Optical absorption of Nd3+, Sm3+ and Dy3+ in bismuth borate glasses with large radiative transition probabilities

Optical absorption of Nd3+, Sm3+ and Dy3+ in bismuth borate glasses with large radiative transition probabilities

Optical Materials 18 (2002) 403±417 www.elsevier.com/locate/optmat Optical absorption of Nd3‡, Sm3‡ and Dy3‡ in bismuth borate glasses with large ra...

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Optical Materials 18 (2002) 403±417

www.elsevier.com/locate/optmat

Optical absorption of Nd3‡, Sm3‡ and Dy3‡ in bismuth borate glasses with large radiative transition probabilities M.B. Saisudha, J. Ramakrishna

*

Department of Physics, Indian Institute of Science, Bangalore 560 012, India Received 9 February 2001; accepted 3 July 2001

Abstract This paper reports on the optical properties of Nd3‡ , Sm3‡ and Dy3‡ in bismuth borate glasses, with Bi2 O3 content varying from 30 to 60 mol%. The variation of the optical properties with composition plays a dominant role in determining a good laser host material. The variation of the Judd±Ofelt intensity parameters Xt …t ˆ 2; 4; 6† and the radiative transition probabilities and the hypersensitive band positions, with composition, have been discussed in detail. The changes in position and intensity parameters of the transitions in the optical absorption spectra are correlated to the structural changes in the host glass matrix. The variation of X2 with Bi2 O3 content has been attributed to changes in the asymmetry of the ligand ®eld at the rare earth ion site and to the changes in their rare earth±oxygen (R±O) covalency, whereas the variation of X6 strongly depends on nephlauxetic e€ect. The shift of the hypersensitive band shows that the covalency of the R±O bond increases with increase of Bi2 O3 content, due to increased interaction between the rare earth ions and the non-bridging oxygens. The radiative transition probabilities of the rare earth ions are large in bismuth borate glasses, suggesting their suitability for laser applications. Ó 2002 Published by Elsevier Science B.V. Keywords: Optical absorption studies; Rare earth ions; Glasses

1. Introduction The possible use of glasses doped with rare earth ions as solid state lasers, solar concentrators, phosphors, etc., has created considerable interest in the study of optical absorption and ¯uorescence properties of rare earth ions in glasses. The investigations of absorption and luminescent properties of the Nd3‡ [1±6], Sm3‡ [7± 10] and Dy3‡ [11] ions have indicated that the optical properties of these rare earth ions can be a€ected by varying the glass composition, thus

*

Corresponding author. Fax: +091-080-3602602, 3341683. E-mail address: [email protected] (J. Ramakrishna).

opening up the possibility of engineering application-friendly compositions. The intensities of the transitions for the rare earth ions have been estimated successfully using the Judd±Ofelt theory [12,13]. This theory de®nes a set of three intensity parameters Xt …t ˆ 2; 4; 6† which are sensitive to the environment of the rare earth ion. From these parameters, important optical properties such as radiative transition probability for spontaneous emission, radiative lifetime of the excited states, and branching ratios (which predict the ¯uorescence intensity of laser transitions) can be estimated and used further, to examine the dependence of the spectroscopic parameters on the glass composition. In order to increase the laser eciency of a particular

0925-3467/02/$ - see front matter Ó 2002 Published by Elsevier Science B.V. PII: S 0 9 2 5 - 3 4 6 7 ( 0 1 ) 0 0 1 8 1 - 1

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M.B. Saisudha, J. Ramakrishna / Optical Materials 18 (2002) 403±417

transition, the stimulated emission cross-section of that transition should be made as large as possible. It is therefore important to optimize the relation between the glass composition, the Xt parameters and the relative transition probability (which determines the stimulated emission crosssection). On the basis of these ®ndings the composition can be optimized to yield favourable spectroscopic properties for a given laser application. The glass formation range of bismuth borate glass is extensive (25±60 mol% Bi2 O3 ), with refractive index ranging from 1.9 to 2.3 and it has strong ultraviolet absorption [14]. Structural groups like boroxol, pentaborates, and diborates containing three- and four-coordinated borons, and ring- and chain-type metaborate groups containing non-bridging oxygens and networkforming bismuth groups are found to be in bismuth borate glasses for di€erent bismuth oxide concentrations. Hence it would be interesting to study the optical properties of Nd3‡ , Sm3‡ and Dy3‡ ions and their dependence on the composition in bismuth borate glasses and compare them with other glass systems.

con®guration. The transition probability depends on the extent of admixture. 2.1. The oscillator strength The intensity of an absorption band is expressed in terms of a quantity called the ``oscillator strength''. Experimentally, it is given by the area under the absorption band, and can be expressed in terms of the absorption coecient a…k† at a particular wavelength k and is given by [15] Z mc2 a…k† dk ; …1† fmeas ˆ 2 pe N k2 where a…k† ˆ …2:303†OD…k†=d is the measured absorption coecient at a given wavelength k. OD…k† is the optical density ‰log10 …I=Io †Š as a function of wavelength k, d is the thickness of the sample, m and e are the mass and charge of the electron, respectively, c is the velocity of light and N is the number of rare earth ions per unit volume. The absorption bands in glasses are relatively broad because of the disorder and are generally not pure Gaussians. It is usually a good approximation to use a Gaussian error curve [16] e ˆ emax 2

