Effect of ZnO and Bi2O3 addition on linear and non-linear optical properties of tellurite glasses

Journal of Non-Crystalline Solids 353 (2007) 333–338 www.elsevier.com/locate/jnoncrysol

Effect of ZnO and Bi2O3 addition on linear and non-linear optical properties of tellurite glasses E. Yousef a, M. Hotzel b, C. Ru¨ssel a

c,*

Department of Physics, Faculty of Science, Al-Azhar University, Assiut, Egypt b Institut fu¨r Optik und Quantenelektronik, Jena University, Jena, Germany c Otto-Schott-Institut, Jena University, Jena, Germany Received 21 June 2006; received in revised form 6 December 2006 Available online 1 February 2007

Abstract Glasses in the system TeO2–Bi2O3–ZnO were studied with respect to their linear refractive indices and optical absorption in the UV– vis range. The third order non-linear refractive indices were measured using degenerated four wave mixing (DFWM). The optical Kerr susceptibilities calculated hereof were in the range from 5.49 to 6.58 · 1013 esu and hence 34–41 times larger than that of fused SiO2. They are roughly proportional to values theoretically calculated by the theory of Lines.  2006 Elsevier B.V. All rights reserved. PACS: 61.43.Fs; 81.05.Kf; 78.20.Ci Keywords: Non-linear optics; Tellurites

1. Introduction In the two past decades, tellurite glasses have attracted a great deal of interest [1–7], due to their potential use as fiber amplifiers and non-linear optical devices [3–7]. The latter is caused by the high non-linear refractive index. For the determination of non-linear refractive indices, various methods such as three wave mixing, four wave mixing and z-scan have been used [1]. The linear refractive indices of tellurite glasses are also notably large and usually in the range from 1.95 to 2.3 [2,8]. While pure TeO2 can only be obtained by rapid quenching, e.g. by twin roller techniques, binary or multinary TeO2-based glasses exhibit fairly large glass forming ranges. Especially glasses containing heavy metal oxides have been reported to possess a high degree of optical non-linearity [2–7]. The addition of highly polarizable components, such as Nb2O5 or PbO increases the optical non*

Corresponding author. Tel.: +49 3641 636105; fax: +49 3641 948502. E-mail address: [email protected] (C. Ru¨ssel).

0022-3093/$ - see front matter  2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2006.12.009

linearity. It was reported that such additions lead to remarkable changes in the physical, especially the optical properties [4]. For example the electron phonon interaction [9] gives a contribution to the third order optical susceptibility in ternary tellurium containing glasses. Tellurite glasses, therefore, are regarded as promising optical materials for up conversion laser and non-linear optical materials, which exhibit high third order nonlinear optical susceptibilities [3–6]. This paper provides a study on the preparation and the linear as well as non-linear optical properties of glasses in the system TeO2/Bi2O3/ZnO.

2. Theory Generally, the polarization, P, of a material at high light intensities is given by P¼

1 X n¼1

vðnÞ  E

ð1Þ

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with E = electric field and v(n) the nth order optical susceptibility tensors. For an isotropic medium, v(2) is zero, and v(3) is given by vð3Þ ðx; x1 ; x2 ; x3 Þ ¼ N  f ðx1 Þ  f ðx2 Þ  f ðx3 Þ  cðx; x1 ; x2 ; x3 Þ

ð2Þ

with x = x1 + x2 + x3, N is the particle density, f(xn) are the local field vectors and c(x; x1, x2, x3) is the second molecular hyperpolarizability. The Kerr susceptibility v(3) is related to the non-linear refractive index defined by n ¼ n0 þ n2 I;

