. The temporalcharacteristics of the luminescence were detected using theInSb infrared photodiode in conjunction with a fast preamp-lifier with a response time of �0.5 �s and analyzed using adigital 200 MHz oscilloscope �Tektronix TDS 410�. All thefluorescence decay characteristics were measured at 300 K.To isolate the luminescence signals, bandpass filters eachwith �80% transmission at 1700 nm or 2850 nm with a halfwidth of 25 nm and an extinction coefficient of �10−5 out-side this band were used.

III. EXPERIMENTAL RESULTS

A. Fluorescence emission from the 6H13/2 level

The fluorescence emission from the 6H13/2 excited stateof Dy3+ was measured for a �Dy3+�=4 mol %; see Fig. 2.The emission cross section across the entire fluorescencespectrum was determined after the emission cross section atthe fluorescence peak �2880 nm� was calculated using

�emis��̄� =�̄4Aij

8�n2c

I��̄��I���d�

, �1�

where �̄=2.88�10−4 cm, Aij =1 /�R=21.36 s−1, n=1.48,

c=2.9979�1010 cm s−1 and I��̄� /�I���d�=3.355�104

cm−1. The calculation gave �emis�2880 nm�=2.98�10−21 cm2.

B. Luminescence decay of the 6H11/2 and 6H13/2 levels

Figures 3 and 4 show the emission decay characteristicsat 1700 and 2860 nm, respectively, for �Dy3+�=0.5 mol %.The measured luminescence decay time of the 6H11/2 levelwas �2=1.25 �s and the calculated radiative lifetime, �R

=13.7 ms giving the luminescence efficiency �l=�i /�R=9�10−5. For comparison, �R=13.5 ms was obtained forZBLA glass.6

Figure 5 shows that the measured decay time of the6H13/2 excited state decreases as a function of �Dy3+�, seeTable I. On the other hand we observed that the 6H11/2 ex-cited state luminescence efficiency and decay time do notdepend on �Dy3+�. We calculated, using Judd–Ofelt theorythat the radiative lifetime, �R, of the 6H13/2 excited state is46.8 ms �which is similar to the 51.2 ms determined forZBLA glass�6 and, with the measured lifetime �1=631 �sfor �Dy3+�=0.5 mol %, �l=1.3%. The multiphonon nonra-diative decay rate �Wnr� from this level was calculated to be1563 s−1 using the relation Wnr= �1 /�1�− �1 /�R� for �Dy3+�=0.5 mol %. In the Judd–Ofelt calculation,7 the spectro-

FIG. 1. �Color online� Simplified energy level diagram of the Dy3+ ionshowing the probe wavelengths used to examine the fluorescence transitionswith peak wavelengths at 1700 and 2880 nm. The spectrum was obtainedusing pulsed laser excitation at 1350 nm �pulse duration of 4 ns and 10 mJmean energy�.

FIG. 2. Measured fluorescence spectrum of the 6H13/2→ 6H15/2 transition.

FIG. 3. �Color online� Measured luminescence decay at 2860 nm measuredafter pulsed laser �4 ns� excitation �E=12 mJ� at 1125 nm inDy3+�0.5 mol %�-doped ZBLAN at T=300 K. The best fit to the lumines-cence decay is represented by a red line �R2=0.987�.

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scopic intensity parameters 2, 4, and 6 were 4.56�10−20, 0.97�10−20, and 2.27�10−20 cm2, respectively forDy3+-doped ZBLAN.8 Note that these values of the intensityparameters are somewhat different from the intensity param-eters determined in a previous study.9 Values of the angulartensor operator ��U����2 used in the Judd–Ofelt calculationwere obtained from the literature10 for the radiative transi-tions of Dy3+ in LaF3 �aquoions� and are listed in Table II.The refractive index n=1.48 for ZBLAN.

