Solid State Communications 149 (2009) 1029–1032

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Solid State Communications

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Enhanced electronic transition probabilities and line intensities of Er+3 ion in a(W, La)-tellurite glass as revealed from Judd–Ofelt analysisArnab Ghosh, Radhaballabh Debnath ∗Central Glass and Ceramic Research Institute, 196, Raja S. C. Mullick Road, Kolkata-700 032, India

a r t i c l e i n f o

Article history:Received 9 January 2009Received in revised form31 March 2009Accepted 3 April 2009 by P. ShengAvailable online 8 April 2009

PACS:78.66.Jg78.20.Ci

Keywords:A. (W, La)-tellurite glass:Er+3A. Superior photonic materialD. Judd–Ofelt analysisE. Enhanced oscillator strength

a b s t r a c t

A series of tellurite glasses containing dispersed Er2WO6 nanocrystals of different concentration wasprepared, and the optical properties of the best luminescent sample (1 g mol% of Er2O3) were inves-tigated by Judd–Ofelt theory. The intensity parameters Ω2(= 8.410 × 10−20 cm2), Ω4(= 4.833 ×10−20 cm2), Ω6(= 2.027 × 10−20 cm2) of the Er+3 ion in the glass were determined and thenused to calculate parameters such as the radiative transition probabilities (Ar ), radiative life-times(τf ), fluorescence branching ratios (βc ) and the integrated emission cross-section (Σσ ) of differenttransitions. The experimental optical constant and the calculated oscillator strength values (P) sug-gest that the Er+3 ions in the glass can most effectively be excited by 4I15/2→4 F7/2 (489 nm) and4I15/2→2 H11/2 (522 nm), 4I15/2→4 F9/2 (653 nm) and 4I15/2→4 I13/2 (1533 nm) transitions whilethe spontaneous emission rate (Ar ) values show that strong visible emissions should occur respec-tively through (4F9/2→4 I15/2) and (4S3/2→4 I15/2) transitions and strong NIR emissions through(4I13/2→4 I15/2), (4S3/2→4 I11/2), (4F9/2→4 I13/2), (4I11/2→4 I15/2), (4S3/2→4 I13/2) transitions. The spec-troscopic parameters show that the glass is a superior photonic material compared to other known Er+3doped glass and crystals.

© 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Rare earth ion activated glasses and crystals are vital com-ponents of present-day optics and opto-electronics [1–22]. Theirpotential applications in solid state lasers [1–3,10,21], optical com-munication [5,10], energy up conversion [7,8,11–15], anti-Stokesluminescence cooling [4] Quantum informatics [18], etc. are wellknown. However, to obtain an appropriate material for practicalapplications, basic studies on various factors, namely crystal fieldstrength of the host, its phonon structure, optimum concentrationof the activator, energy transfer processes, the excited state dy-namics, etc., are very important. Apart from the well-known effectof crystal field of the host on an incorporated ion, a host with lowphonon energy can considerably reduce the nonradiative energyloss of the excited ions through multi-phonon relaxation (MPR).Heavy metal fluoride glasses/crystals have very low phonon ener-gies, so the spectroscopic properties of different rare earth ions inthese hosts have been extensively studied in the last decade. How-ever, because of low thermal stability and low chemical durability,fluoride glasses are no longer considered as the most desired host.On the contrary, an oxide glass with low phonon energy seems

∗ Corresponding author. Tel.: +91 03324838082; fax: +91 03324730957.E-mail address: debnath@cgcri.res.in (R. Debnath).