2. The Judd±Ofelt theory The absorption spectra of rare earth ions serve as a basis for understanding their radiative properties. The sharp absorption lines arising from the 4f±4f electronic transitions can be electric dipole, magnetic dipole or electric quadrupole in character. The quantitative calculation of the intensities of these transitions has been developed independently by Judd [12] and by Ofelt [13]. A brief outline of the Judd±Ofelt theory is given below, for completeness and ready reference. For a free rare earth ion, the electric dipole transitions between two states within the 4f con®guration are parity forbidden, while the magnetic dipole and electric quadrupole transitions are allowed. For an ion in a medium, the electric dipole transitions become allowed due to the admixture of states from con®gurations of opposite parity (for example 4f N 1 5d) into the 4f

…m mo †2 =Dm21=2

;

…2†

where emax ˆ OD…m†=dN . Here, mo is the frequency of the absorption band at which the molar extinction coecient e is maximum. Dm1=2 is the half-bandwidth at half maximum (in cm 1 ). Then, the expression for oscillator strength (Eq. (1)) can be written in energy units (in cm 1 ) as fmeas ˆ 2:303

mc2 2:1289emax Dm1=2 : pe2 N

…3†

According to the Judd±Ofelt theory [17], the oscillator strength of a transition between an initial J manifold …S; L†J and a ®nal J 0 manifold …S 0 ; L0 †J 0 is given by fcal …aJ ; bJ 0 † ˆ

8p2 mm 3h…2J ‡ 1† " # 2 …n2 ‡ 2† Sed ‡ nSmd ;  9n

…4†

M.B. Saisudha, J. Ramakrishna / Optical Materials 18 (2002) 403±417

where 0

0

0

Sed ‰…S; L†J ; …S ; L †J Š X 2 ˆ Xt jh…S; L†J kU …t† k…S 0 ; L0 †J 0 ij

…5†

tˆ2;4;6

and Smd ‰…S; L†J ; …S 0 ; L0 †J 0 Š X 2 ˆ Xt jh…S; L†J kL ‡ 2Sk…S 0 ; L0 †J 0 ij :

…6†

tˆ2;4;6

Sed and Smd represent the line strengths for the induced electric dipole transitions and the magnetic dipole transitions, respectively. The three intensity parameters Xt …t ˆ 2; 4; 6† are characteristic of a given rare earth ion (in a given matrix) and are related to the radial wavefunctions of the states 4f N , the admixing states 4f N 1 5d or 4f N 1 5g and the ligand ®eld parameters that characterize the environmental ®eld. They are given by the expression X 2 As;p N2 …s; t†; …2s ‡ 1† 1 ; Xt ˆ …2t ‡ 1† s;p

t ˆ 2; 4; 6;

…7†

where As;p are the crystal ®eld parameters of rank s and are related to the structure around the rare earth ions. N…s; t† is related to the matrix elements between the radial wavefunctions of 4f and admixing levels, e.g., 5d, 5g and the energy di€erence between these two levels. It has been suggested by Reisfeld [18] that N is related to the nephlauxetic parameter b which indicates the degree of covalency of R±O bond by [19] mf m N…s; t†ab ˆ ; …8† mf where mf and m are the transition energy of the free ion and the ion in a glass, respectively. jhkU …t† kij2 represents the square of the matrix elements of the unit tensor operators U …t† connecting the initial and ®nal states. The matrix elements are calculated in the intermediate coupling approximation [20]. Due to the electrostatic shielding of the 4f electrons by the closed 5p shell electrons, the matrix elements of the unit tensor operator between two energy manifolds in a given rare earth

405

ion do not vary signi®cantly when it is incorporated in di€erent hosts. Therefore, the matrix elements computed for the free ion may be used for calculations in di€erent media and are reported by Weber [21] and Carnall et al. [22]. The reduced matrix elements hkL ‡ 2Ski for magnetic dipole transitions are reported by Neilson and Koster [23]. The line strengths for both electric and magnetic dipole transitions are related to the integrated absorption coecient and are given by [24] Z 8p3 kN K…k† dk ˆ ‰v Sed ‡ vmd Smd Š; 3ch…2J ‡ 1†n2 ed bond …9† 2

where ved ˆ n…n2 ‡ 2† =9 and vmd ˆ n3 are the terms which correct the e€ective ®eld at a well-localized centre in a medium of isotropic refractive index n, K…k† is the absorption coecient at mean wavelength k, N is the concentration of the rare earth ions, c is the velocity of light, h is Planck's constant, e is the electronic charge and J is the total angular momentum of the initial state. Using the values of the integrated absorption coecient the oscillator strength fcal of various bands can be calculated using the expression Z mm2 K…k† dk N pk2 Z mm2 K…m† dv; ˆ Np

fcal ˆ fcal

or …10†

where m is the electron mass. 2.2. Radiative transition probability for induced electric dipole emission The Xt values obtained from the absorption measurements are used to calculate the radiative transition probability, radiative lifetime of the excited states and branching ratios (which predict the ¯uorescence intensity of the lasing transition). The radiative transition probability Arad …aJ ; bJ 0 † for emission from an initial state aJ to a ®nal bJ 0 is given by [25]

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M.B. Saisudha, J. Ramakrishna / Optical Materials 18 (2002) 403±417

Arad …aJ ; bJ 0 † ˆ

64p4 m3 e2 3hc3 …2J ‡ 1† " # n…n2 ‡ 2†2 3 Sed ‡ n Smd :  9

…11†

In the case of electric dipole emission, this equation becomes Arad …aJ ; bJ 0 † ˆ