The reduction of the 6H13/2 decay time with increased�Dy3+� may indicate though not conclusively energy transferfrom the 6H13/2 level to the OH− radical whose relevant ab-sorption feature is shown in Fig. 6 for Ho3+-doped ZBLAN�Ref. 11� which was fabricated in a similar way to thecurrent samples. The absorption spectrum shown inFig. 6 is similar to the absorption spectrum measuredfor OH− �2.5�1018 cm−3�-doped ZBLAN glass12 andOH−�0.1 mol %�-doped yttrium lithium fluoride �YLF� crys-tal where it was determined that the OH− molecules dissoci-

ate during the crystal growth to produce OmHn complexes.13

The strong overlap between the 6H15/2→ 6H13/2 absorptionband of Dy3+ �solid line� and the OH− radical absorption �redsolid line� is clearly shown in Fig. 6. Using the absorptioncross section �OH�3440 cm−1�=5�10−20 cm2 determinedfrom the data supplied in Ref. 12 and the absorption coeffi-cient =0.0102 cm−1 measured for the OH− band in ourZBLAN samples, we estimate the OH− radical concentrationto be 2�1017 cm−3. The energy transfer process Dy3+

→OH− was also investigated using

� = 1

�1+ Wt�−1

, �2�

which assumes that the transfer mechanism is dominated byexcitation migration through 6H13/2 levels, where �1 in theintrinsic lifetime of the 6H13/2 level and Wt is the transfer rateconstant that is expected to be linearly dependent on �Dy3+�due to energy migration that is involved in the energy trans-fer to OH− in ZBLAN �or Wt=a N, where N= �Dy3+� inmol %�. The best fit to the 6H13/2 level experimental decaytimes is shown as the solid line in Fig. 5, which gave theintrinsic total decay time �1=641 �s and the transfer prob-ability rate a=1.10�102 mol %−1 s−1. This rate of energytransfer is negligible compared to multiphonon decay ratedetermined for the 6H13/2 level.

The nonradiative decay rates �Wnr� determined for the6H11/2 and 6H13/2 excited states were used in the “energy-gap” law, expressed as Wnr=C exp�−�E� in order to deter-mine the constants C �in s−1� and �in cm�. Using the valuesWnr=8�105 s−1 and �E=2351 cm−1 for the 6H11/2 leveland Wnr=1539 s−1 and �E=3520 cm−1 for the 6H13/2 level,the estimated values of the constants are C=2.314�1011 s−1 and =5.349�10−3 cm. Thus the estimated ex-cited state lifetime of the thermally coupled 6H9/2, 6F11/2 and6H7/2, 6F9/2 levels was 100 ns ��E=1879 cm−1� and 9 ns��E=1435 cm−1�, respectively.

TABLE I. Measured decay time and luminescence efficiency of the 6H13/2level of Dy3+ in ZBLAN at T=300 K.

�Dy3+��mol %�

Decay time �2

��s� Luminescence efficiency ��

0.5 631 0.01361 591 0.01272 550 0.01184 508 0.0109

TABLE II. Values of the matrix elements of the unit angular tensor operator��U����2 and radiative decay rates of 6H11/2 and 6H13/2 levels of Dy3+ inZBLAN.

Transition �̄

�nm� ��U�2��2 ��U�4��2 ��U�6��2Aed

�s−1�

6H11/2→ 6H13/2 �4253� 0.2508 0.4990 0.0275 3.86H11/2→ 6H15/2 �1696� 0.0960 0.0346 0.6447 68.26H13/2→ 6H15/2 �2865� 0.2453 0.4136 0.6818 21.4

FIG. 4. �Color online� Measured luminescence transient measured at 1700nm after pulsed laser �4 ns� pump at 1358 nm for Dy:ZBLAN �0.5 mol %�at T=300 K. The best fit to the measurements is represented by a red line�R2=0.99�.

FIG. 5. Measured decay time of the 6H13/2 level �open triangles� as a func-tion of �Dy3+�. The best fit to the decay time using Eq. �2� provided theparameters �1=641 �s and transfer constant a=109.8 �mol %�−1s−1.

