Erbium-doped tellurite glasses with high quantum efficiency and broadband stimulated emission cross section at 1.5 μm

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Erbium-doped tellurite glasses with high quantum eﬃciency and broadband stimulated emission

cross section at 1.5 lm

R. Rolli

^a,*

, M. Montagna

^a

, S. Chaussedent

^b

, A. Monteil

^b

, V.K. Tikhomirov

^c

, M. Ferrari

^d

aDipartimento di Fisica and INFM, Universitaadi Trento, via Sommarive 14, 38050 Povo-Trento, Italy

bLaboratoire POMA-UMR CNRS 6136, Universiteed’Angers, 2 bd. Lavoisier, 49045 Angers, France

cMechanical Materials Manufacturing Engineering and Management, Wolfson Building, Universityof Nottingham, Nottingham, NG7 2RD, UK

dConsiglio Nazionale delle Ricerche CeFSA, IFN––Sezione di Trento, via Sommarive 14, 38050 Povo-Trento, Italy Received 23 April 2002; accepted 12 July 2002

Abstract

Optical transitions of Er^3þion in two tellurite glasses of molar composition 75TeO₂:12ZnO:10Na₂O:2PbO:1Er₂O₃ and 75TeO2:12ZnO:10Na2O:2GeO2:1Er2O3 were investigated. The measured absorption and emission spectra were analysed by Judd–Ofelt and McCumber theories, in order to obtain radiative transition rates and stimulated emission cross sections. It was found that these glasses have high and broadband absorption and stimulated emission cross sections at 1.5lm. For the metastable⁴I13=2 level, by comparing the measured lifetime with the calculated radiative decay time, quantum eﬃciency higher than 80% was found.

PACS:42.70.Ce; 78.20.Ci; 78.40

Keywords:Tellurite glasses; Erbium; Judd–Ofelt parameters; Absorption and stimulated emission cross sections

1. Introduction

Rare earth-activated tellurite glasses are very attractive materials for photonics applications, such as optical ampliﬁers in the second and third

telecommunications windows (at 1.3 and 1.5 lm, respectively) and frequency up-converters [1–5].

They have a wide transmission region (0.35–5 lm), good glass stability and corrosion resistance, the lowest vibrational energy (about 780 cm¹) among oxide glass formers, low process temperature, and a high refractive index which increases the local ﬁeld correction at the rare-earth ion site and leads to an enhancement of the radiative transition

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*Corresponding author. Tel.: +39-04-61881679/61881695;

fax: +39-04-61881696.

E-mail address:rolli@science.unitn.it(R. Rolli).

PII: S 0 9 2 5 - 3 4 6 7 ( 0 2 ) 0 0 0 9 2 - 7

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rates [1,6–8]. In addition, tellurite glasses have high non-linear refractive index, and can ﬁnd applica- tion for second harmonic generation [9].

In this work we have investigated optical transitions of Er^3þ in two erbium-doped tellurite glasses of molar composition 75TeO2:12ZnO:

10 Na2O:2PbO:1Er2O3 (sample denominated S1) and 75TeO2:12ZnO:10Na2O:2GeO2:1Er2O3 (sample denominated S2). The change in the proportion of PbO and GeO2 constituents results in a slight change of the linear refractive index, which is required for a formation of core-clad ﬁbre structure.

The measured absorption and emission spectra were analysed by Judd–Ofelt (J–O) and McCumber theories, in order to obtain radiative transition rates and stimulated emission cross sections. By comparing the calculated transition rate with the measured lifetime, the quantum eﬃciency of the metastable⁴I13=2level was determined.

2. Experimental

Tellurite glasses were prepared by melting batches of the constituents. The batches were made in the glove box under nitrogen gas atmosphere to avoid contamination with the hydroxyl OH and water. Powdered TeO2, ZnO, PbO, GeO2, Er2O3

and Na2CO3 of 99.999% purity were supplied by Aldrich and Alfa-Aesar. The melting was carried out in a Pt crucible for 2 h at 750 °Cin air atmosphere. The melt was cast in a pre-heated to 270

°Cmould. The resulting glass sample was annealed for 10 h in the mould while gradually decreasing the temperature down to the room temperature.

