Linear and non-linear optical study of fluorotellurite glasses as function of selected alkaline earth metals doped with Er3+

Optics and Laser Technology 111 (2019) 184–190

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Linear and non-linear optical study of fluorotellurite glasses as function of selected alkaline earth metals doped with Er3+

T

⁎

I. Fuks-Janczareka, R. Miedzinskia, , M. Rebenb, El Sayed Yousefc,d a

Faculty of Mathematics and Natural Science, J. Dlugosz University in Czestochowa, Al. Armii Krajowej 13/15, Czestochowa, Poland Faculty of Materials Science and Ceramics, AGH - University of Science and Technology, al. Mickiewicza 30, 30-059 Cracow, Poland c Research Center for Advanced Materials Science (RCAMS), King Khalid University, Abha 61413, P. O. Box 9004, Saudi Arabia d Physics Dep., Faculty of Science, King Khalid University, P. O. Box 9004, Abha, Saudi Arabia b

H I GH L IG H T S

of the NLO susceptibility by changing the alkaline metals content. • Modification melt-quenching method gives a good quality optical materials. • Applied technique was used to determine the third order nonlinear susceptibility. • Z-scan • The Er ions in the host glass increases the third order NL susceptibility. 3+

A R T I C LE I N FO

A B S T R A C T

Keywords: Optical materials Alkaline earth metals Z-scan method Two photon absorption Rare earth ions Energy gap

A systematic characterization of optical and chemical properties of fluorotellurite glasses based on 70TeO2-5Mx Oy -10P2O5-10ZnO-5PbF2 glasses as function of alkaline earth metals as network modifiers were studied and analysed. The Z-scan results show that all the compounds have NLO properties such as nonlinear refractive index (n2 ) and two photon absorption (β ). Finally, using (n2 ) and (β ) we also determined the third-order nonlinear optical susceptibility χ 〈3〉. It was found that the alkaline earth metals elements, have an influence on such NLO properties. Based on the ability of the lattice modifiers to decrease the band-gap energy while simultaneously increasing the linear refractive index of the TeO2-based glass, we investigated how these modifiers affect the non-linear refractive index.

1. Introduction A large number of heavy-metal oxide (HMO) glasses doped with rare-earth (RE) ions have been studied for several decades and are still attracting interest from the basic point of view as well as for applications in lasers, amplifiers, displays, modulators, switches, optical limiters, and sensors, among other applications. Indeed, a variety of HMO glasses (e.g., tellurites [1], germanates and antimony [2]) still need to be studied with a focus on their large transmittance from the visible to the near-infrared, small phonon energies, large chemical stability, large acceptance of RE ions doping, and high non-linear (NL) optical response. Among the HMO used for photonics and telecommunication, the tellurium oxide glasses (TOG), apart from their high linear and NL refractive indices, show several advantages when compared with other glasses [3]. Tellurite matrices are characterized by the low phonon energy, high refractive index, good transparency at mid-infrared, good

⁎

thermal and chemical stability as well as high RE ion solubility. High third-order optical nonlinearities (TONL) of tellurite glasses is attributed to the high polarizability of a lone pair of electrons in the Te4+ ions, and a high percentage of TeO4 trigonal bipyramid (tbp) [4,5]. Tellurite glasses were rediscovered in 1952, but remained virtually unknown to materials and device engineers until 1994 when unusual spectroscopic, NL and dispersion properties of alkali and alkaline earthmodified tellurite glasses and fibres were reported. Detailed spectroscopic analysis of Pr3+, Nd3+, Er3+, and Tm3+ doped tellurite glasses revealed its potential for use in laser and amplifier devices for optical communication wavelengths [6–8]. In this study, we have used new tellurite matrices, namely the TeO2–P2O5-ZnO-PbF2 basic glass, modified with three alkaline earth metals undoped and doped with erbium ions. The alkaline earth metals are one group of elements on the periodic table. The elements (Mg - magnesium, Sr - strontium, Be - beryllium) located in Group IIA of the periodic table. Alkaline earth metals

Corresponding author. E-mail addresses: [email protected] (I. Fuks-Janczarek), [email protected] (R. Miedzinski), [email protected] (M. Reben).

https://doi.org/10.1016/j.optlastec.2018.09.041 Received 7 June 2018; Received in revised form 7 September 2018; Accepted 18 September 2018 0030-3992/ © 2018 Elsevier Ltd. All rights reserved.