053103-3 Gomes, Librantz, and Jackson J. Appl. Phys. 107, 053103 �2010�

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C. Pump excited state absorption from the 6H11/2 level

Up-conversion emission from the 4F9/2, 6F3/2, 6F5/2, and6F7/2 excited levels has been observed in Dy3+-dopedZBLAN fiber lasers pumped with a Nd-YAG laser operatingat �1.3 �m �Ref. 5� or a Yb3+-doped silicate fiber laseroperating at 1.1 �m.4 It has been observed in this work thatthe energy level decay processes above the 6H11/2 level arestrongly quenched by multiphonon emission, however, anexception occurs for the 4F9/2 excited state because it is wellseparated, by �7750 cm−1, from the next lower level. It issuspected that ESA processes responsible for exciting the4F9/2 level have a low efficiency and populate the 4F9/2 levelonly under strong pump conditions5 where the intermediate6F3/2 level has enough population to allow for the absorptionof a third pump photon at �1.3 �m.

In the present investigation no visible emission was ob-served and we could only observe pump ESA, labeled ESA1for 1350 nm pump photons by measuring the change in therise time of the 1700 nm luminescence from the 6H11/2 levelas a function of the laser excitation wavelength. For cwpump excitation at �1300 nm �Ref. 5� ground state absorp-tion �GSA� �6H15/2→ 6F11/2, 6H9/2�, ESA1 �6H11/2→ 6F3/2�,and ESA2 �6H13/2→ 6F7/2� are possible and two photon ab-sorption �TPA� can take place. For cw pump excitation at�1100 nm,4 GSA �6H15/2→ 6F9/2, 6H7/2� and ESA3 �6H13/2→ 6F5/2� are possible and TPA can also take place. If short��4 ns� pulses in the range 1100–1400 nm are used to ex-cite Dy3+-doped ZBLAN, only ESA1 leads to TPA. PumpESA from the 6H13/2 level cannot occur when pumping with4 ns pulses at either 1100 or 1300 nm because the 6H13/2level is populated on a time scale ��1.3 �s� much longerthan the probe pulse width and the 6H13/2 level is left un-populated during the probe pulse.

Figure 4 shows that the luminescence from the 6H11/2level, measured at 1700 nm after laser excitation at 1358 nmfor �Dy3+�=0.5 mol %, exhibits a rise time that can be usedto get the spectral characteristics of ESA1. The strength ofESA1 and its wavelength dependence was obtained by fitting

a function to the 1700 nm luminescence transient that in-cludes a contribution by ESA1 to the total rise time. Ourfitting function is given by

I�t� = I0��exp�− t/�1�� − �1 − fESA�exp�− t/�rise�1��

− fESA exp�− t/�rise�2��� , �3�

where fESA is the factor �or ESA fraction� that accounts forthe rise time increase due to ESA1. �rise�1� is the decay timeconstant due to 6F11/2, 6H9/2→ 6H11/2 nonradiative decay and�rise�2� is due to the sequential nonradiative relaxations 6F3/2→ 6F5/2→ 6F7/2→ 6H5/2→ 6F9/2, 6H7/2→ 6F11/2, 6H9/2 pro-duced by ESA1. The experimental values of �rise�1� and �rise�2�which were equal to 0.7 and 0.98 �s were lengthened by the0.55 �s response time of the InSb detector. Figure 7 showsthe technique used to get the parameter fESA. The fESA pa-rameter was obtained from a best fit to the luminescencetransient measured at 1700 nm using Eq. �3�. The parameterfESA is related to the increase in the rise time of the 1700 nmluminescence and it is obtained by integrating Eq. �3� giving�rise=�rise�1�+ fESA��rise�2�−�rise�1��. Figure 8 shows that themeasured 6H11/2 luminescence decay lengthens when the ex-citation wavelength is tuned within the ESA1 band �at 1302nm� compared to when it is tuned outside the ESA1 band �at1373 nm�.

We have estimated that the value of 6F11/2, 6H9/2 coupledenergy level lifetime to be 100 ns as a result of six phononemission �i.e., N=6�. We postulate that the ESA1 process inour spectroscopic experiment should involve some interme-diate vibronic state �IVS�. The IVS must be reached by theemission of �N−K� phonons, where K�6 so that the IVScan be populated in a time �t=4 ns, i.e., the probe pulseduration. This condition implies that the nonradiative decayrate WnR

�N−K�=2.5�108 s−1. The order of the multiphononemission �N−K� was calculated using the calibrated energy-

FIG. 6. �Color online� Measured absorption spectrum ofDy3+�0.5 mol %�-doped ZBLAN and Ho3+�2 mol %�-doped ZBLANshowing the 6H15/2→ 6H13/2 transition �solid line� and OH− radical �orOmHn� absorption band �red solid line�.