ð3Þ 2

n ¼ n0 þ n2 hE i

ð4Þ

with n0 = linear refractive index, I = light intensity and h i denotes the time average. The non-linear refractive index n2 in SI units can be transferred into n2 in the cgs system:  2 m 40p n2 n2 ½esu ð5Þ ¼ cn0 x with c = speed of light (3 · 108 m/s). The optical Kerr susceptibility v(3) is related to both the linear, n, and the non-linear refractive indices, n2: n0 vð3Þ ½esu ¼  n2 ½esu: ð6Þ 3p 3. Experimental Glasses with the compositions (95  x)TeO2 Æ 5Bi2O3 Æ xZnO (x = 15, 20 and 25) and 90TeO2 Æ 10Bi2O3 Æ xZnO (x = 15, 20 and 25) were prepared from reagent grade TeO2 (99.999, Ferak), Bi2O3 (99.9, Merck) and ZnO (99.5, Chemapot). The batches were placed in a gold crucible and heated at a temperature of 850 C. The melt was allowed to cool to 700 C and then cast in a graphite mould. Subsequently, the samples were transferred to an annealing furnace and kept at 250 C for 2 h. The furnace was then switched off and allowed to cool. From the glassy samples, prisms of the dimension 30 · 15 · 15 mm3 were cut. The prisms were ground and polished using water as a liquid component. The prisms were used to measure the linear refractive indices at wavelengths of 643.8, 589.3, 546.1, 479.98 and 435.8 nm using a precision goniometer (SGo 1.1, Pra¨zisionsmchanik Freiberg, Germany). The accuracy of the measurement is ±1 · 105. To measure non-linear refractive indices as well as absorption spectra, flat samples with a thickness of 1 mm were prepared. Degenerate four-wave mixing (DFWM) was applied to measure n2. The experimental setup used has already been described in Ref. [10]. A Ti sapphire laser system delivering 150 fs pulses of a wavelength of 800 nm was used. The pulse energies were in the range from 3 to 4 lJ with a repetition rate of 10 s1. Due to the small repetition rates and the short duration of the pulses, thermo optical effects are negligible. The DFWM setup used tuneable laser splitters, each of them consisted of a rotatory

half-wave plate and a glan prism. This enables an easy adjustment of the intensities of the three pump beams. Two of the pump beams were sent through delay stages. The first served to adjust the temporal overlap of two of the pump beams, whereas the second delay stage was tuned to set the third pump beam to a delay Dt in relation to the other two pulses. The three beams were focused onto the sample by a lens with the focal length of 12.5 cm. The angle between the pump beams was 4. All three beams had approximately the same intensity and were linearly polarized in the same direction. For each time delay, the measured signals were averaged over at least 30 laser pulses. In order to minimize the effect of pulse energy fluctuations, for each pulse, the DFWM signal was divided by a reference signal obtained by a reference detector measuring the pulse energy. For a Kerr like non-linearity and negligible absorption in the sample at the respective wavelength, the maximum DFWM signal intensity, IDFWM, is given by [11]: 2

I DFWM ¼ const

jvð3Þ j 2 3 L I ¼ const0 jn2 j2 L2 I 3 n4

ð7Þ

with I = intensity of the pump beams, L = length of the sample; the constant depends on the used definitions. The signal intensity depends on jn2j2 and hence no statement on the sign of n2 is possible. The signal intensity was references to a fused silica plate with a thickness of 517 lm, the jn2j values were calculated using Eq. (8): sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi I DFWMðsampleÞ jn2 ðsampleÞj ¼ jn2 ðref:Þj I DFWMðref:Þ  2 Lðref:Þ 1  Rðref:Þ  : ð8Þ LðsampleÞ 1  RðsampleÞ The last term in Eq. (8) introduces a correction of the reflection losses at the samples and reference surfaces (which are notably different for tellurite glass and fused silica). The reflectivity R was calculated from the linear refractive indices using Fresnel equation. The non-linear refractive index n2 of fused silica was assumed to be 3 · 1016 cm2/W [11]. Absorption spectra were recorded in the wavelength range from 200 to 3200 nm using a Shimadzu 3101PC spectrometer at samples with thicknesses of 1 and 11 mm. The 1 mm sample was located in the reference beam in order to eliminate reflection losses which depend on the linear refractive index. The densities were measured by a helium pycnometer (AccuPyc 1330) with an accuracy of ±0.03%. 4. Results The densities of the as prepared glasses are summarized in Table 1, column 5. They are all in the range from 5.87 to 6.27 g · cm3. The density increases with increasing Bi2O3 and ZnO concentrations. The linear refractive indices measured for various wavelengths as well as the Abbe numbers

