Nd3+-doped TeO2–MoO3–ZnO tellurite glass for a diode-pump 1.06 μm laser

Journal of Non-Crystalline Solids 506 (2019) 32–38

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Nd3+-doped TeO2–MoO3–ZnO tellurite glass for a diode-pump 1.06 μm laser J.L. Liu, W.C. Wang, Y.B. Xiao, S.J. Huang, L.Y. Mao, Q.Y. Zhang

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T

State Key Laboratory of Luminescent Materials and Devices, Institute of Optical Communication Materials, South China University of Technology, Guangzhou 510640, PR China

A R T I C LE I N FO

A B S T R A C T

Keywords: Tellurite glass Thermodynamic method Glass-forming region Nd3+-doped Optical characteristics

Nd3+-doped TeO2–MoO3–ZnO (TMZ) tellurite glass with excellent glass-forming ability and optical property is explored for laser material applications. The glass-forming region is predicted via the “thermodynamic method” and then confirmed by some few sets of experiment. The fundamental characteristics of the TMZ glass such as glass structure, optical and spectroscopic properties are also investigated in detail by Raman, absorption, emission spectra and fluorescence decay curves. Interestingly, the vitrification, thermal and optical property of the present glass is significantly improved with the addition of MoO3. Furthermore, the TMZ glass has a higher emission cross section (3.12 × 10−20 cm2) and spectroscopic figure of merit (6.01 × 10−24 s·cm2) for the Nd3+: 4 F3/2 → 4I11/2 transition. All results indicate the potential applications of the TMZ glass in laser materials.

1. Introduction Solid-state-laser with high power at 1.06 μm has attracted extensive attention due to its potential applications in the fields of high-energy laser weapon, laser communication, laser radar, laser medical, etc. [1–6]. As an attractive rare-earth (RE) for 1.06 μm laser output, Nd3+ ion is not only easy to obtain laser output due to the four-level system but also possesses both the absorption and emission bands from ultraviolet (UV) to near-infrared (NIR) spectral range. Moreover, the emission of Nd3+ at 1.06 μm can be conveniently available upon the excitation of high-power Xe lamp and commercial 808 nm laser diode (LD) [7,8]. As is well known, Nd3+ has three emission peaks that located at around 0.9, 1.06 and 1.33 μm, which corresponds to the 4F3/ 4 4 F3/2 → 4I11/2 and 4F3/2 → 4I13/2 transitions, respectively. 2 → I9/2, Extensive studies have shown that the optical and spectroscopic properties of these optical transitions are strongly linked with the chemical composition of the glass matrix [9,10]. Therefore, it becomes a research hotspot in the fields of laser glass and fiber lasers that finding a suitable glass matrix combined with excellent glass-forming ability and optical property. In this respect, tellurite glass combining with the advantages of low phonon energy (~700 cm−1), wide infrared transmittance (~6 μm), high RE solubility (~10 × 1020 ions/cm3) and high refractive index (~1.9–2.3) has demonstrated tremendous potential and prosperous application [11–14]. Lower phonon energy is beneficial for weakening the multi-phonon relaxation rate and improving the quantum efficiency of RE ions. On the other hand, the disadvantages of tellurite glass, such

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as low laser damage threshold, poor thermal stability and low mechanical strength [12–16], have severely limited the development of the related materials and components. Continuous efforts have been devoted to the research, development, and exploration of new tellurite glass. A stark example is that Wang et al. [11] found the addition of WO3 can remarkably increase the glass transition temperature and thermal stability of TeO2eWO3 tellurite glass. Furthermore, Kosuge [17] and Feng [18] confirmed that such improvements benefit from the formation of TeeOeW bond, which prevents the ordered arrangement of the tellurium and tungsten polyhedrons. In our previous work, a series of tellurite glass systems have been systematically studied and the high-efficient near- and mid-infrared luminescence or laser output successfully achieved from several RE-doped tellurite fibers [19,20]. Basing on our early investigation, we noticed that even though Mo and W belong to the same subgroup of VI and have a similar electronic layer structure, TeO2–MoO3 glass system has a much larger glass-forming range (TeO2 content: 41.5–87.5 mol%) [21], more excellent glassforming ability and comparable thermal stability than TeO2–WO3 glass [22]. For instance, Chung et al. [23,24] found that the addition of MoO3 can effectively improve the local environment of RE ions in glass and extend the Raman bandwidth. On the other hand, as a common glass component, ZnO is generally considered to be a network intermediate and serves to enhance the degree of polymerization and the anti-crystallization ability of tellurite glass. Herein, a new TeO2–MoO3–ZnO (TMZ) tellurite glass is proposed for exploring its potential applications in laser materials. In the present work, the optimal glass-forming region of the TMZ

Corresponding author. E-mail address: [email protected] (Q.Y. Zhang).

https://doi.org/10.1016/j.jnoncrysol.2018.11.030 Received 27 September 2018; Received in revised form 14 November 2018; Accepted 27 November 2018 0022-3093/ © 2018 Elsevier B.V. All rights reserved.