FIG. 7. �Color online� Rise time of the 1700 nm emission using the rela-tionship rise�t�=1− �1− fESA�exp�−t /�rise�1��− fESA exp�−t /�rise�2��, where�rise�1�=0.7 �s, �rise�2�=0.98 �s, and fESA=0.7 for laser excitation at 1353nm. Note that the experimental rise times were lengthened by the 0.55 �sresponse time of the infrared detector. The red solid line exhibits the non-radiative decay �or the rise time of 6H11/2 luminescence� when the ESA1absorption is excited by the laser excitation wavelength that gives �rise�2�.The dashed line in Fig. 5 exhibits the nonradiative decay of 6H9/2, 6F11/2levels �or the rise time of 6H11/2 level� that gives �rise�1�.

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gap law for Dy3+-doped ZBLAN giving �N−K�= �1 /� �ln�WnR

N−K /C�, where and C are the energy-gaplaw constants. Using the local phonon energy �

=331 cm−1 one obtains �N−K�=3.82, which means that fourphonons are emitted before the absorption of a second pumpphoton. One must consider, however, that two phonons areemitted after TPA according to GSA: 6H15/2→ 6F11/2, 6H9/2and ESA1: �6H11/2+2� �→ 6F3/2+2� . Nevertheless, theshape of the ESA1 spectrum from the IVS will be equal tothe spectrum from the equilibrium position of 6H11/2 levelbecause the total energy involved is the same for both ESAprocesses.

Figure 9 shows the pump ESA factor, fESA obtained froma best fit to the 1700 nm luminescence plotted as a functionof the excitation wavelength. It can be observed that the TPA�Fig. 10�a�� follows approximately with GSA,6 see Fig.10�b�. One may obtain the ESA1 spectrum �or S���� from thenormalized TPA and GSA spectra using

S��� =TPA���GSA���

. �4�

The solid line in Fig. 10�c� shows the resultant ESA1 spec-trum using Eq. �4�.

Using the Judd–Ofelt theory the ESA1 cross section wasdetermined. The rate of spontaneous emission from 6F3/2 ex-cited state was calculated using values of ��U����2 obtainedfrom the literature,10,14 where the reduced matrix elementswere first calculated for Dy3+ ions in LaCl3 �aquoions�. AllU��� parameters that were used in the calculation are listed inTables III and IV. The absorption cross section is given by

FIG. 8. �Color online� Measured luminescence transient of the 6H11/2 levelmeasured at 1700 for 1302 nm and 1373 nm laser excitation wavelengths.Pulse energy=10 mJ with a 4 ns pulse duration. T=300 K.

FIG. 9. The fESA parameter determined for laser excitation in the range�1100–1400 nm� for Dy3+�0.5 mol %�-doped ZBLAN. The solid line repre-sents the best fit using three Gaussian functions.

FIG. 10. �a� TPA comprising a best fit to the fESA parameter using threeGaussian functions, �b� GSA measured for Dy3+�0.5 mol %�-doped ZBLANand �c� the generated ESA spectrum obtained using Eq. �4�.

TABLE III. Values of the matrix elements of the unit angular tensor opera-tor ��U����2 and the radiative rates of 6F3/2 level of Dy3+ in ZBLAN. Calcu-lated value of �R was equal to 1.23 ms.