E. Yousef et al. / Journal of Non-Crystalline Solids 353 (2007) 333–338

335

Table 1 Densities, linear refractive indices and Abbe numbers of the studied glasses Sample

Density in g/cm3

Composition TeO2

A B C D E F

Bi2O3

80 75 70 75 70 70

5 5 5 10 10 10

ZnO

15 20 25 15 20 25

5.870 5.898 5.951 6.090 6.160 6.267

Linear refractive indices at

Abbe number td

643.8 nm

589.3 nm

546.06 nm

479.98 nm

435.8 nm

C0

D

e

F0

g

2.1387 2.1209 2.103 2.161 2.1452 2.1284

2.1543 2.136 2.118 2.178 2.1612 2.144

2.1698 2.151 2.132 2.195 2.1773 2.1596

2.2064 2.1861 2.165 2.234 2.2149 2.196

2.2452 2.2234 2.201 2.275 2.2554 2.235

Error

±0.0002 ±0.0002 ±0.001 ±0.001 ±0.0002 ±0.001

17.05 17.4 18.03 16.12 16.7 16.9

Error in density: ±0.001.

calculated hereof are summarized in Table 1, columns 6–11. The refractive indices are in the range from 2.1 to 2.275 and increase with increasing Bi2O3 and decreasing ZnO concentrations. The Abbe numbers te ¼ ðnC  1Þ= ðnF0  nC0 Þ are in the range from 16.9 to 18. Fig. 1 shows a plot of (aht)1/2 versus ht (with a = polarizability) for all glasses studied. From the linear correlations observed, the optical band gap energy, Eg, can be calculated from Tauc equation [12]:

2.50

2.00

Ln (α)

1.50

2

aðtÞ ¼

ðht  Eg Þ : ht

1.00

ð9Þ

0.8TeO 2 - 0.5Bi 2 O3 - 0.15 ZnO 0.75TeO 2 - 0.5Bi 2 O3 - 0.2 ZnO 0.7TeO 2 - 0.5Bi 2 O3 - 0.25 ZnO

The optical band gab energies, Eg, lie in the range from 2.57 to 2.63 eV. In Fig. 2, a plot ln(a) versus ht is shown. The observed linear correlations enable the calculation of Urbach energies, DE [13]: ht : ð10Þ DE Optical band gap energies, Eg and Urbach energies are summarized in Table 2, columns 2 and 3, respectively.

0.7TeO 2 - 0.1Bi 2 O3 - 0.2 ZnO 0.65TeO 2 - 0.1Bi 2 O3 - 0.25 ZnO

0.00 2.80

ln a ¼

6.00

3.10

Fig. 2. Plot of lna versus ht, symbols see Fig. 1. Lines: regression lines (all regression coefficients > 0.99).

0.75TeO 2 - 0.5Bi 2 O3 - 0.2 ZnO 0.7TeO 2 - 0.5Bi 2 O3 - 0.25 ZnO

Sample

Optical band gab energies in eV

0.7TeO 2 - 0.1Bi2 O3 - 0.2 ZnO

) 1/2 (cm -1/2 eV 1/2 )

3.00

Energy (eV)

0.75TeO 2 - 0.1Bi 2 O3 - 0.15 ZnO

5.00

2.90

Table 2 Optical band gap energy (see Eq. (9)), Urbach energies (see Eq. (10)), Sellmeier gap energy and dispersion energy (see Eq. (11))