2

64p4 m3 e2 n…n2 ‡ 2† 2 e 3hc3 …2J ‡ 1† 9 X  Xt jh…S; L†J kU …t† k…S 0 ; L0 †J 0 ij2 : tˆ2;4;6

…12† The total radiative emission probability AT …aJ † of the excited state SLJ [4 F3=2 …Nd3‡ †; 4 G5=2 …Sm3‡ † and 6 H15=2 …Dy3‡ †] is given by the sum of the Arad …aJ ; bJ 0 † terms calculated over all terminal states b: X AT …aJ † ˆ Arad …aJ ; bJ 0 †: …13† bJ 0

The ¯uorescence branching ratio bR is given as bR ˆ is

Arad …aJ ; bJ 0 † : AT …aJ †

…14†

The radiative lifetime sR of the emission state

sR ˆ

1 : AT …aJ †

…15†

3. Experimental The rare-earth-ion-doped bismuth borate glass samples were prepared using appropriate amounts of analar-quality Bi2 O3 , H3 BO3 and rare earth oxides of high purity (99.9%). These raw materials were thoroughly mixed and melted in a platinum crucible, in the range 800±1000 °C. The melt was air quenched by pouring it on a thick aluminium plate and covering it immediately with another aluminium plate. The samples were then annealed at 300±350 °C for 5±6 h to remove thermal strains. All samples were characterized by X-ray technique and were found to be amorphous.

The systems studied in the present work are: (a) 3Nd2 O3 :97[xBi2 O3 :…100 x†B2 O3 ] …BBN30± BBN60† (b) 3Sm2 O3 :97[xBi2 O3 :…100 x†B2 O3 ] …BBS30± BBS60† (c) 1:5Dy2 O3 :98.5[xBi2 O3 :…100 x†B2 O3 ] …BBD30 ±BBD60† (x ˆ 30, 40, 50 and 60 mol%). 3 Mol% Dy2 O3 doped bismuth borate glasses melt above 1000 °C and due to the limitations of our furnace temperature, we could not prepare samples with 3 mol% Dy2 O3 . However, bismuth borate glasses doped with 1.5 mol% Dy2 O3 melt below 1000 °C and we could successfully prepare glasses doped with 1.5 mol% Dy2 O3 . Beyond 60 mol% Bi2 O3 , glasses could not be prepared due to phase separation. The sample density is measured by the Archimedes method using xylene as the immersing liquid. The refractive index of the glasses is measured by the Brewster angle method using He±Ne laser (632 nm line) as the source. It may be pointed out that the refractive index did not vary signi®cantly with wavelength, and hence, we have measured n at a single wavelength for each sample using He±Ne laser as the source. Optical absorption measurements were made using a Hitachi U-3400 spectrophotometer, using optically polished glass samples of size 5 mm 5 mm  1 mm (at room temperature) in the wavelength range 200±2400 nm (50 000±4166 cm 1 ). 4. Results 4.1. Oscillator strengths The absorption spectra of Nd3‡ , Sm3‡ and Dy3‡ doped bismuth borate glasses are shown in Figs. 1(a)±(c). The oscillator strengths for di€erent absorption bands of Nd3‡ , Sm3‡ (low-energy region) and Dy3‡ are determined using Eq. (3) and are given in Tables 1±3. The oscillator strengths for Sm3‡ are arranged into two groups [10], one ``low-energy'' group corresponding to transitions up to 10 700 cm 1 and the other ``high-energy'' group corresponding to transitions in the energy range 17 600±32 000

M.B. Saisudha, J. Ramakrishna / Optical Materials 18 (2002) 403±417

Fig. 1. Optical absorption spectra of (a) Nd3‡ , (b) Sm3‡ and (c) Dy3‡ ions in xBi2 O3 :…100

cm 1 . Since Judd±Ofelt equation, Eq. (4), is applicable to cases where the high f-splittings are small compared to the f±d energy gap, it is not appropriate to use the high-energy levels for the calculation of Xt . For Sm3‡ in bismuth borate

407

x†B2 O3 glasses.

glasses, the Xt parameters are determined only for the low-energy region. In the high-energy region, due to strong ultraviolet absorption by Bi3‡ ions, Sm3‡ peaks are not well resolved. In Dy3‡ ion also, peaks in the high-energy region are not well

408

M.B. Saisudha, J. Ramakrishna / Optical Materials 18 (2002) 403±417

Table 1 Refractive index, density, Judd±Ofelt parameters of Nd3‡ (3 mol%) in xBi2 O3 :…100 Transitions from the ground state 4 I9=2 !

4

F3=2 F5=2 , 2 H9=2 4 F7=2 , 4 S3=2 4 F9=2 , 4 G5=2 , 2 G7=2 (HST) 2 K13=2 , 4 G9=2 , 4 G7=2 2 G9=2 , 4 G11=2 , 2 D3=2 4

k (nm)

BBN30 874 802 746 680 582 525 473

BBN40

BBN50

fcal

fmeas

fcal

fmeas

fcal

fmeas

fcal

229 763 711 80 1940 575 58

229 763 711 82 1940 568 55

256 856 802 90 2017 641 65

259 860 800 92 2017 637 62

295 941 865 96 2172 709 66

294 943 864 100 2172 708 69

320 1017 931 110 2328 773 77

321 1024 937 108 2329 768 75

0.327% 5.511  0.0136 10.03  0.024 1.92  0.01 4.646  0.165 2.898  0.036 5.854  0.111