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in their pure forms are generally shiny and silvery. They rarely occur in their pure form because they are highly reactive. Alkaline earth metals have two electrons in their outermost electron shell, which take relatively little energy to remove. They have smaller atomic radii than the alkali metals and have relatively low ionization energies in their first two electrons, because of which the, alkaline earth metals exist with a 2+ charge most of the time. They are most commonly found in ionic compounds or as ions [9]. The purpose of this work is to determine the NL refractive index of tellurite glass prepared with different lattice modifiers by using a nanosecond Z-scan technique. The relationship among the obtained nonlinear refractive index with the linear refractive index, two photon energy, band gap energy and glass structure are discussed. 2. Preparation of tellurium glasses The fluorotellurite glass compositions were designed based on the substitution of PbO with PbF2. With respect to the effective radius, fluorine (F) is the first element in the Halogen group (group 17) in the periodic table. It is the most electronegative element, given that it is the top element in the Halogen Group, and therefore is very reactive. This replacement in the glass structure can minimize the OH - ions absorption in the IR spectra at 2.8, 3.5 and 4.25 μ m. Glasses with the composition (z – 5) TeO2-5MxOy -10P2O5-10ZnO-5PbF2 in mol%, where Mx Oy =(MgO, SrO, BaO) as well as their counterparts doped with 600 ppm Er2 O3 , were prepared by mixing specified weights of raw materials [10]. To eliminate water or hydroxyl group, as, prepared glass batches were pre-heated at 200, 300 and 400 °C. The batches were melted in gold crucible in an electric furnace at 850 °C for 30 min. To improve glass homogeneity the melt was stirred during melting. The melt was poured out onto a graphite mould. Subsequently, the sample was transferred to an annealing furnace and kept for 2 h at 320 (below Tg−15 °C). Then the furnace was switched off and the glass sample was allowed to cool. The compositions of the glasses are listed in Table 1. Based on the XRD analysis of all the glasses obtained, it can be found that they are amorphous [11], this confirmed the literature statement that formation range of the tellurite glass system with potential M ions is wider than the borate or the silicate system and there is no immiscible range in these kind of glasses. Other laser induced properties of those glasses has been studied earlier. The mid-infrared spectroscopy, optical transmission, optical transmission, photoluminescence and photoinduced changes of diagonal piezooptics and NL optics refractive indices coefficient measurements of these materials has been studied by other authors [13].

Fig. 1. DSC curves of the obtained glasses. Table 2 Thermal characteristic of glasses.Tg - glass transition temperature, Cp - the specific heat, Tc - the onset of crystallization temperature. Sample

Tg [°C]

ΔCn [°C]

Tc [°C]

ΔTC [°C]

MgO MgO:Er2O3

352 356

0.167 0.158

457 466

105 110

SrO SrO:Er2O3

349 358

0.157 0.161

456 463

107 105

BaO BaO:Er2O3

349 355

0.154 0.162

455 461

106 106

presented in Table 2. In the present investigation, all of the glasses have an endothermic change between 349 °C and 356 °C, which is attributed to the glass transition temperature, Tg . It is worth noticing that under doping the glass transition temperature is shifted towards higher values. Glasses, during heating, demonstrates, apart from the thermal effects characteristic for typical phase transition occurring in glassy state, and additional exothermal effect connected with article [11]. The thermal stability parameter provides a good estimate of the tendency of the glass to crystallize. Based on thermal analysis (DTA) curves it can be found that the onset crystallization temperature of glasses with Er3+ ions in comparison to the glasses without RE is slightly shifted towards higher temperatures. This is evidence of the decreasing ability of the glass for crystallization, manifested by increased values of the index of thermal stability of the glass ΔT = (Tc−Tg ) .