0.8TeO 2 - 0.5Bi 2 O3 - 0.15 ZnO

5.50

0.75TeO 2 - 0.1Bi 2 O3 - 0.15 ZnO

0.50

0.65TeO 2 - 0.1Bi 2 O3 - 0.25 ZnO

A B C D E F

4.50

4.00

3.50

(

Error

3.00

Urbach energies in eV

Sellmeier gap energy in eV

Dispersion energy in eV

2.63 2.63 2.63 2.57 2.63 2.63

0.066 0.065 0.065 0.054 0.065 0.064

6.46 6.53 6.63 6.33 6.39 6.44

21.01 20.85 20.77 21.06 20.89 20.69

±0.01

±0.001

±0.02

±0.05

2.50

2.00 2.70

2.75

2.80

2.85

2.90

2.95

3.00

3.05

3.10

Energy (eV) Fig. 1. Plot of (aht)1/2 versus ht: (s) sample A, () sample B, (h) sample C, ($) sample D, (·) sample D and (n) sample F. Lines: regression lines (all regression coefficients > 0.99).

In Fig. 3, DFWM measurements of samples B and C as well as of a fused silica reference sample are shown. Fig. 4 shows DFWM measurements for samples A and E as well as for the fused silica sample. The lines drawn are attributed to a least squares fit of a Gaussian shape. As shown in Figs. 3 and 4, the curves exhibit symmetrical shape. Thus, the process responsible for the optical non-linearity

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E. Yousef et al. / Journal of Non-Crystalline Solids 353 (2007) 333–338

ica was assumed to be 3 · 1016 cm2/W). They all lie in the range from 5.1 to 5.9 · 1015 cm2/W. In Table 3, column 3, v(3) values calculated from the respective jn2j values using Eq. (6) are summarized.

DFWM-signal [arbitrary units]

3.0 2.5 2.0

5. Discussion

1.5

The dependency of the linear refractive index on the photon energy, E = ht, can be described by the Sellmeier gap energy, ES, and the dispersion energy, Ed [5,14]:

1.0 0.5

1 ES E2 ¼  : n2 ðEÞ  1 Ed ES  Ed

0.0 -1500

-1000

-500

0

500

1000

1500

Δt [fs]

Fig. 3. Degenerated four wave mixing measurements of (s) fused silica reference sample, () sample B and (j) sample C. The signal of fused silica is multiplied by the factor of 100 for better visibility.

DFWM-signal [arbitrary units]

3.0 2.5 2.0 1.5 1.0 0.5 0.0

-1500

-1000

-500

0

500

1000

1500

Δt [fs]

Fig. 4. Degenerated four wave mixing measurements of (n) fused silica reference sample, (j) sample A and (s) sample E. The signal of fused silica is multiplied by the factor of 100 for a better visibility.

ð11Þ

Fig. 5 shows a plot of 1/(n2(E)  1) versus E2 for the samples studied. From the linear regression, values of ES and Ed are obtained. They are summarized in Table 2, columns 4 and 5. The values of ES are in the range from 6.33 to 6.63 eV and those of Ed in the range from 20.69 to 21.06 eV. The values for both ES and Ed are in a fairly narrow range and do not vary systematically with composition. In the plot (aht)1/2 versus ht (see Fig. 1), linear correlations were observed for all glasses studied. This is evidence for a direct transition responsible for the UV cut off. The optical band gap energies calculated from this plot are in the range from 2.57 to 2.63 eV. Optical band gap energies reported in the literature are mostly in the range of 2.8– 3.5 eV [15–19]. For binary TeO2–WO3 [17], TeO2–ZnO and TeO2–Nb2O5 [18] glasses values of around 3.45 and 3.1 eV were respectively obtained. Adding alkali oxides to the TeO2–Nb2O5 glasses resulted in a decrease of the optical band gap energies of 2.7–3 and 3.1–3.3 for Na2O [16] and Li2O [18], respectively. The optical band gab energies of the studied TeO2–Bi2O3–ZnO system are hence smaller than those reported up to now in the literature for comparable tellurite glasses. By analogy, the values for the