0.304% 6.260  0.0153 9.483  0.038 2.03  0.01 4.288  0.154 3.001  0.053 6.020  0.112

Table 2 Refractive index, density, Judd±Ofelt parameters of Sm3‡ (3 mol%) in xBi2 O3 :…100 k (nm)

6

1515 1472 1368 1224 1075 938

F1=2 (HST) 6 F3=2 6 F5=2 6 F7=2 6 F9=2 6 F11=2

RMS deviation Density …g=cm3 † N …1020 cm 3 † Refractive index X2  10 20 cm2 X4  10 20 cm2 X6  10 20 cm2

BBN60

fmeas

RMS deviation Density …g=cm3 † N …1020 cm 3 † Refractive index X2  10 20 cm2 X4  10 20 cm2 X6  10 20 cm2

Transitions from the ground state 6 H5=2 !

x†B2 O3 glasses

Oscillator strength …f  10 8 †

0.206% 7.039  0.0110 9.155  0.014 2.13  0.01 4.244  0.240 3.309  0.116 6.117  0.164

0.364% 7.609  0.0122 8.659  0.014 2.21  0.01 4.122  0.172 3.303  0.060 6.058  0.136

x†B2 O3 glasses

Oscillator strength …f  10 8 † BBS30

BBS40

BBS50

BBS60

fmeas

fcal

fmeas

fcal

fmeas

fcal

fmeas

fcal

84 147 220 385 264 49

77 152 218 386 264 44

89 171 264 445 302 55

85 177 261 447 301 50

76 163 264 476 333 58

73 168 260 479 330 55

62 163 280 525 363 61

60 166 278 526 364 60

1.729% 5.814  0.0121 10.58  0.021 1.84  0.01 3.639  0.106 5.662  0.188 4.468  0.136

resolved. Hence they are not taken in the calculation of the intensity parameters Xt . All the transitions of Nd3‡ , Sm3‡ and Dy3‡ are electric dipolar with signi®cant intensities in the observed frequency range, except for the 6 H15=2 ! 6 H13=2 transition …3500 cm 1 † of Dy3‡ , which has a very small magnetic dipolar contribution also [26]. However, its overall intensity is

1.433% 6.444  0.0198 9.791  0.031 1.99  0.01 3.555  0.210 6.030  0.158 4.490  0.152

1.202% 7.177  0.0101 9.336  0.012 2.09  0.01 2.812  0.174 5.602  0.211 4.556  0.169

0.623% 7.830  0.0168 8.921  0.018 2.20  0.01 2.105  0.138 5.544  0.204 4.597  0.196

very small and, therefore, is not taken into consideration while calculating the intensity parameters. 4.2. Intensity parameters The best set of intensity parameters Xt …t ˆ 2; 4; 6† (for a given rare earth ion) is obtained

M.B. Saisudha, J. Ramakrishna / Optical Materials 18 (2002) 403±417 Table 3 Refractive index, density, Judd±Ofelt parameters of Dy3‡ (1.5 mol%) in xBi2 O3 :…100 Transitions from the ground state 6 H15=2 !

6

H11=2 F11=2 , 6 H9=2 (HST) 6 F9=2 , 6 H7=2 6 F7=2 , 6 H5=2 6 F5=2 6 F3=2 6

RMS deviation Density …g=cm3 † N …1020 cm 3 † Refractive index X2  10 20 cm2 X4  10 20 cm2 X6  10 20 cm2

k (nm)

x†B2 O3 glasses

Oscillator strength …f  10 8 † BBD30

1680 1269 1090 896 802 752

409

BBD40

BBD50

BBD60

fmeas

fcal

fmeas

fcal

fmeas

fcal

fmeas

fcal

107 553 236 176 85 18

104 553 234 181 82 15

141 724 302 243 118 23

143 724 302 245 114 22

172 866 376 302 145 29

174 866 375 304 141 27

193 875 363 329 167 33

196 875 363 330 163 31

1.105% 5.799  0.0123 5.396  0.012 1.90  0.01 3.977  0.114 1.567  0.055 1.534  0.046

0.568% 6.539  0.0212 5.052  0.016 2.01  0.01 4.923  0.187 1.626  0.056 1.959  0.071

0.500% 7.011  0.0182 4.630  0.012 2.13  0.01 5.224  0.189 1.851  0.060 2.195  0.082

0.520% 7.530  0.0253 4.344  0.014 2.20  0.01 5.382  0.255 1.173  0.038 2.390  0.115

from the experimental oscillator strengths and the calculated doubly reduced matrix elements using the expression for oscillator strength, Eq. (10), by least squares analysis. The intensity parameters determined for Nd3‡ , Sm3‡ and Dy3‡ for all the concentrations of Bi2 O3 are listed in Tables 1±3. In order to estimate the accuracy of the intensity parameters thus obtained, the root-mean-square deviations …dRMS † are calculated; dRMS is given by "P #1=2 …fcal fmeas †2 P 2 dRMS ˆ ; …16† fmeas where fcal and fmeas are the calculated and measured oscillator strengths, respectively, and the summation is taken over all the bands used to calculate Xt parameters. The intensity parameter X2 for Nd3‡ and Sm3‡ in bismuth borate glasses decreases from 4:646 10 20 to 4:122  10 20 cm2 and from 3:639  10 20 to 2:105  10 20 cm2 , respectively, with increase in Bi2 O3 content from 30 to 60 mol% with a slope change at 40 mol% Bi2 O3 (Figs. 2(a) and (b)). X6 for Nd3‡ and Sm3‡ increases from 5:854  10 20 to 6:058  10 20 cm2 and from 4:468  10 20 to 4:597  10 20 cm2 , respectively, with increase in Bi2 O3 content from 30 to 60 mol% (Figs. 4(a) and (b)). For Dy3‡ , the intensity parameters X2 and X6 increase by a large amount from 3:977  10 20 to

Fig. 2. Variation of X2 with Bi2 O3 content in (a) Nd3‡ , (b) Sm3‡ and (c) Dy3‡ ions in xBi2 O3 :…100 x†B2 O3 glasses.