Transition 6F3/2→ �̄

�nm� ��U�2��2 ��U�4��2 ��U�6��2Aed

�s−1�

6F5/2 �12 474� 0.0220 0.0261 0.0 0.03416F7/2 �4470� 0.0133 0.0107 0.0 0.4156H5/2 �3282� 0.1396 0.1344 0.0 11.336H7/2 �2433� 0.2420 0.1184 0.0 44.186F9/2 �2384� 0.0 0.0307 0.0119 2.196F11/2 �1813� 0.0 0.0174 0.0348 8.416H9/2 �1803� 0.0 0.1231 0.3622 83.886H11/2 �1347� 0.0 0.1928 0.0396 59.206H13/2 �1023� 0.0 0.0 0.3943 436.756H15/2 �752� 0.0 0.0 0.0612 170.50

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�i→fabs ��� =

�̄4

8�c

gf

gi�

J�

AJ�ed����� , �5�

where ����=S��� /�S���d� is the lineshape of the ESA1spectrum S���, g=2J+1 �i for the initial and f for the finalstates�, and c the speed of light. The absorption cross sectiondue to ESA1 was calculated to be 8.37�10−20 cm2 using

Eq. �5� and �̄=1337 nm �average excitation wavelength or

centroid�, ���̄�=0.00805 nm−1 and J�AJ�ed=816.9 s−1 �i.e.,

the total radiative decay rate of the 6F3/2 excited state�. TheESA1 spectrum was scaled using this value of the cross sec-tion; see Fig. 10�c�.

We can also estimate the cross-section for ESA2 fromEq. �5� using the calculated value of the total radiative decayrate of the 6F7/2 excited level, J�AJ�

ed=782.5 s−1 �calculated

from Judd–Ofelt theory� and �̄=1335 nm assuming that theshape of ESA2 spectrum is identical to the ESA1 spectrum,

i.e., ���̄�=0.00805 nm−1. This gives ��1335 nm�=4.68�10−20 cm2.

IV. DISCUSSION

We have shown that the decay time of the 6H13/2 level,the upper laser level of the 6H13/2→ 6H15/2 transition, isdominated by multiphonon emission. For comparison, the5I6→ 5I7 transition of Ho3+ at 2889 nm �i.e., �E=3461 cm−1� in ZBLAN, which has an experimental decaytime and calculated radiative lifetime of 3.5 and 5.9 ms, re-spectively, provides a multiphonon decay rate of 116.2 s−1;11

a value which can be used to estimate the electron-phononcoupling factor �S0� for Dy3+. The probability of multiplephonon generation is given by PN

+ �exp�−�2n̄+1�S0�

��S0N /N!��n̄+1�N, where n̄= �exp�� /KT�−1�−1 is the occu-

pation number of the local phonon of average energy � =331 cm−1, n̄ is equal to 0.2402 at T=300 K, and N is theaverage number of phonons created, i.e., N=10.5 for �E=3461 and 3490 cm−1, respectively, for the 5I6

→ 5I7 �Ho3+� and 6H13/2→ 6H15/2 �Dy3+� transitions inZBLAN. Using S0=0.31 for Ho3+-doped ZBLAN, one ob-tains S0=0.401 for Dy3+-doped ZBLAN.

We can now compare our results with previous studies ofDy3+-doped crystals. The decay time of the 6H13/2 level inDy3+:YLF has been calculated to be 3.2 ms using measure-ments of the absorption spectra, the Judd–Ofelt theory, andestimations of the rates of multiphonon relaxation based onwell-known phenomenological expressions.15 The measureddecay time of the 6H13/2 level, however, is as short as305 �s for �Dy3+�=5 at. %.16 In the pioneering study of3 �m emission in Dy3+-doped BaY2F8, it was establishedthat the decay time of the 6H13/2 level of �1.3 ms at 295 Kremains essentially unchanged up to �Dy3+�=10 at. %.17 Thedecay time of the 6H13/2 level in Dy3+-doped BaY2F8 ishighly temperature dependent18 suggesting that it is the emis-sion of phonons and not interactions between Dy3+ ions thatprimarily affects the decay of the 6H13/2 level in Dy3+-dopedcrystals.

We will use a rate equation analysis to describe the cwoperation of Dy3+-doped ZBLAN fiber lasers. Figure 11shows the simplified energy level scheme used to describethe Dy3+-doped ZBLAN laser system for cw laser pumpingof the n4 level �6F11/2, 6H9/2�. n1, n2, n3, n4, n5, n6, n7, and n8

are the populations of the 6H15/2, 6H13/2, 6H11/2, 6F11/2, 6F9/2,6F7/2, 6F5/2, and 6F3/2 energy levels of Dy3+, respectively, andn1+n2+n3+n4+n5+n6+n7+n8=1 and nOH=1. The n4, n5,

TABLE IV. Experimental values of intrinsic ��2, �3� and radiative lifetimes ��R2, �R3�, luminescence branchingratios ��31, �32�, multiphonon decay rates �WnR�21�, WnR�32�� and Wt as a function of �Dy3+� in ZBLAN.WnR�65�, WnR�54�, and WnR�43� were calculated by using the calibrated “energy-gap law” for Dy3+ in ZBLAN�in this work�. Luminescence measurements were made at T=300 K.