Journal of Non-Crystalline Solids 506 (2019) 32–38

J.L. Liu et al.

3. Results and discussions 3.1. Predicted and experimental glass-forming region The exploration of new glass materials first requires designing a stable glass composition that can resist the risk of crystallization and phase separation. In the present work, the optimal glass-forming region of the TMZ system is forecasted by using the “thermodynamic method” [25–28]. Based on the predicted glass-forming region (enclosed by the solid red line) of TMZ glass, the experimental glass-forming region (enclosed by the blue dotted line) is finally determined by some few sets of experiment (marked in blue dots), as shown in Fig. 1. The data marked in brown and green dots come from Ref. [21]. It is inspiring to see that the TMZ glass exhibits an extremely large experimental glassforming region, which indicates the excellent glass forming ability and thermal stability of the present glass. In addition, the large glassforming region also facilitates the flexible adjustment of the glass composition and properties over a wide range. However, although the calculated optimal glass-forming region of TMZ system is located in the experimental range, it should be noted that there are some differences between them and the predicted glass-forming region is much smaller than the experimental one. Possible reasons are as follows: 1) This calculation method is only based on the thermodynamics theory and ignores the influence of dynamics factors during the glass formation; 2) In order to facilitate solving the thermodynamic equations, the concentration x is adopted instead of the activity α. However, the glass melt is not a regular solution, which leads to a certain error; and 3) The eutectic point is the optimized composition to form a glass due to the characteristics of lowest temperature and high viscosity. The range of the glass region should be around at the range of eutectic point to 1/2 of the composition [29]. All these factors are responsible for a smaller predicted glass-forming region than the experimental one.

Fig. 1. The experimental and calculated glass-forming region of TMZ glass system.

glass system is predicted by using “thermodynamic theory”, and its actual glass-forming region is confirmed under the guidance of prediction. After comparing their physicochemical properties and vitrification ability, the optimized composition of 70TeO2–20MoO3–10ZnO is selected for the Nd3+ doping to investigate its optical and spectroscopic properties.

2. Experimental The glass-forming region of the TMZ glass was predicted via the “thermodynamic method” and then confirmed by some few sets of experiment. Two sets of glass samples with different glass compositions were determined according to the experimental glass-forming region of TMZ system (Fig. 1). The molar compositions of the undoped and Nd3+doped TMZ glass samples are (90 − x)TeO2–xMoO3–10ZnO (x = 5, 10, 15, 20, 25, and 30) and (70 − y)TeO2–20MoO3–10ZnO–yNd2O3 (y = 0.05, 0.3, 0.5, 0.7, 1, and 2), respectively. A batch of 20 g with high purity raw materials was thoroughly mixed and then melted in an electric furnace at 750 °C for 1 h. After melting, the transparent melts were poured on a preheated copper plate (~250 °C). Subsequently, the annealing process was carried out at 350 °C for another 4 h in a muffle furnace and then cooled to the room temperature at the cooling rate of 2 K/min. The transparent glass samples were cut into the size of 10 × 20 × 1 mm3 and then optical polished for the subsequent measurements. Differential scanning calorimeter (DSC, Germany, Netzsch, STA449C Jupiter, ± 1 °C accuracy) was performed in the N2 protected atmosphere at a heating rate of 10 K/min to determine the glass transition and crystallization temperatures. The glass density was measured with the Archimedes drainage method in distilled water and the errors were determined by the accuracy of the weighing instrument. The refractive index of the glass was tested by using a Metricon Model 2010 prism coupler and the accuracy is ± 0.0005, all results were shown in Table 3. The Raman spectrum was carried out via Raman spectrometer (Renishaw in Via, Gloucestershire, UK) to analyze the glass structure. UV–Vis-NIR absorption spectra were recorded on a Perkin-Elmer Lambda 900 UV/VIS/NIR spectrophotometer with a spectral resolution of 1 nm. Static luminescence spectra were monitored by an iHR320 spectrometer (Jobin-Yvon Corp., Horiba Scientific) pumped by the 808 nm LD. Finally, the decay curves were collected by using a digital oscilloscope (TDS3012C, Tektronix) equipped on the iHR 320 spectrometer. All the measurements were carried out at room temperature.