410

M.B. Saisudha, J. Ramakrishna / Optical Materials 18 (2002) 403±417

Fig. 3. Variation of X4 with Bi2 O3 content in (a) Nd3‡ , (b) Sm3‡ and (c) Dy3‡ ions in xBi2 O3 :…100 x†B2 O3 glasses.

Fig. 4. Variation of X6 with Bi2 O3 content in (a) Nd3‡ , (b) Sm3‡ and (c) Dy3‡ ions in xBi2 O3 :…100 x†B2 O3 glasses.

5:382  10 20 cm2 (Fig. 2(c)) and from 1:534 10 20 to 2:390  10 20 cm2 (Fig. 4(c)) with Bi2 O3 . X4 for all the three ions shows an initial increase up to 50 mol% of Bi2 O3 and then decreases (Figs. 3(a)±(c)).

nm) is investigated as a function of glass composition to study the nature of the R±O bond. The peak wavelengths for Nd3‡ , Sm3‡ and Dy3‡ are found to shift towards longer wavelength from 581.8 to 584.2 nm, from 1512 to 1525.1 nm and from 1268.8 to 1272.9 nm, respectively, with increase in Bi2 O3 content from 30 to 60 mol% (Figs. 5(a)±(c)). The variation of spectral pro®les of the transitions 4 I9=2 ! 4 G5=2 ; 4 G7=2 (HST) and 4 I9=2 ! 4 F7=2 ; 4 S3=2 of Nd3‡ with glass composition is also investigated. In these transitions, two peaks are distinguished by the Stark splitting and the relative intensity ratio between the peaks varies with glass composition. The peak intensities of the shortwavelength and long-wavelength components are designated as IS and IL , respectively. Increase in the intensity ratio IL =IS is found to indicate a shift of the centre of gravity of the absorption spectra to longer wavelengths [28]. This indicates an increase

4.3. Hypersensitive transitions The position and intensity of certain electric dipole transitions of rare earth ions are found to be very sensitive to the environment of the rare earth ion. Such transitions are termed as hypersensitive transitions by Jorgensen and Judd [27]. Hypersensitivity of a transition has been shown to be proportional to the nephlauxetic ratio b, which is a measure of the covalency of the R±O bond [19]. In bismuth borate glasses, the position of the peak wavelengths of the hypersensitive bands of Nd3‡ (6 I9=2 ! 4 G5=2 ; 2 G7=2 ; 581.8 nm), Sm3‡ (6 H5=2 ! 6 F1=2 ; 1512 nm) and Dy3‡ (6 H15=2 ! 6 F11=2 ; 1262

M.B. Saisudha, J. Ramakrishna / Optical Materials 18 (2002) 403±417

411

Fig. 5. Variation of peak wavelength kp of hypersensitive bands of (a) Nd3‡ , (b) Sm3‡ and (c) Dy3‡ ions in xBi2 O3 :…100 x† B2 O3 glasses.

in the covalency of the Nd±O bond. As pointed out by Krupke [29] the transition intensities of 4 I9=2 ! 4 G5=2 ; 2 G7=2 and 4 I9=2 ! 4 F7=2 ; 4 S3=2 are 2 determined mainly by X2 jhkU …2† kij and X6 jhk 2 U …6† kij terms, respectively. Therefore, from the relationship between the intensity parameters and relative intensity ratio IL =IS (which varies with glass composition in these transitions), the e€ect of Nd±O bond on the intensity parameters can be obtained. In bismuth borate glasses, the Stark splitting of the transition 4 I9=2 ! 4 G5=2 ; 4 G7=2 of Nd3‡ is not well resolved. The dependence of X2 on the intensity ratio IL =IS is therefore not clear. The spectral pro®le of the transition 4 I9=2 ! 4 F7=2 ; 4 S3=2 of Nd3‡ for di€erent Bi2 O3 concentrations is shown in Fig. 6. The relationship between the intensity parameter X6 and the intensity ratio IL =IS (IS ˆ 742 nm and IL ˆ 749 nm) is shown in Fig. 7.

Fig. 6. Variation of spectral pro®le of the transition 6 I9=2 ! 4 F7=2 ; 4 S3=2 of Nd3‡ with Bi2 O3 content in xBi2 O3 :…100 x†B2 O3 glasses.