0038-1098/$ – see front matter© 2009 Elsevier Ltd. All rights reserved.doi:10.1016/j.ssc.2009.04.002

to be the right choice. Amongst the various oxide glasses, tellu-rite glasses have considerably low phonon energy, alongwith theirhigh refractive index and greater power to dissolve high concentra-tion of rare earth ions. So both theoretical and experimental studieson the optical properties of rare earth ions in tellurite glasses havebecome a subject of interest in recent years.In the present work we have synthesized a series of (W, La)-

tellurite glasses containing dispersed Er2WO6 nanocrystals [23]of different concentration. In the Er2WO6 crystal, each tungstenion in the structure has six oxygens forming an octahedron, thecorners of which are shared by Er+3 ions. In this way Er+3 ions arefound to have two types of eightfold oxygen coordination [24]. Wewere interested inmaking a theoretical study on the spectroscopicproperties of Er+3 ions in the glass with the following objectives:(1) to see the crystal field effect on the optical properties of Er+3;and (2) to present a model Judd–Ofelt calculation with referenceto the fact that many of the Judd–Ofelt analyses of rare earth ionsfound in literature are not rigorous and very often are erroneous,particularly in terms of use of refractive index of the host anddetermining the integrated absorption value of the activator ionunder the band concerned.

2. Materials and methods

(W, La)-tellurite glasses of different composition (mol%): (80 to90)TeO2, [(10 to 5)−x]BaO, 2x[PbF2+WO3], (5−y)La2O3, yEr2O3,

1030 A. Ghosh, R. Debnath / Solid State Communications 149 (2009) 1029–1032

100

120

547 nm

80

60

40

0.2 0.4 0.6 0.8 1.0 1.2 1.40.0

Er2O3 Concentration (mol%)

1.6

140

20

Em

issi

on In

tens

ity (

a.u)

Fig. 1. Plot of 548 nm (4S3/2→4 I15/2) green luminescence peak intensity of Er+3in the glasses of different Er2WO6 concentration vs. Er2O3 concentrations.

0 < y < x ≤ 5, were melted at 700–750 C in an electricalfurnace using a platinum crucible. All the chemicals used were ofAR grade (Sigma–Aldrich). The molten glass in each case was castand then annealed for 12 h at 300 C in an annealing furnace. Theglass samples were then allowed to generate Er2WO6 nanocrystalsin the matrix [23] by ageing for a week at ambient temperature.As expected, all the samples were optically transparent afterthe growth of the nanocrystals. The polished samples were thenchecked for optical homogeneity and a sample of glass (averagethickness d = 1.15 mm) containing 1 g mol% of Er2O3 andshowing the best optical luminescence properties was chosen forthe present study. A sample of base glass of good optical qualityand of nearly similar average thickness (d = 1.15 mm) was alsoprepared, and its absorption spectrumwas recorded to subtract thecontribution of the base glass from the Er+3-glass absorption.The density of the glass was measured by the method of

Archimedes principle (D = 5.36 g/cc). The refractive indexof the glass as a function of wavelength of light was measuredusing an UVISEL ellipsometer (HORIBA JOBIN YVON, Model HR460 FUV AGAS). The absorption spectra were recorded at 303 Kin a UV–VIS–NIR absorption spectrophotometer (Shimadzu, Japan;model: 10001).To sort out the best luminescent glass, quantitative lumines-

cence spectra of the glasses of different Er2WO6 concentrationswere recorded at room temperature in a Perkin Elmer LS55 Spec-trofluorimeter using the front surface illumination technique, tak-ing each time a fixed quantity of the powdered glass in a grooveof definite volume on a brass plate and keeping the emission andexcitation slits as well as the lamp condition the same. A plot ofthe 548 nm (4S3/2→4 I15/2) green luminescence peak intensity ofEr+3 in the glasses of different Er+3 concentration vs. Er+3 concen-trations is shown in Fig. 1. The plot clearly shows that the glasscontaining 1 mol% of Er+3 ions is the best luminescent glass.