is fast in comparison to the duration of the laser pulses. The signal intensity of the tellurite glasses is 250–300 times larger than that of fused silica. In Table 3, column 2, nonlinear refractive indices which were calculated from the DFWM signals using Eq. (7) are shown (jn2j of vitreous silTable 3 Non-linear refractive indices, experimental Kerr susceptibilities v(3) and v(3)/d2 theoretically calculated from Eq. (12) Sample A B C D E F Error

jn2j in 1015 cm2/W 5.1 5.2 5.1 5.4 5.9 5.7 ±0.05

v(3) in 1013 esu 5.66 5.69 5.49 6.11 6.58 6.27 ±0.05

v(3)/d2 calculated (Eq. (12)) in ˚2 1012 esu/A 2.62 2.42 2.22 2.94 2.73 2.55

Fig. 5. The dependency of the refractive indices as a function of the photon energy (illustrated as 1/(n2  1) versus (ht)2: (d) sample A, (j) sample B, () sample C, (s) sample D, (h) sample E and () sample F. Lines: regression lines (all regression coefficients > 0.9995).

E. Yousef et al. / Journal of Non-Crystalline Solids 353 (2007) 333–338

Urbach energy which are in the range from 0.054 to 0.066 eV are smaller than reported for other glass systems, such as TeO2–Na2O–Nb2O5 [19], TeO2–Nb2O5 [20] or TeO2–PbO [21]. The Urbach energy is caused by the band tails associated with the valence and conduction bands extending into the band gap. This is attributed to the fluctuation of internal fields due to the disordered structure in non-crystalline materials. Here, the Urbach energy corresponds to the width of localized states and hence is a measure for the disorder in amorphous solids. Glasses with smaller Urbach energies hence have a smaller tendency for bond rupture and defect formation [22,23]. According to the theory of Lines [24,25], the non-linear optical susceptibility of metal oxides depend on the linear refractive index, the photon energy of the light used as well as on the Sellmeier gap energy, ES. Additionally, it is affected by the Te–O bond length in the respective glass composition v

ð3Þ



n2 ðEÞ þ 2 ¼K 3

3 

ðn2 ðEÞ  1ÞE6S ðE2S  E2 Þ4

 d 2;

ð12Þ

where d is the metal oxygen bond length and K is ˚ 2. 0.26 · 1012 esu eV2 A According to Kim et al. [5], this concept, developed for crystalline oxides, is also valid for tellurite glasses. Since d is not known exactly, in Table 3 column 4, v(3)/d2-values are summarized for the respective glass compositions. Kim et al. [4] inserted as Te–O bond length for glasses in ˚ which is reported to the system La2O3–TeO2: d = 2.01 A be equivalent to that of the Te–O bond for the calculation of v(3) values. Fig. 6 shows a plot of the experimental v(3) values against the v(3)/d2 values, theoretically calculated using Eq. (12). The solid line is a regression line drawn through the origin. The measured v(3) values are roughly propor-

Fig. 6. Experimental optical Kerr susceptibility v(3) as a function of v(3)/d2 calculated using Eq. (12): (s) samples A–C (5 mol% Bi2O3) and (d) samples D–F (10 mol% Bi2O3). Solid line: regression line through the origin (regression coefficient 0.982).