X6 increases with IL =IS indicating an increase in covalency of the Nd±O bond. 4.4. Radiative transition probability and branching ratios Using Xt parameters, the radiative transition probability Arad for spontaneous emission, radiative lifetime of the excited state from which ¯uorescence is observed and branching ratios of Nd3‡ , Sm3‡ and Dy3‡ are calculated and presented in Tables 4, 5 and 6 for the 4 F3=2 , 4 G5=2 and 4 F9=2 levels, respectively. Arad , which depends on the intensity parameters and the refractive index n of the host material via the local ®eld correction, is found to increase with Bi2 O3 content, with a slope

412

M.B. Saisudha, J. Ramakrishna / Optical Materials 18 (2002) 403±417

Fig. 7. Variation of X6 with intensity ratio IL =IS of the transition 6 I9=2 ! 4 F7=2 ; 4 S3=2 of Nd3‡ ions in xBi2 O3 :…100 x†B2 O3 glasses.

change around 45±50 mol% Bi2 O3 for all the three ions (Figs. 8(a)±(c)). 5. Discussion 5.1. Hypersensitive transitions and the R±O covalency Jorgensen [30] has proposed that the positions of the hypersensitive bands change due to ``nephlauxetic'' e€ect. The nephlauxetic e€ect [31]

arises from an expansion of the partially ®lled fshell due to charge transfer from the ligands to the core of the central ion. Hence, this e€ect may be used as a measure of the covalency of the bonds between the rare earth ion and the surrounding oxygens in the glass. With increase in the overlap of the oxygen orbitals and the 4f orbitals, the energy level structure of the rare earth ion contracts, and leads to a shift of hypersensitive bands towards longer wavelength (lower energies). Henrie and Choppin [28] have reported that in halide complexes [NdI3 (gas), NdBr3 (liq), NdI3 (sol), Nd[EDTA]] the degree of covalency of the Nd±O bond increases in the order Cl < Br < I, as indicated by the shift of the peak wavelength of the hypersensitive transition of Nd3‡ to longer wavelengths. In bismuth borate glasses, the peak wavelength of the hypersensitive transitions for all the three ions shifts towards longer wavelengths with Bi2 O3 content, indicating an increasing covalent nature for the R±O bond. Here, close packing of the structure takes place with the formation of BO4 and BiO4 units and results in increased interaction between the rare earth and charged non-bridging oxygens (NBO). Bi2 O3 is a strong network former and oxygens are packed closely in bismuth borate matrix [32]. As pointed out earlier [29], the intensity of the transition 4 I9=2 ! 4 G5=2 ; 2 G7=2 is mainly determined by X2 jhkU …2† kij2 and the intensity of the transition 2 4 I9=2 ! 4 F7=2 ; 4 S3=2 by X6 jhkU …6† kij . It is observed that the dependence of the intensity parameter X2 on the intensity ratio IL =IS of the transition 4 I9=2 ! 4 G5=2 ; 2 G7=2 could not be ascertained due to poor resolution of the crystal ®eld split levels,

Table 4 Radiation transition probability Arad , radiative lifetime sR and branching ratios bR of Nd3‡ (3 mol%) in xBi2 O3 :…100 1

Transitions from 4 F3=2 !

m …cm †

4

5438 7500 9500 11 378

I15=2 I13=2 4 I11=2 4 I9=2 P A …s 1 † sR …ls† 4

x†B2 O3 glasses

BMN30

BMN40

BMN50

BMN60

A …s 1 † b

A …s 1 † b

A …s 1 † b

A …s 1 † b

33 644 2994 1809

41 812 3776 2290

50 987 4649 2944

57 1125 5305 3374

0.006 0.118 0.546 0.331

5480  58 182  2

0.006 0.117 0.546 0.331

6919  217 145  4

0.006 0.114 0.539 0.341

8630  264 116  4

0.006 0.114 0.538 0.342

9860  134 101  2

M.B. Saisudha, J. Ramakrishna / Optical Materials 18 (2002) 403±417

413

Table 5 Radiation transition probability Arad , radiative lifetime sR and branching ratios bR of Sm3‡ (3 mol%) in xBi2 O3 :…100 Transitions from 4 G5=2 !

m …cm 1 †

6

8690 9889 10 786 11 282 12 890 14 286 15 587 16 788 17 824

F9=2 6 F7=2 6 F5=2 6 F3=2 6 H13=2 6 H11=2 6 H9=2 6 H7=2 6 H5=2 P A …s 1 † sR …ls†

BBS30

BBS40

BBS50

x†B2 O3 glasses

BBS60

A …s 1 †

b

A …s 1 †

b

A …s 1 †

b

A …s 1 †

b

3.7 6.2 28 3.8 9.6 70 212 263 165

0.005 0.008 0.036 0.005 0.013 0.092 0.278 0.346 0.216

4.9 8.7 36 4.9 13 98 286 363 230

0.005 0.008 0.035 0.005 0.012 0.094 0.274 0.348 0.220

4.9 9.8 36 4.6 16 111 301 419 260

0.004 0.008 0.031 0.004 0.013 0.095 0.259 0.361 0.224

4.9 11.8 36 4.2 19 134 329 508 314

0.004 0.009 0.027 0.003 0.014 0.098 0.242 0.374 0.231

761  10 1315  17

1043  16 959  14

1163  28 860  21

1361  33 735  18

Table 6 Radiation transition probability Arad , radiative lifetime sR and branching ratios bR of Dy3‡ (1.5 mol%) in xBi2 O3 :…100 Transitions from 4 F9=2 !

m (cm 1 )

