Optical Materials 31 (2009) 1636–1639

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Optical Materials

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Energy transfer in crystalline Er3+,Yb3+:Sc2O3

Henning Kühn *, Matthias Fechner, Andreas Kahn, Hanno Scheife, Günter HuberInstitut für Laser-Physik, Universität Hamburg, Luruper Chaussee 149, D-22761 Hamburg, Germany

a r t i c l e i n f o

Article history:Received 3 March 2009Accepted 30 March 2009Available online 9 May 2009

PACS:33.50.�j42.55.Rz42.70.Hj

Keywords:Energy transferLaser materials

0925-3467/$ - see front matter � 2009 Elsevier B.V. Adoi:10.1016/j.optmat.2009.03.014

* Corresponding author.E-mail address: HKuehn@physnet.uni-hamburg.de

a b s t r a c t

The use of Yb3+ as a sensitizer for Er3+ doped laser materials is a common technique because of the highYb3+ absorption cross sections. Energy transfer processes from Yb3+ to Er3+ in Sc2O3 are studied by twodifferent methods. Transfer parameters describing the interactions between Er3+ and Yb3+ ions areobtained on the one hand from the ratio of emitted photons around 1.55 lm by Er3+ ions and around1 lm by Yb3+ ions at cw excitation of Yb3+, on the other hand by lifetime measurements of Yb3+ ionsin the codoped samples. Laser experiments are performed to study the suitability of Er3+,Yb3+:Sc2O3 asa laser material. Comparisons with energy transfer in Er3+,Yb3+:glass are made.

� 2009 Elsevier B.V. All rights reserved.

1. Introduction Yb3+ excitation into the 2F5/2 level is described by the following rate

The Er3+ laser at a wavelength around 1.55 lm [1] plays animportant role in telecommunication applications as well as lidarmeasurements [2]. Yb3+-sensitization of Er3+ is a common tech-nique used in diode pumped glass lasers, especially fiber lasers[3]. Due to the low absorption cross sections of Er3+ around975 nm it is difficult to excite a sufficient amount of Er3+ ions forreaching the laser threshold. Therefore the laser material is cod-oped with Yb3+ which has a significantly higher absorption crosssection than Er3+ at 975 nm. The excited Yb3+ ions transfer theenergy nonradiatively to the Er3+ ions. Due to the energy matchbetween the 4I11/2 level of Er3+ and the 2F5/2 level of Yb3+ the energytransfer is resonant.

Er3+ doped sesquioxides have significant advantages comparedto Er3+:glass. They have a higher thermal conductivity, a higherhardness as well as higher peak emission cross sections and nar-rower emission peaks due to the crystallinity of the material. Todescribe the dynamical processes in the system and to comparethe transfer efficiency from Yb3+ to Er3+ with efficiencies measuredin other host materials, it is important to determine transferparameters, describing the coupling between Yb3+ and Er3+ ions.

2. Rate equation model

Fig. 1 shows the energy level diagram of the relevant levels ofEr3+,Yb3+:Sc2O3. The dynamical behaviour of the system under

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(H. Kühn).

equations:

dN2F5=2

dt¼WpN2F7=2

�N2F5=2

sYb� kyeN2F5=2

N4 I15=2þ keyN4 I11=2

N2F7=2

dN4 I11=2

dt¼ �

N4I11=2

s4 I11=2

þ kyeN2F5=2N4 I15=2

� keyN4 I11=2N2F7=2

dN4 I13=2

dt¼

gN4 I11=2

s4 I11=2

�N4 I13=2

s4I13=2

NYb ¼ N2F7=2þ N2F5=2

NEr ¼ N4 I15=2þ N4 I13=2

þ N4I11=2ð1Þ

Upconversion and excited state absorption processes have beenneglected because of the low excitation intensity in the performedexperiments.

N2F5=2, N2F7=2

, N4 I11=2, N4 I13=2

and N4 I15=2are the densities of the Yb3+,

Er3+ ions, respectively, in the corresponding levels. NYb and NEr arethe total densities of the dopant ions. The symbols sYb, s4 I11=2

ands4 I13=2

are the fluorescence lifetimes of the corresponding levelsmeasured in samples without codoping, g is the branching ratiofor the decay of the Er3+ ions from the 4I11/2 level into the 4I13/2 le-vel including radiative and nonradiative decays and Wp is theabsorption rate of the Yb3+ ions (absorbed photons per secondand per Yb3+ ion). The parameters kye and key describe the transferfrom Yb3+ to Er3+ and from Er3+ to Yb3+, respectively.