3. Thermal stability of glasses

4. Linear optics studies

The studies of differential scanning calorimetry (DSC) have been performed to determine the thermal stability of the glasses obtained. DSC curves (see Fig. 1) for the studied glass with and without Er3+ dopant have been obtained to determine the glass transition temperature Tg values, the specific heat ΔCp accompanying the glass transition and the temperature exothermal events. The detailed results are

Optical absorption spectra of the examined glasses have been studied to determinate the linear absorption coefficient α (cm−1) and energy gap Eg (eV). First the transmittance spectra T (λ ) in range 200–1100 nm was determined based on reflectance R (λ ) spectrum [13]:

T (λ ) ≈ (1−R2 (λ ))expα (λ) d Table 1 Composition of examined glasses. Glass name

TeO2 (%)

Mx Oy

(1)

In equation above d is the sample thickness. Therefore, absorption spectrum is given by: P2O5 (%)

10ZnO (%)

PbF2 (%)

(%)

Er2O3 (ppm)

MgO MgO:Er2O3

70 70

5 MgO 5 MgO

10 10

10 10

5 5

0 600

SrO SrO:Er2O3

70 70

5 SrO 5 SrO

10 10

10 10

5 5

0 600

BaO BaO:Er2O3

70 70

5 BaO 5 BaO

10 10

10 10

5 5

0 600

α (λ ) =

1 (1−R2 (λ )) ln t T (λ )

(2)

The estimated absorption spectra are presented in Fig. 2. As we can see, absorption spectra for doped and undoped glasses can be detailed into three regions. The high absorption region covers the spectral range <480 nm. The second, absorption region covers spectral range 480–1060 nm. The last, transparent region begins from 1060 nm. The characteristic absorption peaks are detectable at 522, 654 and 973 nm 185

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Fig. 4. Tauc’s plot and calculated energy gap of the examined glasses.

Fig. 2. Optical absorption spectra of examined glasses.

and they are observably only for samples doped with Er2O3. Mentioned peaks corresponding to the transition 4I15/2 →2 H11/2 ,4 I15/2 →4 F9/2 and 4I 4 15/2 → I11/2 , respectively. For the high absorption region of semiconductor, the relation between absorption coefficient α and photon energy hν can be determined using Tauc’s relation [14]:

(αhν )1/ r = αt (hν−Eg )

(3)

where αt is the constant, also known as a band tailing parameter, r is the power factor of transition mode and Eg is an energy gap. The value of the r factor denotes the nature of the transition. For direct allowed transitions r is 1/2 , for direct forbidden transitions r is 3/2 , for indirect allowed transitions r is 2 and value r = 3 is adequate for indirect forbidden transitions. Hence, it is very important to verify the type of transition before the Tauc’s graphs are plotted. To be able to do that, therefore Eq. (3) should be rewritten as follows:

ln(αhν ) = r ln(hν−Eg ) + ln(αt )

Fig. 5. Plots of ln(α ) = f (hν ) (solid lines) allow to calculate the Urbach energy. Dashed lines represent the function ln(α ) = ln(αt ) + (hν/ Eu ) .

(4)

Linear approximation of the experimental results indicates the power factor of the transitions mode. The empirically estimated r factor for 70TeO2-5BaO-10P2O5-10ZnO-5PbF2 sample indicates direct allowed type of transition (r = 1/2 ). As we can see in Fig. 3, experimental data can be approximated using linear function:

ln(αhν ) = 0.476ln(hν−Eg ) + 4.976

Table 3 Linear optical properties of 70TeO2-X-10P2O5-10ZnO-5PbF2 glasses.