6

21 217 17 756 15 422 13 559 12 139 11 082 10 221 8812

H15=2 6 H13=2 6 H11=2 6 H9=2 6 H7=2 6 H5=2 6 F7=2 6 F5=2 P A …s 1 † sR …ls†

BBD30

BBD40

BBD50

x†B2 O3 glasses

BBD60

A …s 1 †

b

A …s 1 †

b

A …s 1 †

b

A …s 1 †

b

235 805 78 20 22 4.6 6.1 8.7

0.199 0.683 0.066 0.017 0.019 0.004 0.005 0.007

359 1217 118 30 31 6.2 8.5 13.1

0.201 0.683 0.066 0.017 0.017 0.003 0.005 0.007

500 1637 157 40 43 8.8 11.9 17.3

0.207 0.678 0.065 0.017 0.018 0.004 0.005 0.007

586 1885 180 44 43 7.5 11.4 19.8

0.211 0.679 0.065 0.016 0.016 0.003 0.004 0.007

1179  30 848  45

whereas X6 increases with increase of IL =IS of the transition 4 I9=2 ! 4 F7=2 ; 4 S3=2 . Increase of IL =IS indicates an increase in the covalency of the Nd±O bond. Since the intensity of the transition 4 I9=2 ! 4 F7=2 ; 4 S3=2 is determined by X6 , it is an indicator of the covalency of the R±O bond. It is interesting to compare the behaviour of X2 and X6 of Nd3‡ in other glass matrices ± like lead borate [33], alkali silicate and alkali borate glasses [1]. In Nd3‡ doped alkali silicate and borate glasses, the dependence of X2 on the intensity ratio is very small. This implies that X2 is dominated by crystal ®eld parameters rather than the covalency parameter. In lead borate glasses the variation of X2 with the intensity ratio is not clear due to the poor resolution of the Stark splitting. However, X6 is found to in-

1781  25 561  46

2415  40 414  52

2777  10 360  40

crease with increase of IL =IS (which increases with modi®er content) in lead borate, alkali silicate and alkali borate glasses. This indicates an increase in the covalency of the Nd±O bond with Bi2 O3 content. 5.2. Intensity parameters The covalency of the R±O bond increases with increase in Bi2 O3 content as indicated by the shift of the hypersensitive bands towards longer wavelengths, by the increase in the intensity of the transition 4 I9=2 ! 4 F7=2 ; 4 S3=2 . This implies that N…s; t† increases with Bi2 O3 content. The intensity parameter X2 is found to decrease with increase of Bi2 O3 content for Nd3‡ and Sm3‡

414

M.B. Saisudha, J. Ramakrishna / Optical Materials 18 (2002) 403±417

Fig. 9. Proposed rare earth site model. represent nearest oxygen neighbours surrounding the rare earth.

Fig. 8. Variation of Arad with Bi2 O3 content in (a) Nd3‡ , (b) Sm3‡ and (c) Dy3‡ ions doped in xBi2 O3 :…100 x†B2 O3 glasses.

(Figs. 2(a) and (b)). This indicates that As;p should decrease with increase of Bi2 O3 so that X2 can decrease, though N…s; t† increases (see Eq. (7)). Addition of Bi2 O3 to B2 O3 converts three-coordinated boron …B3 † to four-coordinated boron …B4 †, resulting in the conversion of boroxol units to pentaborate groups [32]. The fraction of B4 in the form of diborate units is maximum around 40 mol% in bismuth borate glasses. With further addition of Bi2 O3 to B2 O3 , back-conversion of B4 to B3 takes place with the formation of non-bridging oxygens. It has been proposed [34] that in oxide glasses, a rare earth ion is surrounded by eight neighbouring oxygens belonging to the corners of BO4 , BiO4 or any other glass-forming tetrahedra (Fig. 9). Each tetrahedron donates two oxygen atoms, forming an edge of the cube. Bi2 O3 can form its own network without involving the borate groups. The presence of oxygen not bonded to any boron as in 3Bi2 O3 :5B2 O3 supports this conclusion

[35]. The monotonic decrease of X2 and hence the asymmetry of the crystal ®eld at the rare earth site with increase in Bi2 O3 content for Nd3‡ and Sm3‡ indicates that the rare earth ions in bismuth borate glasses might be surrounded only by bismuth groups and due to this the appearance and disappearance of borate groups do not a€ect the symmetry of the ligand ®eld at the rare earth site. The intensity parameter X2 of Dy3‡ in bismuth borate glasses increases signi®cantly with Bi2 O3 content (Fig. 3(c)). This implies that X2 is mainly dependent on N…s; t† rather than As;p . As 4f electrons in the rare earth atoms are well shielded by outer 5s and 5p shells, the e€ective nuclear charge increases with increasing atomic number from Nd to Dy, causing a reduction in the size of the 4f shell and a decrease in atomic or ionic radius from Nd  to 0.91 A).  Consequently, the Dy±O to Dy (1 A distance is smaller than Nd±O or Sm±O distances. This leads to stronger nephlauxetic e€ect, and an increase of X2 . The X4 parameter for all the three ions increases slightly up to 40±45 mol% Bi2 O3 and then decreases. This behaviour of X4 could not be attributed to either As;p or N…s; t† independently. It must be dependent on both terms. As mentioned earlier,