3.2. Raman spectrum analysis The basic structural units of tellurite glass are [TeO4] trigonal bipyramid (tbp), [TeO3] trigonal pyramid (tp), and intermediate [TeO3+δ] polyhedron. Each of them has a pair of lone pair electrons (LPE) [13]. The special internal structure of tellurite glass not only improves the RE solubility but also provides more than one electric dipole environment for RE ions. Fig. 2(a) shows the Raman spectrum of TMZ glass with varying glass composition. Overall, the spectrum exhibits two continuous broadband scattering bands, which is composed of the characteristic vibration bands of Te − O polyhedron, Mo–O polyhedron and possible TeeOeMo bond. The Raman spectrum of the TMZ glass can be further deconvoluted into nine Gaussian peaks, 70TeO2−20MoO3−10ZnO glass is taken as an example to illustrate the structure information as shown in Fig. 2(b). The fitting degree is 99.99%, indicating the accuracy of the fits. Four characteristic Raman peaks of tellurite (denoted as A, B, C and D) [15,30–32] and five characteristic vibration peaks of Mo − O groups (denoted as V, W, X, Y and Z) can be easily identified according to the previous work [32–35]. The Raman frequencies and assignments are summarized in Table 1 and the Raman frequencies deviation of [MoO6] octahedron and [MoO4] tetrahedron in TMZ glass are displayed in Fig. 2(c). The Raman frequencies of the present TMZ glass are similar to other molybdate-tellurite glass and corresponding crystals. The peak shift usually means a change in bond length of the vibration group and a deformation of the basic structural unit. Definitely, this shift would cause the glass network more disordered and induce the change of physical properties. The presence of various structural units in TMZ glass not only conducive to the production of inhomogeneous broadening spectra but also improve the solubility of RE ions [13,36]. Additionally, the maximum phonon energy of the 70TeO2−20MoO3−10ZnO glass is 929 cm−1. The lower phonon energy is beneficial to reduce the probability of RE non-radiative transition. 33

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Table 1 Frequencies and assignments of Raman bands for 70TeO2 − 20MoO3 − 10ZnO glasses. Position

Raman shift ( ± 1 cm−1)

Structural units

Ref.

Peak Peak Peak Peak

A B C D

432 613 667 727

[15,30–32] [15,30–32] [15,30–32] [32]

Peak Peak Peak Peak Peak

V W X Y Z

363 504 789 878 929

v1δ(Te − O − Te) v2[TeO4] v2[TeO4] δ[TeO3]& [TeO3+1] or Te − O − Mo linkage [MoO4]&[MoO6] [Mo2O2] bridge [MoO6] [MoO4] [MoO4]

[33] [32] [35] [34] [34]

Fig. 3. Differential scanning calorimeter curves of TMZ glass (T ± 1 °C).

content. The Tg of the TMZ glass is between 339 and 363 °C and the △T is above 100 °C, indicating a high laser damage threshold and excellent anti-crystallization stability of the present glass. Moreover, the thermal stability of TMZ glass is significantly improved with the addition of MoO3 when compared with TeO2 − ZnO glass [16], as stated in Table 2. The thermal characteristics of the glass are closely related to the glass structure. Through the previous analysis from Raman spectra, we speculate that the addition of MoO3 effectively prevents the ordering of Te4+ ligands and Mo6+ ligands and thus promotes the formation of Te − O − Mo bonds in the present glass. On the other hand, the mutual transformation of the [MoO6] octahedron and [MoO4] tetrahedron and distortion of the ligand structure in the glass are happened due to the content variation of MoO3, TeO2, and O2−. Additionally, various units of Te4+ eventually lead to a more disordered glass structure, resulting in the weakened or even disappeared crystallization peak, as shown in Fig. 3. The characteristic temperatures of the TMZ glass are listed in Table 2.

Fig. 2. (a) Raman spectrum of TMZ glass. (b) Gaussian deconvolution on 70TeO2 − 20MoO3 − 10ZnO glass. (c) The Raman frequencies deviation of [MoO6] octahedron and [MoO4] tetrahedron.