Further the glass sample of typical size 110:4 cm³ was removed from the mould and polished.

Optical absorption spectra in the ultraviolet, visible and near infrared (UV–VIS–NIR) regions were measured at room temperature by a double beam spectrometer with a resolution of 0.5 nm.

Room temperature emission spectra at 1.5 lm were performed using the 514.5 nm line of an Ar^þ- ion laser as the excitation source and dispersing the luminescence light with a 320 mm single-grat- ing monochromator with a resolution of 2 nm. The light was detected using an InGaAs photodiode and lock-in technique.

3. Judd–Ofelt analysis

Table 1 reports the refractive indices of the two samples at 543.5 and 632.8 nm measured using a prism coupler technique.

Fig. 1 shows the UV–VIS–NIR absorption spectra of the two tellurite glasses. The inhomo- geneously broadened bands are assigned to the transitions from the⁴I15=2 ground state to the excited states of the Er^3þ ion, according to [10].

The radiative transitions within the 4fⁿ conﬁg- uration of a rare earth ion can be analysed by using the Judd and Ofelt theory [11,12]. In the framework of the J–O theory, the theoretical oscillator strengthsP_cal^ed are expressed as a sum of transition matrix elements, involving intensity parameters Xq with q¼2;4;6 [11–14], which depend on the host matrix

Table 1

Refractive indices at 543.5 nm and 632.8 nm of the tellurite glasses of molar composition 75TeO2:12ZnO:10Na2O:2PbO:

1Er2O3(sample S1) and 75TeO2:12ZnO:10Na2O:2GeO2: 1Er2O3

(sample S2)

Sample n@ 543.5 nm n@ 632.8 nm

S1 2:0570:001 2:0340:001

S2 2:0400:001 2:0180:001

Fig. 1. Room temperature absorption spectra in the UV–VIS–

NIR spectral regions of the tellurite glasses of molar composition 75TeO2:12ZnO:10Na2O:2PbO:1Er2O3 (a) and 75TeO2: 12ZnO:10Na2O:2GeO2:1Er2O3 (b). The ﬁnal states of the

4I15=2!^2Sþ1LJtransitions are labelled. The assignment of the levels is made following Ref. [10].

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P_cal^edðJ;J⁰Þ ¼ 8p²mc 3hkð2Jþ1Þ

ðn²þ2Þ² 9n

X

q¼2;4;6

Xq

haSL;JkU^ðqÞka⁰S⁰L⁰;J⁰i²; ð1Þ

wherek is the mean wavelength of the transition andnis the refractive index. Because the transition matrix elements hkU^ðqÞki are essentially the same from host to host, we used the values calculated by Morrison [15,16]: using the set of free-ion parameters obtained by Carnall in aqueous solution [17], Morrison has computed the reduced matrix elements between all of the intermediate-coupled wave functions representing the multiplets of the electronic conﬁguration 4fⁿ of the free ion.

The intensity parameters, called J–O parameters, are then obtained by the chi-square method [18]. This method minimises the relative diﬀerences between the theoretical oscillator strength and the experimental one,P_exp^ed, measured in the absorption spectrum

P_exp^ed þP_cal^md¼mc² pe²

2303 N_A

Z

band

eðmÞdm; ð2Þ

where eðmÞ is the molar absorptivity, m is the wavenumber and N_A is the Avogadro’s number.

Each value of the oscillator strength is weighed by its own uncertainty. These uncertainties have been evaluated by considering the reliability of the absorption bands integration including the baseline subtraction. Table 2 reports the obtained J–O parameters together with the root mean square (r.m.s.) deviations of the oscillator strengths, calculated as

r:m:s:¼ 1 N3

X^N

i¼1

P_exp^edðiÞ

"

P_cal^edðiÞ#1=2

; ð3Þ

whereNis the number of ﬁtted bands. The values of X4 andX6are in agreement with the values reported by Reisfeld and Eckstein for tellurite glasses [14,19], whereas the values ofX2are lower than the ones reported in [14,19] and are more similar to the values reported by Ryba-Romanowski [20], Pan et al. [7] and Jaba et al. [5] for Er^3þ in tellurite glasses.