3. Theory and estimation of different spectroscopic parametersof the Er+3 ions in the glass

To estimate the crystal field strength surrounding the Er+3 ionsof the glass we have used Judd–Ofelt theory. In 1962, Judd [25]and Ofelt [26], working independently, developed the theory ofelectronic transition line intensities of Ln+3 ions in crystals, whichis very elegant and universal in estimating the optical and laserproperties of Ln+3 ions in crystals and glasses. According to theJudd–Ofelt theory [25,26], the electric and magnetic dipole line

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

Opt

ical

Den

sity

Wavelength [nm]

1.8

0.0600 800 1000 1200 1400 1600

Fig. 2. Base glass corrected absorption spectrum of Er+3 in the tungstate telluriteglass (___) vis-à-vis that of the base glass (. . .). The sample thickness d ∼ 1.15 mmin both cases.

strength of an electronic transition from an initial (S, L)J state tothe final (S ′, L′)J ′ state is given respectively by the expressions

Sed(J, J ′) = ΣΩtt=2,4,6

|〈(S, L)J‖U t‖(S ′, L′)J ′〉|2 (1)

Smd(J, J ′) = (eh/4πmc)2|〈(S, L)J‖L+ 2S‖(S ′, L′)J ′〉|2 (2)

where e = electronic charge, h = Planck’s constant, c = speedof light, m = mass of electron, 〈(S, L)J‖U t‖(S ′, L′)J ′〉 is thereduced matrix element of the irreducible tensor operator ofrank t calculated in the intermediate coupling approximation anddepends only on the Ln+3 ion concerned. The values of the squareof the reduced matrix elements for various transitions of differentLn+3 ions have already been calculated by Carnall et al. [27] andKaminskii [28], and are available in literature. Ωt (t = 2, 4, 6) arethe three intensity parameters called the Judd–Ofelt parametersarising from the static crystal field. The value of magnetic dipoleline strength (Smd) does not depend on the host material and it isan exclusive property of the rare earth ion itself. The probabilitiesof magnetic dipole transitions are generally lower than those ofelectric dipole transitions. The magnetic dipole line strength (Smd)of a transition is related to the magnetic dipole oscillator strength(Fmd) by the equation

Fmd = [8π2mc/3h(2J + 1)λmax]Smd. (3)

The Fmd values of different transitions of a series of Ln+3 ionshave also been calculated by Carnall et al. [28]. The experimentalintegrated absorption of a transition of a Ln+3 ion is related to theelectric dipole line strengths Sed(J → J ′) of the transition by theexpression

Smeased (J → J ′) = 9n/(n2 + 2)2[3ch(2J + 1)2 · 303/8π3e2ρλmaxd

×

∫J→J ′OD(λ)dλ− nSmd

](4)

where Smeased (J → J ′) is themeasured electric dipole line strength, nis the refractive index of the host, λmax is the mean wavelength ofthe absorption band, d is the thickness of the sample under study,ρ is the concentration of lanthanide ions (ions/cm3) in the host,and

∫J→J ′ OD(λ)dλ represents the experimental integrated optical

density in thewavelength range of the band,which can be obtainedby calculating the total area under the band.The base glass corrected absorption spectrumof Er+3 ions in the

glass along with that of the base glass is given in Fig. 2. To calculatethe Judd–Ofelt intensity parameters of the Er+3 ions of the glass

A. Ghosh, R. Debnath / Solid State Communications 149 (2009) 1029–1032 1031

Table 1Measured and calculated values of electric dipole line strength, magnetic dipole line strength of different transitions and the three Judd–Ofelt parameters of Er+3 ions in theglass.

Absorption λmax (nm) Smeased (×10−20 cm2) Smd (×10−20 cm2) Scal(×10−20 cm2) 1Sed ∆S2ed4I15/2→4 I13/2 1533 3.67 0.38 3.63 0.04 0.00164I15/2→4 I11/2 976 1.35 1.04 0.31 0.09614I15/2→4 I9/2 800 0.95 0.86 0.09 0.00814I15/2→4 F9/2 653 3.60 3.52 0.08 0.00644I15/2→4 S3/2 546 0.57 0.45 0.12 0.01444I15/2→2 H11/2 522 8.16 8.17 −0.01 0.00014I15/2→4 F7/2 489 1.60 1.98 −0.38 0.1444

Ω2 = 8.410× 10−20 cm2 ,Ω4 = 4.833× 10−20 cm2 ,Ω6 = 2.027× 10−20 cm2 .*rms−1Sed = 0.26× 10−20 cm2 .