For steady state excitation the time derivatives in equation sys-tem (1) become zero. Hence, equation system (1) can be solved.The fluorescence lifetimes and the branching ratio have been mea-sured and the absorption rate is known from the intensity of the

Fig. 2. Emission cross sections of Er3+:Sc2O3 calculated by the reciprocity methodfrom an absorption spectrum.

Fig. 3. Spectrum of an Er3+,Yb3+:Sc2O3 sample.

Fig. 1. Energy level diagram of Er3+,Yb3+:Sc2O3.

H. Kühn et al. / Optical Materials 31 (2009) 1636–1639 1637

excitation laser and the absorption cross sections of Yb3+:Sc2O3.Therefore the solutions of equation system (1) are the densitiesof the ions in the excited states as functions of the unknownparameters kye and key.

The absorption rate of the excitation photons by the Yb3+ ions isgiven by WpN2F7=2

. If nonradiative decays of the 4I13/2(Er3+) level canbe neglected, the emission rate from the 4I13/2 level is given bygN4 I11=2

=s4 I11=2. To verify this assumption, the emission cross sec-

tions around 1.55 lm (Fig. 2) have been calculated by the reciproc-ity method from an absorption spectrum of an Er3+:Sc2O3 crystal.

From the emission cross sections a radiative lifetime of 6.1 msof the 4I13/2 level has been calculated using the Füchtbauer–Laden-burg equation. A comparison to the measured fluorescence lifetimeof 5.7 ms results in a nonradiative decay rate that is negligiblecompared to the radiative decay rate. From the ratio of the emis-sion and the absorption rate a conversion efficiency

� ¼gN4I11=2

s4 I11=2WpN2F7=2

ð2Þ

can be defined, describing the fraction of the Yb3+ excitation ratetransformed into the Er3+ emission rate around 1.55 lm.

The transfer parameters kye and key are proportional to the over-lap between the emission and absorption spectra of Yb3+ and Er3+

in Sc2O3. Because of that proportionality, the following relationholds:

a :¼ key

kye¼RrEr

emðkÞrYbabsðkÞdkR

rYbemðkÞrEr

absðkÞdkð3Þ

From emission and absorption spectra of Yb3+ and Er3+ in Sc2O3

[4,5] the proportionality factor a between key and kye has beendetermined to be 0.56.

N4 I11=2and N2F7=2

as solutions of equation system (1) can besubstituted into Eq. (2). The assumption of low excitation densities(NYb � N2F5=2

, NEr � ðN4F11=2þ N4F13=2

Þ) is applied here. With a mea-

sured �, the remaining unknown parameters are kye and key. UsingEq. (3) to eliminate key leads after some algebraic manipulations to

kye ¼�

gNErsYb � �NErsYb � �aNYbs4 I11=2

ð4Þ

3. Experimental results and discussion

3.1. Determination of kye by continuous wave excitation

Codoped crystalline Sc2O3 films with different Er3+,Yb3+ concen-trations have been grown on a-Al2O3 substrates by Pulsed LaserDeposition (PLD) [6,7]. The thicknesses of the films were 500–1000 nm. To determine the energy transfer parameters kye thefilms have been excited by a cw Ti:Al2O3 laser at 940 nm. Er3+

has negligible absorption at that wavelength so that only theYb3+ ions were absorbing the light. The emission spectra of thesamples were measured in a wavelength interval from 950 nm to1680 nm, using a Ge-detector (Fig. 3) [8]. This interval containsthe emissions from the 2F5/2 level of Yb3+ and the 4I11/2 and 4I13/2

levels of Er3+. The emission from the 2F5/2 level of Yb3+ and the4I11/2 level of Er3+ around 975 nm could not be clearly separatedbecause of the spectral overlap of those energy levels. The emissionspectra I(k) were converted from energy per wavelength interval tophotons per wavelength interval. The ratio � between the numberof photons emitted around 1.55 lm to the number of absorbedphotons was calculated from the emission spectra:

� ¼R 1650 nm

1400 nm IðkÞdkR 1650 nm950 nm IðkÞdk

ð5Þ

This was done under the assumptions that nonradiative decayof both ions into the ground state is negligible and upconversionprocesses could be neglected due to the low excitation density,so that for every absorbed photon, one photon was emitted inthe wavelength interval between 950 nm and 1650 nm.