After obtaining the J–O parameters, the total spontaneous emission probabilities and the radiative lifetimes sR of the most important excited states of Er^3þ have been estimated. They are reported in Table 3. The electric dipole contributions have been computed as follows [21]:

A_edðWJ;W⁰J⁰Þ ¼ 64p⁴e²

3hk³ð2Jþ1Þv_ed X

q¼2;4;6

Xq

haSL;JkU^ðqÞka⁰S⁰L⁰;J⁰i²; ð4Þ whereXq is the set of J–O parameters determined from the chi-square minimisation, k is the mean wavelength of the transition, v_ed¼nðn²þ2Þ²=9 is the local ﬁeld correction, and hkU^ðqÞkiare the reduced matrix elements tabulated by Morrison [15,16]. The magnetic dipole contributions only depend on the magnetic dipole operator and are given by

A_mdðWJ;W⁰J⁰Þ ¼ 4p²e²h

3k³m²c²ð2Jþ1Þv_md

haSL;JkðLþ2SÞ^ð1Þka⁰S⁰L⁰;J⁰i²; ð5Þ where v_md¼n³ is the local ﬁeld correction and hkðLþ2SÞ^ð1Þki are the magnetic dipole matrix elements also tabulated by Morrison in the intermediate-coupled wave functions set [15,16]. The radiative lifetime of an excited state iis then gov- erned by sRðiÞ ¼ ðP

jAði;jÞÞ¹, where Aði;jÞ ¼ Aedði;jÞ þAmdði;jÞ and the summation is over all the terminal states j. Finally, the emission branching ratios were given byb_ij¼Aði;jÞsRðiÞ.

When two emitting states are separated by a small energy gap, the thermalization phenomenon was taken into account. For instance,²H11=2,⁴S3=2

and ⁴F5=2, ⁴F3=2 pairs of emitting levels are in thermal equilibrium and were commonly treated by considering the Boltzmann distribution.

Table 2

Intensity parametersXq(in units of 10²⁰cm²) in the tellurite glasses of molar composition 75TeO2:12ZnO:10Na2O:2PbO:

1Er2O3(sample S1) and 75TeO2:12ZnO:10Na2O:2GeO2:1Er2O3

(sample S2)

Sample X2 X4 X6 r.m.s.

S1 5.22 1.55 1.13 1:6310⁷

S2 5.62 1.50 1.18 1:8510⁷

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The lifetime of the ⁴I13=2 level (sexp) was measured after excitation at 514.5 nm, for both tellurite samples [22] and it results to be 3:30:2 and 2:90:2 ms for sample S1 and S2 respectively.

The quantum eﬃciencygof the luminescence from the ⁴I13=2 level is determined fromg¼sexp=sR [7].

A quantum eﬃciency of 94% and 83% is found for the metastable ⁴I13=2 level in samples S1 and S2, respectively.

Table 4 reports, for comparison, the J–O parameters X_q, the radiative lifetime sR and the measured lifetimesexpof the⁴I13=2level for our samples

Table 3

Calculated radiative transition rates (s¹) for electric dipole transitions,Aed, and magnetic dipole transitions,Amd, branching ratiosb, and radiative lifetimessR(ms) of Er^3þin the tellurite glasses of molar composition 75TeO2:12ZnO:10Na2O:2PbO:1Er2O3(sample S1) and 75TeO2:12ZnO:10Na2O:2GeO2:1Er2O3(sample S2)