Level�energy position�a

RadiativeLifetimeb

Intrinsic totaldecay timeb

BranchingRatioa

WnR�i→ j��s−1� b

6F3/2 �i=8� �13 250 cm−1� ¯ �8=0.3 ns ¯ 6.6�106

6F5/2 �i=7� �12 400 cm−1� ¯ �7=9 ns ¯ 6.6�106

6F7/2 �i=6� �11 300 cm−1� ¯ �6=152 ns ¯ 6.6�106

6H7/2, 6F9/2 �i=5� �9116 cm−1� ¯ �5=6 ns ¯ 1.7�108

6H9/2, 6F11/2 �i=4� �7798 cm−1� ¯ �4=100 ns ¯ 1�107

6H11/2 �i=3� �5897 cm−1� �R3=13.7 ms �3=1.25 �s �expt.� �32=0.052 �31=0.948 8�105 �expt.�6H13/2 �i=2� �3491 cm−1� �R2=46.8 ms �2=641 �s �expt.� �21=1 1539 �expt.�

�Dy3+��mol %�

�2b �expt.���s�

Wt

�s−1� b

0.1 636.5 110.2 632 22.20.3 627.3 34.10.5 618.9 55.71 598.7 110.22 561.7 220.23 529 330.34 500 439.9

aEnergy level position obtained from Ref. 6.bExperimental and calculated values obtained in this work.

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n6, n7, and n8 populations, however, can be considered neg-ligible in ZBLAN. The rate equations for the simplified sys-tem for 1325 nm pumping are

dn1

dt= − RPn1 +

n2

�R2

+ WnR�21�n2 +B31

�R3

n3 + Wtn2, �6�

dn2

dt= − RESA2n2 −

n2

�R2− WnR�21�n2 +

�32

�R3n3

+ WnR�32�n3 − Wtn2, �7�

dn3

dt= RPn1 + RESA2n2 −

n3

�3, �8�

where RP=�14�IP /h�P� is the pump rate �s−1�, IP is the in-tensity of the pump light �W cm−2�, and h�P is the photonenergy of the pump radiation. �ij represents the lumines-cence branching ratio and �Ri

is the radiative lifetime of the6H13/2 and 6H11/2 excited states where i=2 and 3, respec-tively. RESA2=�26�IP /h�P�, where �26=4.68�10−20 cm2.Experimental values of the intrinsic total decay times ��2, �3�and radiative lifetimes ��R2, �R3� and the luminescencebranching ratios ��31, �32�, the multiphonon decay rates�WnR�21�, WnR�32�� and Wt as a function of �Dy3+� inZBLAN are listed in Table IV. �4, �5, and �6 lifetimes werecalculated using the “energy-gap law.”

The calculated evolution of the excited state populations�in mol %� obtained by numerical simulation of the rateequations for �Dy3+�=0.5 mol % using a pumping rate of8500 s−1 �or IP=484 kW cm−2� is shown in Fig. 12�a�,where one can see that equilibrium occurs in a time shorterthan 1 ms. At equilibrium, the populations n2 and n1 were

taken and the population inversion �n=n2−n1 was obtainedfor �Dy3+�=0.5 and 1 mol % as a function of the pump in-tensity at 1325 nm; see Fig. 12�b�, which indicates a thresh-old pump intensity of �98 kW cm−2. Figure 13 shows thepopulation inversion obtained for �Dy3+�=0.5 mol % as afunction of the pump intensity for two cases: �i� one thatincludes ESA2 �red solid line� and �ii� one that has ESA2switched off �black solid line�. One can see that the threshold

FIG. 11. Simplified energy level diagram for Dy3+-doped ZBLAN used forthe rate equation analysis showing how the 6H9/2, 6F11/2 states are populatedby optical pumping at 1300 nm, ESA from the 6H13/2 level, the 2.96 �mlaser transition and the energy transfer process �ET� to the OH− radical. Then4, n5, n6, n7, and n8 populations were not used in the simulation becausethey have short lifetimes �see data of Table IV�.