M.B. Saisudha, J. Ramakrishna / Optical Materials 18 (2002) 403±417

with the addition of Bi2 O3 , B3 groups get converted progressively to B4 groups till about 40 mol% Bi2 O3 and B4 to B3 back-conversion takes place thereafter. Thus increase of X4 till about 40± 45 mol% Bi2 O3 shows that it depends mainly on N…s; t† (R±O covalency) in this composition range and thereafter X4 decreases implying that it depends more on As;p (crystal ®eld asymmetry). X6 increases with increase in Bi2 O3 content for all the three ions (Figs. 4(a)±(c)). This indicates that N…s; t† is responsible for the increase and that the strength of the covalency of the R±O bond increases with Bi2 O3 content. The nephlauxetic e€ect and the electrostatic interaction between rare earth ions and NBOs are the two factors which increase the covalency of the R±O bond. Thus in Nd3‡ and Sm3‡ doped bismuth borate glasses, only As;p plays an important role in the variation of X2 with Bi2 O3 content, while in Dy3‡ doped glasses, only N…s; t† is dominant in determining X2 . X6 mainly depends on N…s; t† for all the three ions. Generally, it is observed that in silicate and borate glasses [2,6,7,36,37], X2 is determined by the asymmetry of the ligand ®eld at the rare earth site (i.e. As;p ) and the nephlauxetic e€ect ‰N…s; t†Š, while, X6 depends only on the nephlauxetic e€ect. On the other hand in phosphate glasses, all the three parameters depend strongly on the ionic radius of the modi®er [1].

415 2

This introduces a factor n…n2 ‡ 2† =9 in the radiative transition probability in Eq. (8) and 2 …n2 ‡ 1† =9n in the stimulated emission cross-sections …r† of the ¯uorescence lines of rare earth ions. Since n ranges from 1.9 to 2.3, the factor n…n2 ‡ 2†2 =9 in the radiative transition probability ranges from 4 to 9. Because of the strong dependence on refractive index the radiative decay rates for equal Xt values can be signi®cantly different. Because of large values of Arad , r is quite high for the lasing transitions of the rare earth ions in bismuth borate glasses. r is given by r…aJ ; bJ 0 † ˆ

k4p Arad …aJ ; bJ 0 †; 8pcn2 Dkeff

…18†

where kp is the peak wavelength of the ¯uorescence line of rare earth ions. Dkeff is the e€ective bandwidth of the ¯uorescence line. r for the ¯uorescence lines of Nd3‡ , Sm3‡ and Dy3‡ ions in bismuth borate glasses is calculated from the

5.3. Radiative transition probability for electric dipole emission and branching ratios The radiative transition probability in bismuth borate glasses is large and the refractive index of the host glass plays a dominant role. Refractive index n of the bismuth borate glasses increases with Bi2 O3 content from 1.9 to 2.3 as shown in Tables 1±3. The increase of Arad with n can be explained as follows: the ratio of the e€ective ®eld at the ion site in the glass to the applied ®eld Eo in the simple isotropic tight binding approximation is given by [38] Eeff  1 ‡ 1=3…n2 Eo

1† ‡   

…17†

Fig. 10. Lasing transitions of (a) Nd3‡ …4 F3=2 ! 4 I11=2 †, (b) Sm3‡ …4 G5=2 ! 4 H7=2 † and (c) Dy3‡ …4 F9=2 ! 6 H13=2 † ions in xBi2 O3 :…100 x†B2 O3 glasses.

416

M.B. Saisudha, J. Ramakrishna / Optical Materials 18 (2002) 403±417

¯uorescence spectra using radiative transition probability. The stimulated emission cross-section of the ¯uorescence line of Nd3‡ ions in bismuth borate glasses [39] has been calculated and is found to be large. The large stimulated emission cross-sections are attractive features for low-threshold, high-gain applications and are utilized to obtain CW laser action. In tellurite glasses [40] and the lead borate glasses [33], doped with Nd3‡ , the radiative transition probabilities are large and hence the stimulated emission cross-sections. Laser action has been observed in tellurite systems. The radiative transition probabilities in bismuth borate glasses are of the order of those reported in tellurite glasses and hence can be utilized as laser host material. In bismuth borate glasses, large quantities of rare earth ions can be doped and, therefore, can be utilized for high-concentration mini-lasers. The branching ratios are evaluated for each transition and probable lasing transitions of the rare earth ions are as shown in Figs. 10(a)±(c). The branching ratios of the lasing transitions are high compared to other transitions. 6. Conclusions Using the Judd±Ofelt theory, the three intensity parameters, spontaneous emission probabilities and radiative lifetimes of Nd3‡ , Sm3‡ and Dy3‡ ions doped in bismuth borate glasses are determined. The changes in the position and the intensity parameters of the transitions in the optical absorption spectra of the ions are correlated to the structural changes in the host glass matrix. The shift of the hypersensitive bands of Nd3‡ (4 I9=2 ! 4 G5=2 ; 2 G7=2 ; 581.8 nm), Sm3‡ (6 H5=2 ! 6 F1=2 ; 1512 nm) and Dy3‡ (6 H15=2 ! 6 F11=2 ; 1268.8 nm) shows that the covalency of the R±O bond increases with increase of Bi2 O3 content, due to the increased interaction between rare earth ions and NBOs. The variation of the spectral pro®le of the transition 4 I9=2 ! 4 F7=2 ; 4 S3=2 also indicates an increase in the covalency of the R±O bond. The variation of the intensity parameter X2 with Bi2 O3 content for Nd3‡ and Sm3‡ implies that As;p play an important role in determining the inten-

sity, while in Dy3‡ doped bismuth borate glasses nephlauxetic e€ect plays a dominant role. X6 mainly depends on nephlauxetic e€ect …N…s; t†† for all the three ions. The radiative emission probability for all the three ions is high as in tellurite glasses, which have been successfully used as laser host material. This indicates that the bismuth borate glasses may also be useful as laser host material.

Acknowledgements The authors gratefully acknowledge Prof. Y.V.G.S. Murthy for extending the experimental facilities and for fruitful discussions

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