Transition Sample S1 Sample S2

Aed Amd b sR Aed Amd b sR

4I13=2!⁴I15=2 208 77.8 1.0000 3.50 211 76.2 1.0000 3.48

4I11=2!⁴I15=2 294 0 0.8476 2.89 302 0 0.8508 2.82

4I11=2!⁴I13=2 35.9 16.9 0.1524 36.3 16.6 0.1492

4I9=2!⁴I15=2 305 0 0.7681 2.52 287 0 0.7540 2.63

4I9=2!⁴I13=2 88.3 0 0.2227 90 0 0.2366

4I9=2!⁴I11=2 1.46 2.19 0.0092 1.45 2.15 0.0094

4F9=2!⁴I15=2 2862 0 0.9073 0.317 2772 0 0.9046 0.326

4F9=2!⁴I13=2 136 0 0.0430 132 0 0.0431

4F9=2!⁴I11=2 129 13.2 0.0450 132 13 0.0474

4F9=2!⁴I9=2 9.15 5.73 0.0047 9.58 5.62 0.0050

4S3=2&²H11=2!⁴I15=2 3371 0 0.7481 0.222 3434 0 0.7487 0.218

4S3=2&²H11=2!⁴I13=2 910 8.66 0.2038 927 8.47 0.2038

4S3=2&²H11=2!⁴I11=2 76.3 1.10 0.0172 77.2 1.08 0.0171

4S3=2&²H11=2!⁴I9=2 134 0.09 0.0298 135 0.09 0.0293

4S3=2&²H11=2!⁴F9=2 4.84 0.02 0.0011 5.03 0.02 0.0011

4F7=2!⁴I15=2 6514 0 0.7818 0.120 6478 0 0.7883 0.122

4F7=2!⁴I13=2 1034 0 0.1241 970 0 0.1181

4F7=2!⁴I11=2 459 0 0.0550 443 0 0.0539

4F7=2!⁴I9=2 262 25.8 0.0346 264 25.2 0.0352

4F7=2!⁴F9=2 12.8 22.9 0.0043 12.9 22.5 0.0043

4F7=2!⁴S3=2 0.048 0 0.000006 0.05 0 0.000006

4F7=2!²H11=2 1.21 0 0.0001 1.25 0 0.0002

4F5=2&⁴F3=2!⁴I15=2 3022 0 0.4873 0.161 3059 0 0.4948 0.162

4F5=2&⁴F3=2!⁴I13=2 2255 0 0.3636 2219 0 0.3589

4F5=2&⁴F3=2!⁴I11=2 431 0 0.0694 418 0 0.0676

4F5=2&⁴F3=2!⁴I9=2 269 0 0.0434 266 0 0.0430

4F5=2&⁴F3=2!⁴F9=2 210 0 0.0339 207 0 0.0334

4F5=2&⁴F3=2!⁴S3=2 3.18 2.09 0.0009 3.31 2.05 0.0009

4F5=2&⁴F3=2!²²H11=2 5.41 0 0.0009 5.40 0 0.0009

4F5=2&⁴F3=2!⁴F7=2 2.29 1.39 0.0006 2.35 1.37 0.0006

2H9=2!⁴I15=2 2984 0 0.3810 0.128 2991 0 0.3790 0.127

2H9=2!⁴I13=2 3621 0 0.4622 3665 0 0.4644

2H9=2!⁴I11=2 842 75.69 0.1172 850 74 0.1171

2H9=2!⁴I9=2 95.6 1.14 0.0123 98.8 1.12 0.0127

2H9=2!⁴F9=2 53.9 88.3 0.0182 53.5 86.5 0.0177

2H9=2!⁴S3=2 0.70 0 0.00009 0.69 0 0.00009

2H9=2!²H11=2 41.8 1.79 0.0056 41.2 1.76 0.0054

2H9=2!⁴F7=2 24.7 1.83 0.0034 25.6 1.80 0.0035

2H9=2!⁴F5=2 0.89 0 0.0001 0.89 0 0.0001

2H9=2!⁴F3=2 0.21 0 0.00003 0.20 0 0.00003

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and for several other tellurite, phosphate, ﬂuoride and heavy metal oxide containing glasses [23,24].

4. Absorption and stimulated emission cross sections

Absorption cross sections were determined from absorption spectra. The maximum cross section at 1.5 lm is about 7:8510²¹ cm² for both samples. Stimulated emission cross sections at 1.5lm were calculated from McCumber theory [25]. According to the McCumber theory, the absorption and stimulated emission cross sections are related by

reðmÞ ¼raðmÞexp½ðehmÞ=kT; ð6Þ

whereraðmÞ andreðmÞare the absorption and the stimulated emission cross sections,mis the photon frequency,eis the net free energy required to excite one erbium ion from the ground state to the⁴I13=2

level at temperatureT, h is the Planck’s constant andkis the Boltzmann constant.ewas determined by using the procedure developed by Miniscalco and Quimby [26].