From the measured � for the different samples as well as theknown parameters: sYb = 750 ls, s4 I11=2

¼360 ls [8], a = 0.56 andg = 0.99 for Er3+,Yb3+:Sc2O3, Eq. (4) has been used to calculate kye.g has been determined by the ratio of the fluorescences from the4I11/2 and 4I13/2 levels of Er3+:Sc2O3, while s4I11=2

has been measuredin this work. The results for kye are shown in Table 1. The values forthe Er3+(0.5%),Yb3+(5%):Sc2O3 and the Er3+(1%),Yb3+(10%):Sc2O3

sample are probably too small due to the high Er3+ concentrationsthat increase the probability for upconversion processes. The use ofEq. (4) for kye results in a value that is too low because the upcon-version processes are not included in the rate equation model. Themeasured transfer efficiency and therefore the calculated kye forthe Er3+(0.23%),Yb3+(0.4%):Sc2O3 crystal is probably too high

Table 1Determined values for � and kye by the cw excitation method. In lines 3 and 4, thevalues in parentheses are probably too low because of upconversion. The last linedenotes the Er3+(0.23%),Yb3+(0.4%):Sc2O3 laser crystal mentioned in Fig. 5, all otherlines denote values from thin films. For the crystal, reabsorption affects the accuracy.

Er3+,Yb3+:Sc2O3

Er3+- Yb3+- � kye (10�18 cm3/s)

Concentration (%)

0.1 1.0 0.138 11.260.3 3.0 0.194 9.150.5 5.0 0.182 (4.43)1.0 10.0 0.224 (5.19)0.3 0.5 0.331 8.510.3 1.0 0.300 9.370.3 2.0 0.255 11.990.5 0.5 0.480 9.921.0 0.5 0.634 9.170.23 0.4 0.462 (25.19)

Table 2Determined values for kye by lifetime measurements of Yb3+. The values in the lastline belong to the Er3+(0.23%),Yb3+(0.4%):Sc2O3 laser crystal (compare Fig. 5).

Er3+,Yb3+:Sc2O3

Er3+- Yb3+- sYbcd(ls) kye (10�18 cm3/s)

Concentration (%)

0.0 3.0 7500.3 3.0 413 10.830.3 2.0 410 11.030.3 1.0 382 12.770.5 5.0 326 10.371.0 10.0 232 8.900.23 0.4 422 13.42

1638 H. Kühn et al. / Optical Materials 31 (2009) 1636–1639

because of reabsorption. Emitted light at wavelengths around 1 lmcan be reabsorbed by the Er3+ or Yb3+ ions, that can decay into the4I13/2 level and emit photons around 1.5 lm or can transfer energyto the Er3+ ions, respectively. Reabsorption is suppressed in thethin films because of their low thickness. Discarding these values,the values of kye are approximately independent of the Er3+,Yb3+

concentrations.

3.2. Determination of kye by lifetime measurements

To substantiate the correctness of the obtained parameters, asecond method for the estimation of kye has been used. The Yb3+

ions have been excited by a pulsed optical parametrical oscillatorat 940 nm. The fluorescence decay curves of Yb3+ have been mea-sured at 1095 nm. The Er3+ ions have no fluorescence at that wave-length. From the decay curves the fluorescence lifetimes of Yb3+ inthe codoped samples have been calculated (Fig. 4, Table 2). The fastdecay during the first microseconds corresponds to the pulse of theoptical parametrical oscillator that could not be filtered completelydue to the small signal intensity of the thin films. For the fit onlythe first 200 ls after the excitation pulse have been used to ex-clude backtransfer from Er3+. Shortly after the excitation pulsethe dynamics of the Yb3+ excitation density is given by:

dN2F5=2

dt¼ �

N2F5=2

sYb� kyeN2F5=2

NEr ð6Þ

Fig. 4. Fluorescence decay curves of Er3+,Yb3+:Sc2O3 samples, in the same order ofappearance as in Table 2. The decay curve of the Er3+(0.23%),Yb3+(0.4%):Sc2O3 lasercrystal (last line in Table 2) cannot be shown because the lifetime was obtained by alinear extrapolation using the pinhole method [9].