(5)

Alternatively, it is now possible to draw up an appropriated Tauc’s plots. As is shown in Fig. 4, the extrapolations of the straights region of the curves to the (αhν = 0) give the values of Eg for direct allowed transitions of the examined materials. The relationship between (α ) and (hν ) is known as the Urbach empirical rule, which is given by this exponential equation: α = αt ·exp(hν / EU ) ⇒lnα = lnαt + (hν / EU ) , where αt is a constant, hν is the incident photon energy and EU is the band tail

Compound

ρ [g/cm2]

n

α [cm−1]

Eg [eV]

EU [eV]

MgO MgO:Er2O3

5.1658 5.1678

2.28 2.29

0.97 4.83

3.45 3.37

0.18 0.27

SrO SrO:Er2O3

5.2073 5.2118

2.27 2.27

1.42 2.06

3.45 3.38

0.17 0.22

BaO BaO:Er2O3

5.2507 5.2517

2.29 2.29

1.03 1.23

3.46 3.44

0.16 0.18

with of the localized states in the optical system energy gap [15]. The behaviour of ln(α ) against hν near the absorption edge is shown in Fig. 5. In Table 3, we present several linear optical properties for tested glasses. We can see that linear refractive index (n) for all glasses is about ∼2.30. We must also focus on the fact that the linear absorption coefficient α for glasses with MgO doped Er2O3 is 4.83 (cm−1), which is the highest value among all the tested glasses. It is well known that band-gap energy Eg is an important parameter to describe the nature of the n2 and χ 〈3〉. Thus, the band gap energy of the glass was determined through the optical absorption coefficient α spectrum using the relation as described by Tauc et al. Fig. 4 shows a linear relation of (αhν )1/2 versus photon energy, which reveals the existence of non-direct optical transition. The obtained values of the band tail width Eg and Eu have been tabulated in Table 3. It is observed that, the values of Eg were decreasing and Eu were increasing with the addition of Er2O3.

Fig. 3. Plot of ln(αhν ) = r ln(hν ) + ln(αt ) . 186

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peak-valley distance ΔTp − v the phase distortion and next the n2 coefficient can be estimated using to the following relations:

ΔTp − v = 0.406(1−S )0.25|Δφ0 |

(13)

and

n2 =

5. Results and discussions As per the commonly known fact, the Z-scan technique devised by Sheik-Bahae et al. [16,17] has been widely used to measure the NL optical properties of material, due to its simplicity and high sensitivity. During a Z-scan measuring process, the nonlinear optical information could be obtained by moving samples and making the relative changes to the focal position of the scanning beam waist to measure the laser normalised transmittance in the far-field. This factor is particularly important for NL optical characterization, where relatively small intensity-dependent modifications in refraction and absorption must be transferred into measurable quantities. In other words, the sensitivity is the parameter describing the experimental ability for measuring small changes in physical quantities. In this paper, we use the classic Z-scan method for obtaining two photon absorption coefficient β , and a thirdorder NL refractive index, coefficient n2 . In this technique of which the setup is presented in Fig. 6 the sample moves along the Z axis from −z to + z points thorough the focal point z = 0 . Comparing a signals from D1 and D2 detectors, the light transmission of the sample S is estimated in the function of the z position. At the focal point, a light intensity I0 is the highest, and the NL optics effects are clearly observable. The sample’s absorption coefficient and refractive index at the focal point are: (6)

n = n 0 + n2·I0

(7)

χR(3) = 2n2 n 02 ∊0 c

q0

(F/m) represents electric permittivity, c is the where ∊0 = speed of light and λ represents the wavelength. Similarly, two photon absorption coefficient is related to the imaginary part of the third-order NL electric susceptibility:

χI(3) = (∊0 cλn02/3π ) β

Z2 ) Z02

can be evaluated when The third-order NL electric susceptibility both the real and imaginary parts are as follows:

χ (3) =

(χR(3) )2 + (χI(3) )2

(m2/V 2)

(17)