Fig. 2 shows the calculated absorption and emission cross sections for the two glasses.

The calculated emission cross sections are very similar to those calculated for other tellurite systems [8,23]. Their very high values are due to the high values of the refractive index (Table 1), since

the stimulated emission cross section of rare earth ions increases with the refractive index as ðn²þ2Þ²=nfor electric dipole transitions, and asn for magnetic dipole transitions [6,8,23].

The gain coeﬃcient g at wavelength k can be estimated by means of the formula [27] gðkÞ ¼ reðkÞN2raðkÞN1, where raðkÞ and reðkÞ are the

Table 4

J–O parametersXq, radiative lifetime,sR, and measured lifetime,sexp, of the⁴I13=2metastable level for our samples and for several other tellurite, phosphate, ﬂuoride and heavy metal oxide containing glasses [23,24]

Glass Xq(10²⁰cm²) ⁴I13=2level

X2 X4 X6 sR(ms) sexp(ms)

75TeO2:12ZnO:10Na2O:2PbO:1Er2O3 5.22 1.55 1.13 3.50 3.3

75TeO2:12ZnO:10Na2O:2GeO2:1Er2O3 5.62 1.50 1.18 3.48 2.9

20PbO:80TeO2:1Er2O3 4.47 1.77 0.86 3.30 1.57

20PbF2:80TeO2:1Er2O3 5.28 1.47 0.89 4.43 3.25

20PbCl2:80TeO2:1Er2O3 4.76 1.67 0.90 3.32 1.57

20PbBr2:80TeO2:1Er2O3 4.32 1.65 0.83 3.26 1.68

10PbCl2:10PbBr2:80TeO2:1Er2O3 4.44 1.51 0.84 3.40 1.98

40PbBr2:60TeO2:1Er2O3 3.13 1.25 0.73 3.27 1.67

3Sr(PO3)2:38AlF3:10MgF2:27CaF2:22SrF2 2.9 1.4 1.5 8.5 8.4

20Sr(PO3)2:30AlF3:10MgF2:22CaF2:18SrF2 4.7 1.6 1.6 6.8 7.7

50Bi2O3:50B2O3 4.1 1.5 1.3 2.6 1.1

52PbO:25Bi2O3:18Ga2O3:5B2O3 5.0 1.4 0.8 2.4 1.8

Fig. 2. Absorption and emission cross sections of Er^3þion at 1.5 lm in the tellurite glasses of molar composition 75TeO2: 12ZnO:10Na2O:2PbO:1Er2O3(a) and 75TeO2:12ZnO:10Na2O:

2GeO2:1Er2O3(b).

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absorption and stimulated emission cross sections at wavelengthk, andN₁andN₂ are the density of ions in the ground and excited state respectively (N1þN2¼N,Nbeing the density of erbium ions).

In the case of total inversion (N2¼N), at 1532 nm we obtain a gain coeﬃcient of 4.06 and 3.78 cm¹ respectively for sample S1 (N ¼4:40510²⁰cm³) and S2 (N ¼4:42610²⁰ cm³).

The eﬀective emission cross section bandwidth Dk is deﬁned as [23] Dk¼R

rðkÞdk=rpeak, where rðkÞis the emission cross section at wavelengthk and rpeak is the value at the peak. The eﬀective bandwidth is 63 and 66 nm, respectively for sample S1 and S2. These values are similar to those of other tellurite glasses [23] and are very large with respect to those of silicate and phosphate glasses [8,23,28].

The large spectral bandwidth of the stimulated emission cross section makes these glasses very attractive candidates for broadband ampliﬁers in wavelength-division-multiplexing systems.

5. Conclusions

The optical transitions of Er^3þ in two tellurite glasses were investigated. The measured absorption spectra were analysed by J–O theory and the Xq parameters were estimated. Radiative transition rates were calculated and a comparison between the experimental measured lifetimes and the calculated ones gave a quantum eﬃciency of 94%

and 83% for the metastable⁴I13=2 level in the two glasses. Stimulated emission cross sections in the 1.5lm region were obtained by using McCumber theory. It was found that these glasses have high and very broadband emission cross sections. These properties make these tellurite glasses promising host materials for broadband ampliﬁcation in the third telecommunications window.