FIG. 12. Calculated evolution of the excited state populations �in mol %� ofDy3+ obtained by numerical simulation of the rate equations for pumping at1325 nm and the laser emission at 2.9 �m. In �a� �Dy3+�=0.5 mol %, RP

=8500 s−1 �or IP=484 kW cm−2� and the populations and population inver-sion �in mol %� are calculated as a function of time. In �b� the populationinversion is calculated as a function of the pump intensity for �Dy3+�=0.5and 1 mol %.

FIG. 13. �Color online� Calculated population inversion �in mol %� as afunction of the pump intensity for �Dy3+�=0.5 mol % obtained by numeri-cal simulation of the rate equations for pumping at 1325 nm and the laseremission at 2.9 �m using two cases: �i� with ��ESA2� equal to 3.54�10−20 cm2 and ��GSA� equal to 8.1�10−21 cm2 at 1325 nm and �ii���ESA2�=0. One can see the effect of ESA2 absorption in the populationinversion for this system.

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pump intensity necessary to produce zero population inver-sion remains unchanged at 98 kW cm2. In addition, one cansee that ESA2 process introduces a small decrease in thepopulation inversion, which is estimated to be about 6% fora pump intensity of 800 kW cm2.

One must consider, however, the potential attenuation ofthe laser emission at �2.9 �m by the presence of OH− inthe glass that has a maximum absorption coefficient of�0.010 cm−1 at 2907 nm; see the absorption spectrum inFig. 6. As a consequence, the intensity of laser radiationgenerated inside of the fiber will be attenuated by OH− ab-sorption. One can estimate the transmission T of the laserradiation using T= n=0

� Rn+1 exp�−�2n+1��� for a laser cav-ity composed of an end mirror with 100% reflectivity and anoutput mirror with reflectivity R, n is the number of reflec-tions at the output mirror, is the absorption coefficient ofOH−, and � is the optical fiber length. We estimated a trans-mission of 32.5% at 2907 nm for an optical fiber with �=60 cm and R=0.5, similar to the one used in Ref. 5. Usingthis value for the attenuation of the output, we can correctthe previously calculated threshold pump intensity by in-creasing it by a factor of 3.08 �or 1 /T, where T=0.325� giv-ing 301 kW cm−2, which is consistent with the experimentalvalue of �283 kW cm−2.5

V. CONCLUSIONS

It has been determined that the luminescence efficiencyof the 6H13/2→ 6H15/2�3 �m transition of Dy3+-dopedZBLAN glass at T=300 K is 1.3% which is primarily theresult of large rates of multiphonon emission which forcesthe nonradiative decay rate to be 1539 s−1 compared to theradiative decay rate of 72 s−1. We estimated that a compara-tively large local phonon mode coupling factor �S0� relevantto Dy3+ gives rise to the large rates of phonon emission. Weobserved that the decay time of the 6H13/2 level in oursamples has a slight concentration dependence which we at-tribute to migration-assisted energy transfer to OH− radicalswhich are present in the glass. We did not observe energytransfer processes between Dy3+ ions up to �Dy3+�=4 mol %. It was established that pump ESA not the short

decay times of the metastable energy levels has the biggestimpact on the performance of Dy3+-doped ZBLAN fiber la-sers at the previously demonstrated pump wavelengths of1100 and 1300 nm. These results suggest that fiber laseroperation is temperature dependent which may account forlarge difference in performance of Dy3+-doped ZBLAN fiberlasers pumped at either 1100 nm or 1300 nm because 40%more heat is generated at the former pump wavelength.

ACKNOWLEDGMENTS

The authors thank financial support from FAPESP�Grant Nos. 1995/4166-0 and 2000/10986-0�, CNPq, and theAustralian Research Council.

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