5.1. Nonlinearoptics measurements For the measurement of NL refractive index and NL absorption coefficients, Z-scan method has become a standard tool due to its simplicity, immediate indication of the sign type of nonlinearity and high sensitivity. The normalised change in transmitted intensity can be calculated using the following equation [3]. The NL absorption

(8)

to the experimental result, the β coefficient can be estimated. In Eq. (8) the q0 and Z0 has been represented as follows:

q0 = βI0 Leff

(16)

χ (3)

1

2 2 (1 +

(15)

8.85·10−12

where a 0 is the linear absorption coefficient and n 0 is the linear refractive index. Two photon absorption coefficient is calculated when the aperture S is open. Comparing the theoretical transmission curve:

T (Z ) ≈ 1−

(14)

where S is the fraction transmitted by the aperture. Peak to valley normalised transmittance difference Tp − v was calculated from fitted curves. We focused on sign of NL refraction index n2 of the prepared samples. This quantity is a very important parameter in NL optics and represents decrease or increase in the refractive index when the laser beam interacts with a medium. Laser Gaussian beam induced phase change when focused on the sample and third-order NL refractive index was calculated from signal detection and analysis. Nonlinear refractive index of samples have negative sign with 10−6 [cm2 /GW] order of magnitude. When the TPA provides a prevailing effect, the n2 index can be determined by division of the close and open aperture scans. In this way, the obtained plot can be described using Eq. (12). This situation is illustrated in Fig. 7. As we can see the close/open curve looks like a close aperture scan for materials without NL absorption β = 0 and with only Δn ≠ 0 . The relationship between NL refractive index and the real part of the third-order NL electric susceptibility has been demonstrated in given by the equation below [15]:

Fig. 6. Z-scan setup. BS- beam splitter, F - focusing lens, S - sample, A - aperture, D1 and D2 - detectors.

α = α 0 + β ·I0

λ Δφ0 2πI0 Leff

(9)

and

Z0 = πω02 / λ

(10)

where L is the thickness of the sample, ω0 is the beam waist radius at the focal point (z = 0), λ is the laser wavelength and the Leff is stated as follows:

Leff =

(1−exp−α0 L ) (11)

α0

The second NL optical parameter n2 , in accordance with SheikBahae et al., can be estimated in close aperture mode [16,17]. Close aperture transmittance curve is given in the following way:

T (Z , Δφ0) ≈ 1−

4Δφ0 x (x 2 + 9)(x 2 + 1)

(12)

In the equation above, Δφ0 is the phase distortion of laser Gaussian beam after being passed through the sample and x = z / z 0 . T (Z , Δφ0) plot is symmetrical with a characteristic peak and valley. Measuring the

Fig. 7. Z.-scan example curves. Dashed line - open aperture scan, dotted line closed aperture scan, solid line - closed/open. 187

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Table 4 Nonlinear optical properties of 70TeO2-X-10P2O5-10ZnO-5PbF2 glasses.

Fig. 8. Z.-scan curves for the glasses containing barium oxide with and without erbium oxide.

Compound

β [cm/ GW]

n2 × 10−6 [cm2/GW]

χR〈3〉 × 10−20 [m2/V2]

χI〈3〉 × 10−21 [m2/V2]

χ 〈3〉 × 10−20 [m2/V2]