3.3. Thermal stability analysis Table 2 Composition and thermal properties (T ± 1 °C) of TMZ and TeO2 − ZnO glass.

Thermal analysis is used to investigate the thermal properties of the glass. The thermal stability determines the difficulty of glass preparation and subsequent processing (e.g. fiber drawing). In terms of practicality, a glass matrix with sufficiently high glass transition temperature (Tg) and large temperature difference between initial crystallization temperature (Tx) and glass transition temperature (ΔT = Tx − Tg) is advantageous to obtain a high laser damage threshold and a wide processing working range, respectively. Fig. 3 shows the DSC curves of the TMZ glass. The peak crystallization temperature (Tp) gradually weakens and eventually disappears with the increase of MoO3

System

Tg (°C) Tx (°C) Tp (°C) △T (°C)

(90 − x)TeO2 − xMoO3 − 10ZnO 5

10

15

20

25

30

360 474 510 114

363 484 530 121

348 465 483 117

354 − − −

350 − − −

339 − − −

The error of temperature is ± 1 °C. 34

70TeO2 − 30ZnO [16]

333 440 − 107

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Table 3 Basic physical properties and pictures of TMZ glass. ρ ( ± 0.001 g/cm3)

System

(90 − x)TeO2–xMoO3 − 10ZnO

n ( ± 0.0005)

Picture

633 nm

1309 nm

1533 nm

x=5

5.162

2.034

1.988

1.981

x = 10

5.103

2.032

1.981

1.977

x = 15

5.094

2.068

2.016

2.010

x = 20

5.066

2.071

2.017

2.012

x = 25

4.982

2.068

2.012

2.007

x = 30

4.976

2.102

2.049

2.044

sideband red-shift to near 520 nm.

3.4. Basic physical properties analysis The basic physical parameters and related glass pictures are shown in Table 3. TMZ glass exhibits a large density (~5 g/cm3) and refractive index (n@633 nm > 2.0). With the addition of MoO3, the density of the glass gradually reduces while the refractive index exhibits an opposite tendency. Moreover, it can be clearly observed from the glass photos that the color of the glass gradually become dark as the increase of MoO3 content. Previous work proved that the [MoO4] tetrahedron has an absorption band in the ultraviolet range (300–350 nm) due to the charge transfer state (CTS) effect [37,38]. In contrast, the [MoO6] octahedron has an absorption band ranging from 300 to 475 nm, over the ultraviolet and blue-violet light, resulting in a warm color of the sample [37,38]. Therefore, it can be speculated that the deepened color derives from the CTS effect of the [MoO6] octahedron. To verify the conjecture, we measured the absorption spectrum of the glass samples from the ultraviolet to the visible region. The UV cut-off sideband gradually red-shifts with the increase of MoO3 content, as shown in Fig. 4. The maximum UV cut-off sideband is around 520 nm, which indicates that the gradually deepened color of the glass is indeed derived from the increase of [MoO6] octahedron. Although the position of 520 nm already exceeds the absorption sideband of [MoO6] octahedron at 475 nm, we speculate that this is due to the elongated Mo − O bonds originated from the distortion of [MoO6] octahedron. The reduced excitation energy required for the CTS effect cause the absorption

3.5. Absorption and Judd−Ofelt analysis The optimal glass composition of 70TeO2−20MoO3−10ZnO is selected to investigate its optical and spectroscopic properties by Nd3+ doping as an example. Fig. 5 presents the absorption spectrum of Nd3+doped TMZ glass with different doping concentrations. Six absorption bands at 513 + 526, 585, 682, 748, 804 and 876 nm are observed, which are assigned to the 4I9/2 → (4G7/2 + 4G9/2 + 2K13/2), 4I9/2 → (4G5/2 + 4G7/2), 4I9/2 → 4F9/2, 4I9/2 → (4F7/2 + 4S3/2), 4I9/2 → (4F5/ 4 4 4 2 + H9/2) and I9/2 → F3/2 transitions, respectively. It is noteworthy that the absorption band around 808 nm is very prominent, indicating that the glass can be excited by 808 nm LD effectively. In addition, there is no absorption band below 480 nm in this glass matrix, which is determined by the intrinsic absorption cutoff sideband of the glass. According to the absorption spectrum, J − O intensity parameters Ωt (t = 2, 4, and 6), spontaneous emission probability, branching ratio and radiative lifetime of the Nd3+-doped TMZ glass are calculated to gain a deep understanding of its radiation characteristics, as is shown in Table 4 and Table 5. The concentration of Nd3+ used in the calculation is 0.3 mol%, the refractive index of the sample is n@633 = 2.083. All the six absorption bands are adopted in the calculation. The root-meansquare error is 1.33 × 10−6, guaranteed the accuracy of computation.