Table 2Measured and calculated oscillator strength of different transitions of Er+3 in the glass.

Absorption λmax (nm) Pmeas (×10−6) Ped (×10−6) Pmd (×10−6) Pcal (×10−6) 1P 1P2

4I15/2→4 I13/2 1533 3.10 2.80 0.30 3.07 0.03 0.00094I15/2→4 I11/2 976 1.64 1.26 0.38 0.14444I15/2→4 I9/2 800 1.35 1.22 0.13 0.01694I15/2→4 F9/2 653 6.35 6.21 0.14 0.01964I15/2→4 S3/2 546 1.21 0.96 0.25 0.06254I15/2→2 H11/2 522 18.20 18.22 −0.02 0.00044I15/2→4 F7/2 489 3.82 4.73 −0.91 0.8281

rms−1P = 0.52× 10−6 .

2.0

1.9

1.8

1.7

600400200 800 1000 1200 1400 1600 1800

Wavelength [nm]

0 2000

2.1

Ref

ract

ive

inde

x

1.6

Fig. 3. Refractive index spectrum of the glass as a function of wavelength.

we have first determined the measured Smeased of all the strongabsorption bands of Er+3 with the help of expression (4) by usingtheir base glass corrected integrated optical density values andthe refractive index of the glass at the related band’s wavelength.The refractive index profile of the glass is given in Fig. 3. Althoughmost of the transitions are electric dipole in nature, in the case ofa transition like 4I15/2→4 I13/2 the contribution of magnetic dipoletransitions to the total transition probability is rather high. So wehave included the magnetic dipole contribution in the expressionwhile calculating the line strength of the 4I15/2→4 I13/2 transition.The Smeased values of different transitions are given in Table 1.The three intensity parameters Ω2, Ω4,Ω6, respectively, for

t = 2, 4 and 6, of the Er+3 ions in the glasswere calculated from themeasured electric dipole line strengths Smeased (J → J ′) of differenttransitions, utilizing relation (1) and solving the equations bya least square fitting method. The values of the squares of thereduced matrix elements for the transitions were taken fromKaminskii [28]. The best-fitted values obtained areΩ2 = 8.410×10−20 cm2,Ω4 = 4.833×10−20 cm2, andΩ6 = 2.027×10−20 cm2,respectively.The measured electric dipole line strength of a particular

transition of frequency ν can also be used to obtain the measured

oscillator strength, (P)meas, of the transition using the relation

Pmeas(aJ; bJ ′) = 8π2mν/3h(2J + 1)[(n2 + 2)2/9nSed + nSmd].(5)

The value of nSmd in the expression may be ≥0 depending onthe magnetic dipole contribution to the particular transition.The measured oscillator strength (Pmeas) values determined fordifferent transitions of Er+3 ions in the glass are given in Table 2.Using the best fit values of the three Judd–Ofelt parameters of Er+3ions in the glass, it is also possible to calculate the theoretical valuesof the electric dipole line strengths (Sed) of different transitions(Table 1) with the help of relation (1). In these calculations also,we used the values of squares of the reduced matrix elements|〈(S, L)J‖U t‖(S ′, L′)J ′〉|2 of the different transitions of Er+3 ionfrom Kaminskii [28]. Theoretical total oscillator strengths Pcal fordifferent transitions can be obtained by using the calculated valuesof the electric dipole line strengths (Sed) and relation (5). These arealso shown in Table 2.To check the reliability of the data, the root mean square value

(rms − 1Sed) of the deviations between the measured and thecalculated values of electric dipole line strengths, and the same(rms − 1P) of the deviations between the measured and thecalculated values of total oscillator strengths were determinedwith the help of Eqs. (6) and (7):

rms−1Sed = [Σ(Smeased − Scaled )

2/(p− q)]1/2 (6)

rms−1P = [Σ(Pmeas − Pcal)2/(p− q)]1/2. (7)