MgO MgO:Er2O3

0.86 1.15

2.14 2.57

0.59 0.71

6.76 9.04

0.90 1.15

SrO SrO:Er2O3

0.86 0.96

2.15 2.58

0.60 0.72

6.76 7.54

0.90 1.04

BaO BaO:Er2O3

0.80 0.86

2.13 2.19

0.59 0.61

6.29 6.76

0.86 0.91

the examined fluorotellurite glasses are shown in Table 4. From the obtained results, we can see that in the case of two photons absorption and nonlinear refractive index increased addition of the RE ions. We could not identify the glass whose value would stand out greatly. However, in the case of n2, we see a significant pattern of values in the case of glass containing magnesium oxide. RE dopant induced an additional energy level in the glass system which was responsible for the NLO coefficients. [18–20]. As is shown in Fig. 3, the most probable type of transitions are directs allowed. The increase in of two photon absorption due to the additional erbium ions is associated with the transitions 2 H11/2 and 4 S3/2 to the ground state. Additional ions of Er2O3 in the host system with MgO, increase the TPA about 33%. The glasses with strontium oxide and barium oxide doped with erbium ions have the larger β of about 12% and 7% to compare with undoped glasses. Theoretical calculation presented in [21,22] shows that Eg of the single MgO complex is about 4.45–4.80 eV. This value correspond with two photons of the laser lights which were used in experiment (λ = 532 nm). Therefore, the larger TPA coefficient is observed for the glass with composition: 70TeO2-5MgO-10P2O5-10ZnO-5PbF2 + Er2O3. Additional erbium ions have an influence for the NL refractive index. Moreover, RE salts have considerable effect on the structural, optical, and thermal properties of many types of materials [23]. Er+3 doped material has attracted a lot of research interest due to its significant optical properties. In its trivalent state, at a wavelength of 1.52 μ m, it exhibits a 4 4 transition from its first excite state I13/2 to the ground state I15/2 [24]. +3 When Er is mixed with a host solid material, it induces mixing of states. These states will lead to new transitions due to the partially filled 4f shell is shielded by filled 5s and 5p shell [25]. For the glasses with MgO + Er2O3 and SrO + Er2O3 the n2 increased about 20% as compared to the system without the RE ions. In the case of the material with BaO, additional erbium ions increased the n2 index by about 3%. The obviously obtained n2 also affected χ 〈3〉, whose value for magnesium doped samples is almost twice as high as in modified glasses. Determination of the dispersion of the NL refractive index in solids is important not only from a fundamental point of view but also for practical applications. The solid curve in Fig. 11 shows the theoretical scaling of n2 calculated with an assumption of a simple two-parabolicband model. The NL index of refraction is determined from a KramersKrönig relation and is given by [26]:

Fig. 9. Z.-scan curves for the glasses containing magnesium oxide with and without erbium oxide.

Fig. 10. Z.-scan curves for the glasses containing strontium oxide with and without erbium oxide.

coefficient β is obtained from a best fitting performance of the open aperture measurement on the experimental and theoretical data. Measurements of the NL refractive index n2 were carried out with the traditional closed-aperture single beam using nanosecond laser pulses. Normalized transmittance signal in open and close aperture Z-scan setup is shown in Figs. 8–10. In these figures, we can see normalised transmittance as a function of distance along the Z axis for the fluorotellurite glasses based on 70TeO2-5Mx Oy -10P2O5-10ZnO-5PbF2:

• Fig. 8(a and b) represents the curves for two glasses modified by barium oxide and barium oxide with erbium oxide; Fig. • 9(a and b) demonstrates the results for glasses containing magnesium oxide with and without erbium oxide; • Fig. 10(a and b) shows the received data for glasses modified by

n2 (esu) =

strontium oxide with and without erbium oxide.

These figures represent the intensity dependent open and close aperture Z-scan curves with 532 nm at the iradiattion 2,5 GW/cm2 for Nd:Yag lasers with 5 ns pulses at a repetition rate of 7 Hz. As shown in the figures, matching the theoretical curves to the experimental results is definitely better for glasses without rare earth dopes. At this intensity, the NL behaviour of all the samples completely switches to reverse saturable absorption, which indicates that the free carrier absorption (FCA) plays dominant role. The real and imaginary parts of the third- order NL optical susceptibility χ 〈3〉, the NL refractive index and two photon absorption for

G2 ℏω/ Eg n 0 Eg4

(18)

where: K′ - constant value 3.4 ·10−4 , Eg - energy gap, G2 - dispersion function. The dispersion function is written as follows:

G2 =

2 (1−2x )3 ·Q (1−2x ) −2 + 6x −3x 2−x 3−0, 75x 4−0, 75x 5 + 64·x 6 64·x 6

(19)

where Q (x ) is the unit step function. Fig. 11 shows a plot of our experimentally determined scaled values of n2 as a function of ℏω/ Eg . The solid line is the calculated dispersion function with no adjustable parameters. We show several experimentally data from recent measurement by Refs. [4,5,26,27] on the same plot. Our own measurements 188

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Fig. 11. Data of n2 scaled as n2 n 0 Eg4 / K ′ vs ℏω/ Eg . The triangles represent the data from Ref. [4]. The blue circles show the results of tellurite glasses from Ref. [5]. Our research results are presented by red stars. Blue and black squares presented the results of research taken from the works Ref. [26] and Ref. [27], respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

of several of the same materials that have been studied show excellent and absolute agreement. 6. Conclusion In summary, different TeO2-based glasses were prepared, and its optical and structural properties were also investigated. In the present investigation, all of the glasses have an endothermic change between 349 °C and 356 °C, which is attributed to the glass transition temperature, Tg . It is worth noticing that while doping the glass transition temperature shifts towards higher values. Glasses, during heating, demonstrates, apart from the thermal effects characteristic for typical phase transition occurring in glassy state, an additional exothermal effect. It was found that, the Eg for glasses without RE ions is about 3.45 eV. Not surprisingly, the energy gap decreased with the presence of RE ions. The obtained values of the band tail width Eg and Eu indicate that the values of the energy gap were decreasing and Urbach energy were increasing with the addition of Er2O3. The behaviour of EU can be attributed to the increase in RE ions’ content in the thin glasses which leads to increase in the disordered atoms and defects in the structural bonding. The disorder and defects can introduce localized states at or near the conduction band level which leads to increase in the band tail width EU . Linear optical studies also indicate also that the most probable type of transition of the examined group of the tellurium glasses is direct allowed. We must pay attention that the linear absorption coefficient α for glasses with MgO doped Er2O3 is 4.83 (cm−1) which is the highest value among the tested glasses. NL refractive index and two photon absorption results show an increase in n2 and β values for all the samples when RE ions modifiers are added. Additional ions of erbium have an influence for the NL refractive index. For the glasses with MgO + Er2O3 and SrO + Er2O3 the n2 increased about 20% in comparison to the system without RE ions. In the case of the material with BaO, additional erbium ions increased the n2 index by about 3%. The obviously obtained n2 also affected χ 〈3〉 whose value for magnesium doped samples is almost twice as high as for modified glasses. Mechanisms related to the NL absorption include the saturation of the absorption, effective two- photon absorption and NL optical scattering. Acknowledgments This work was supported by King Khalid University, the Ministry of Education, and Kingdom of Saudi Arabia through a grant (RCAMS/ 189

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the electronic kerr effect in solids associated with two-photon absorption, Phys. Rev. Lett. 65 (1990) 96–99, https://doi.org/10.1103/PhysRevLett.65.96 . [27] F. Santos, M. Figueiredo, E. Barbano, L. Misoguti, S. Lima, L. Andrade, K. Yukimitu, J. Moraes, Influence of lattice modifier on the nonlinear refractive index of tellurite glass, Ceram. Int. 43 (17) (2017) 15201–15204, https://doi.org/10.1016/j. ceramint.2017.08.054 .

[24] T.A. Hanafy, Dielectric relaxation and alternating-current conductivity of gadolinium-doped poly(vinyl alcohol), J. Appl. Polym. Sci. 108 (4) 2540–2549. doi:10. 1002/app.27567. arXiv:http://https://onlinelibrary.wiley.com/doi/pdf/10.1002/ app.27567. [25] T.A. Hamdalla, S.S. Nafee, Experimental and theoretical studies for the gain of the neutron irradiated erbium doped fiber amplifier, Curr. Appl. Phys. 13 (6) (2013) 981–984, https://doi.org/10.1016/j.cap.2013.01.043 . [26] M. Sheik-Bahae, D.J. Hagan, E.W. Van Stryland, Dispersion and band-gap scaling of

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