337

tional to the calculated ones. The slope of the drawn regres˚ 2. The v(3)-values measured are 34–41 times sion line is 2.3 A larger than that of fused silica. The variations of the physical properties with the glass composition should be due to the respective glass structure. In principle, the structure of pure TeO2 glass is composed of TeO4 trigonal bipyramids (tp) with two axial positions occupied by oxygens and two oxygens in equatorial positions. The axial Te–O bonds are somewhat longer than the equatorial ones. The third equatorial position is occupied by a lone pair of electrons. If network modifying oxides, such as ZnO are added, non-bridging oxygens are formed and the TeO4 trigonal bipyramids are transferred into TeO3 trigonal pyramids (tp) [25–29]. Here, the lone pair occupies the apex of the sp3 hybrid orbital. The electronic transition which gives rise to the high non-linear refractive index is that from the non-bonding O2pp orbital to the empty non-bonding Te5d orbital [15]. The effect of conditional glass formers, such as WO3 or V2O5 is reported to be qualitatively the same as that of network modifiers, however, the effect is not as pronounced [30,31]. From wide angle X-ray and neutron scattering, it is known from different systems, such as TeO2/V2O5 [28] or TeO2/Nb2O5/ZnO [29], that the Te–O bond lengths are different; one Te–O ˚ ) than the other two or three Te–O bond is shorter (1.9 A ˚ ). bonds (2–2.1 A The formation of non-bridging oxygen by introducing ZnO is also seen in the increase in density, which is evidence for a more compact glass structure. With increasing ZnO concentration, the linear refractive index decreases for all glasses studied. The non-linear refractive index remains the same within the limits of error (5 mol% Bi2O3) or increases (10 mol% Bi2O3). Since the density of the glass increases, the decrease in the linear refractive index should be due to the low polarizability of Zn2+. Increasing the Bi2O3 concentration from 5 to 10 mol% results in a notable increase in the density, the linear and non-linear refractive indices. This is caused by the high polarizability of the Bi3+ ion. However, as noted above, the increase in the Bi2O3 concentration should also result in the transfer of TeO4 trigonal bipyramids into TeO3 trigonal pyramids. Since this effect should be more pronounced in the case of ZnO (as noted above), it is supposedly not responsible for the increase in the non-linear refractive indices. It should be noted that the effect of increasing ZnO and Bi2O3 concentrations is also seen in the v(3)/d2 values calculated by Eq. (12) (see Table 3, column 4). In principle, the slope of the regression line in Fig. 6 enables the calculation of the Te–O bond length. The result ˚ ), however, is not within the of this calculation (d = 1.52 A range, Te–O bond lengths are expected. As mentioned ˚ above, Kim et al. assumed a Te–O bond length of 2.01 A and inserted this bond length into Lines equation. The ˚ , while that of length of the Bi–O bond is around 2.4 A ˚ for four the Zn–O bond was reported to be 2.03 and 2.15 A and sixfold coordination, respectively. Hence, the variation ˚ ) and of the bond lengths is comparably small (2.20 ± 0.2 A

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E. Yousef et al. / Journal of Non-Crystalline Solids 353 (2007) 333–338

all Me–O bonds occurring in the investigated glass are far ˚. larger than 1.52 A In this context, is should be noted that v(3) can only roughly be estimated from Eq. (12). In our case there seems to be a systematic error. Assuming a more realistic Te–O ˚ , the calculated v(3)-values are in the bond length of 1.9 A average around 57% larger than the measured ones. As recently noted, also the wavelength dependency of v(3) is not correctly given by Eq. (12) [10] as illustrated for the system TeO2–WO3–ZnF2. 6. Conclusions The studied TeO2–Bi2O3–ZnO system shows high linear refractive indices in the range of 2.1–2.25. The experimental Kerr susceptibilities are in the range of 5.49– 6.58 · 1013 esu. They increase with increasing Bi2O3 concentration. Kerr susceptibilities calculated with Lines’ equation are more than 50% larger than the experimentally determined ones. The studied glasses show optical band gap energies in the range from 2.57 to 2.63 eV and Urbach energies which lie between 0.054 and 0.066 eV. Both optical band gap and Urbach energy are smaller than for other glass systems reported in the literature up to now. This indicates low defect concentrations. References [1] E.M. Vogel, M.J. Weber, D.M. Krol, Phys. Chem. Glasses 32 (1991) 231. [2] R. El-Mallawany, Handbook of Tellurite Glasses, Physical Properties & Data, RC Press, Boca Raton, 2002. [3] H.G. Kim, T. Komatsu, K. Shioya, K. Matusita, K. Tanaka, K. Hirao, J. Non-Cryst. Solids 208 (1996) 303.

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