Here p denotes the number of absorption transitions consideredand q the total number of parameters used. The values of rms −1Sed and of rms−1P obtained are 0.26× 10−20 cm2 and 0.52×10−6, respectively; the results demonstrate good reliability of thedata.Using the Ωt values, various important radiative properties

of a radiative transition, such as spontaneous emission rate (Ar ),branching ratios (βc), lifetime of the radiative transition (τf ),and the total emission cross-section [Σσ(J → J ′)], were alsocalculated on the basis of Judd–Ofelt theory by using the followingequations:

Ar(J → J ′) = 64π4e2/3h(2J + 1)(λmax)3

×[n(n2 + 2)2/9Sed + n3Smd] (8)

1032 A. Ghosh, R. Debnath / Solid State Communications 149 (2009) 1029–1032

Table 3The parameters of different radiative transitions of Er+3 in the glass.

Radiative transitions λmax (nm) Ar (s−1) Ared (s−1) Armd (s−1) βc τf (s) Σσ (10−18 cm)4I13/2→4 I15/2 1533 333.21 300.51 32.70 1.000 3.00× 10−3 3.144I11/2→4 I13/2 2686.13 49.61 0.112 2.26× 10−3 1.44→4 I15/2 976 392.53 0.888 1.47

4F9/2→4 I9/2 3553.74 7.84 0.001 174.53× 10−6 0.40→4 I11/2 1973.15 168.31 0.029 2.63

→4 I13/2 1137.56 293.49 0.051 1.50

→4 I15/2 653 5259.90 0.918 9.14

4S3/2→4 I9/2 1719.69 162.93 0.040 244.56× 10−6 1.94→4 I11/2 1239.29 400.55 0.098 2.42

→4 I13/2 848.04 263.76 0.064 0.77

→4 I15/2 548 3261.72 0.798 3.91

Table 4Comparative chart of spectroscopic properties of Er+3 reported in the cases of different hosts vis-à-vis those of the ion in the present glass.

Host Transitions λmax (nm) P (×10−6) Ar (s−1) τcal (s) Σσ (10−18 cm)5GPN: Er 4I13/2→4 I15/2 1532 – 325.1 3.07× 10−3 2.582YAG: Er: 1532 2.04 211 2.008LCB: Er 1532 2.69 233.08 2.5517LKBBT: Er 1532 – 261.8 –7GaTe: Er 1532 2.74 271.6 –Present glass 1533 3.07 333.21 3.00× 10−3 3.14LCB: Er 4S3/2→4 I11/2 1214 – 61.20 0.42LKBBT: Er 1232 – 83.6 –GaTe: Er 1229 – 91.6 –GPN: Er 1232 – 77.9 –Present glass 1239 400.55 2.42LCB: Er 4S3/2→4 I15/2 542 – 1908.61 2.60LKBBT: Er 542 – 2568 –Present glass 548 1.21 3261.72 244× 10−6 3.91

GPN: Er = Er+3 in lead niobium germanate thin film; YAG: Er = Er+3 in yttrium garnet crystal; LCB: Er = Er+3 in lanthanum calcium borate glass; LKBBT: Er = Er+3 inalkali barium bismuth gallium tellurite glass; GaTe: Er = Er+3 in gallium tellurite glass.

βc = A(J → J ′)/ΣA(J → J ′); (9)

τf = 1/ΣAr(J → J ′) (10)

Σσ(J → J ′) = [(λmax)2/8πcn2]Ar(J → J ′). (11)

The terms used in the equations have the usual meanings.The parameters calculated are listed in Table 3. The calculatedspectroscopic parameters of Er+3 ions in the present glass arecompared with those of Er+3 ions in other crystals and glasses tojudge the superiority of the glass as a photonic material for visibleandNIR region. This is shown in Table 4. A comparative assessmentof the data suggests that the present glass is a prospectivecandidate for use as a green solid state laser medium and NIRamplifier for optical communication.

Acknowledgements

The authors gratefully acknowledge the help of D. Datta, ofSaha Institute of Nuclear Physics, Kolkata, India, at some stagesof calculations and thank Mrs. A. Nayak for cooperation duringmelting of the glasses.

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