Acknowledgements

This research was partially supported by the

‘‘Progetto Finalizzato MADESS II’’ CNR project,

a MURST-Coﬁn 99, and a French-Italian Pro- gram Galileo 98-2000.

References

[1] J.S. Wang, E.M. Vogel, E. Snitzer, Opt. Mat. 3 (1994) 187.

[2] A. Mori, Y. Ohishi, S. Sudo, Electron. Lett. 33 (1997) 863.

[3] M. Yamada, A. Mori, K. Kobayashi, H. Ono, T. Kana- mori, K. Oikawa, Y. Nishida, Y. Ohishi, IEEE Photonics Technol. Lett. 10 (1998) 1244.

[4] S. Tanabe, K. Hirao, N. Soga, J. Non-Cryst. Solids 122 (1990) 79.

[5] N. Jaba, A. Kanoun, H. Mejri, A. Selmi, S. Alaya, H.

Maaref, J. Phys. Condens. Matter. 12 (2000) 4523.

[6] M.J. Weber, J.D. Myers, D.H. Blackburn, J. Appl. Phys.

52 (1981) 2944.

[7] Z. Pan, S.H. Morgan, K. Dyer, A. Ueda, H. Liu, J. Appl.

Phys. 79 (1996) 8906.

[8] L. Le Neindre, S. Jiang, B. Hwang, T. Luo, J. Watson, N.

Peyghambarian, J. Non-Cryst. Solids 255 (1999) 97.

[9] A. Narazaki, K. Tanaka, K. Hirao, N. Soga, J. Appl. Phys.

85 (1999) 2046.

[10] R. Reisfeld, Y. Eckstein, J. Non-Cryst. Solids 15 (1974) 125.

[11] B.R. Judd, Phys. Rev. B 127 (1962) 750.

[12] G.S. Ofelt, J. Chem. Phys. 37 (1962) 511.

[13] R.D. Peacock, Struct. Bonding 22 (1975) 83.

[14] R. Reisfeld, Struct. Bonding 22 (1975) 123.

[15] C.A. Morrison, R.P. Leavitt, J. Chem. Phys. 71 (1979) 2366.

[16] R.P. Leavitt, C.A. Morrison, J. Chem. Phys. 73 (1980) 749.

[17] W.T. Carnall, P.R. Fields, K. Rajnak, J. Chem. Phys. 49 (1968) 4412.

[18] K.A. Gschneidner, L. Eyring, in: Handbook on the Physics and Chemistry of Rare Earth, vol. 25, Elsevier, 1998, p. 167.

[19] R. Reisfeld, Y. Eckstein, Solid State Commun. 13 (1973) 741.

[20] W. Ryba Romanowski, J. Lumin. 46 (1990) 163.

[21] M.J. Weber, Phys. Rev. 157 (1967) 262.

[22] R. Rolli, A. Chiasera, M. Montagna, E. Moser, S.

Ronchin, S. Pelli, G.C. Righini, A. Jha, V.K. Tikhomirov, S.A. Tikhomirova, C. Duverger, P. Galinetto, M. Ferrari, Proc. SPIE 4282 (2001) 109.

[23] Y. Ding, S. Jiang, B. Hwang, T. Luo, N. Peyghambarian, Y. Miura, Proc. SPIE 3942 (2000) 166.

[24] H. Ebendorﬀ-Heidepriem, D. Ehrt, M. Bettinelli, A.

Speghini, Proc. SPIE 3622 (1999) 19.

[25] D.E. McCumber, Phys. Rev. 134 (1964) A299.

[26] W.J. Miniscalco, R.S. Quimby, Opt. Lett. 16 (1991) 258.

[27] E. Desurvire, Erbium-Doped Fiber Ampliﬁers, Principles and Applications, John Wiley, New York, 1994.

[28] M. Dejneca, B. Samson, MRS Bulletin 24 (9) (1999) 39.