From the measured lifetimes sYbcdin the codoped system, the

transfer parameters kye can be determined:

kye ¼1

NEr

1sYbcd

� 1sYb

� �ð7Þ

The results are shown in Table 2. Therein the values for thesamples that could not be obtained precisely due to the low dopantconcentrations have not been listed. The values are in agreementfor the ones of Table 1 obtained by the cw excitation method.The results are unaffected by upconversion processes in the Er3+

ions because they were obtained by the measured lifetimes ofthe Yb3+ ions.

4. Laser experiments

To analyze the effects of the measured transfer efficiency (Table1), laser experiments with a codoped Er3+(0.23%),Yb3+(0.4%):Sc2O3

0

Fig. 5. Power characteristics of (a) an Er3+(0.2%):Sc2O3 and (b) anEr3+(0.23%),Yb3+(0.4%):Sc2O3 laser crystal.

H. Kühn et al. / Optical Materials 31 (2009) 1636–1639 1639

crystal and an Er3+(0.2%):Sc2O3 crystal grown by the heat exchangemethod [5] have been performed in an almost concentrical resona-tor with radii of incoupling and outcoupling mirrors of 50 mm. Thelength of the crystal was 4.0 mm. An Ti:Al2O3 cw laser at 975 nmhas been used as a pump source. The incoupling mirror was highlytransmittive for the pump wavelength and highly reflective for thelaser wavelength. The outcoupling mirrors were highly reflectivefor the pump wavelength with different reflectivities for the laserwavelength of 1580 nm. The pump laser beam has been focussedby a f = 50 mm lens into the crystal. For the Er3+:Sc2O3 laser crystala maximum slope efficiency of gs = 5.9% and a maximum outputpower of 33.1 mW has been published recently [10]. It was the firstknown laser action around 1.55 lm of Er3+ doped crystalline Sc2O3.The reason for the low efficiency is excited state absorption at thepump wavelength [4]. The Er3+,Yb3+:Sc2O3 crystal investigated inthis work with Yb3+ ? Er3+ transfer pumping had a lower slopeefficiency of gs = 2.0% and a lower maximum output power of20.6 mW (Fig. 5). The reason for the lower output of the codopedlaser crystal is the low transfer efficiency (Table 2). Another reasonmight be the relatively long lifetime s4 I11=2

¼360 ls of the 4I11/2

level which causes backtransfer from Er3+ to Yb3+ and therefore re-sults in a relatively small � (Table 1). The pump absorption in thecodoped crystal was higher than in the Er3+-doped crystal due tothe high absorption cross section of the Yb3+ ions.

5. Conclusion

By the cw excitation method an energy transfer factorkye = (9.91 ± 1.26) � 10�18 cm3/s for Er3+,Yb3+:Sc2O3 has been ob-tained. The method based on the measurement of the Yb3+ life-times results in kye = (10.78 ± 1.39) � 10�18 cm3/s. The goodmatch between the transfer parameters obtained by the two differ-ent methods shows the reliability of the calculated values. The va-lue for kye is very small compared to kye = 7.1 � 10�15 cm3/s forEr3+,Yb3+:glass (Kigre QX/Er) [11] and kye � 1 � 10�16 cm3/s forEr3+,Yb3+ doped fluoride phosphate glass [12].

The low transfer efficiency is in good agreement with the lowlaser performance of the Er3+,Yb3+:Sc2O3 crystal compared to Er3+,-Yb3+:glass. Kim et al. have achieved a slope efficiency of 44% inEr3+,Yb3+ doped phosphosilicate glass [13].

The low transfer rate from Yb3+ to Er3+ due to the small value ofkye makes the pumping process of Er3+ ions by energy transfer fromexcited Yb3+ ions very inefficient in Sc2O3. Nevertheless, Er3+ dopedSc2O3 is a promising laser material for inband pumping directlyinto the 4I13/2 level [14].

Acknowledgement

We acknowledge the support of the European Commissionwithin the STREP project PI-OXIDE (017 501).

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