Fig. 5. Optical absorption spectrum of Nd3+-doped TMZ glass.

Fig. 4. The absorption spectrum of TMZ glass. 35

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Table 4 The comparison of J–O intensity parameters, spectroscopic quality factor and the values of 1/Ω6 for Nd3+ in different glass hosts. Glass

Ω2 (×10−20 cm2)

Ω4 (×10−20 cm2)

Ω6 (×10−20 cm2)

χ (Ω4/Ω6)

1/Ω6 (×1020 cm−2)

δ (×10−6)

TMZ TZN [42] TWN [10] TNAN [43] Germanate [7] Phosphate [7] Borate [7] Silicate [7]

4.75 ± 0.14 3.8 4.71 3.12 6.93 4.92 6.64 5.01

3 ± 0.09 4.94 4.06 4.84 3.13 2.02 1.52 2.10

3.6 ± 0.11 4.54 3.89 3.28 4.39 5.99 6.12 4.54

0.83 1.09 1.04 0.66 0.71 0.34 0.25 0.46

0.28 0.22 0.26 0.13 0.23 0.17 0.16 0.22

1.33 0.44 − 0.095 − − − −

Table 5 Spontaneous emission probability, branching ratio and radiative lifetime of Nd3+. Initial state

Final state

4

4

F3/2

I9/2 I11/2 I13/2 4 I15/2 4 4

Aed (s−1)

Ar (s−1)

β

τrad (μs)

2079.47 2658.80 543.66 2079.47

2079.47 2658.80 543.66 2079.47

0.394 0.503 0.103 0.394

− 376.1 − −

Errors involved in the fitting and calculation may come from the difference of the reduced matrix elements and absorption spectrum test. In general, Ω2 usually indicates the covalency between RE3+ ions and ligand anions as well as the asymmetry of the local environment around the site of RE. It can be seen from Table 4 that the Ω2 of the present glass is higher than the TeO2 − ZnO and TeO2 − WO3 glasses but lower than the germanate, phosphate, borate and silicate glasses, indicating that there are moderate symmetry and covalent bonding around Nd3+ in the present glass. The parameter Ω6 is considered to be related to the hardness and viscosity of the glass matrix and 1/Ω6 is proportional to the ionicity between RE ions and ligand field [39]. Large 1/Ω6 of the TMZ glass indicates a poor mechanical property, which is consistent with the experiment result. As the reduced matrix elements ‖U(2)‖ are zero for Nd3+: 4F3/2 transitions, hence Ω2 does not affect the stimulated emission parameters [5]. Therefore, the parameters Ω4 and Ω6 have a direct impact on the optical and spectroscopic properties of Nd3+, such as the radiative transition probability and branching ratios. Spectroscopic quality factor (χ = Ω4/Ω6) can effectively estimate the intrinsic intensities of 4F3/2 → 4I9/2 and 4F3/2 → 4I11/2 in Nd3+-doped glass [40]. If χ is smaller than 1, the intensity of the 4F3/2 → 4I11/2 transition will be stronger than that of 4F3/2 → 4I9/2 in the glass matrix. Furthermore, the larger χ value indicates a strong emission at 1.06 μm (4F3/2 → 4I11/2 transition). In this work, the value of χ is 0.83, smaller than 1 but greater than other glass systems, indicating that a high spectroscopic quality in this glass matrix. It is worth noting that the spontaneous transition of Nd3+: 4F3/2 → 4I11/2 is 2658.8 s−1, the fluorescence branch ratio is > 0.5 and the theoretical lifetime is 376.1 μs, which is superior to germanate, phosphate and other tellurite glass systems [8,41–43]. Therefore, it is expected to achieve efficient laser operation from the TMZ glass.

Fig. 6. (a) The NIR emission spectrum of Nd3+-doped TMZ glass. (b) Energy level and energy transfer diagram of Nd3+.

intensities are constantly quenched with further increasing the Nd2O3 concentration. To deeply understand the luminescent mechanism of the Nd3+-doped TMZ glass, the energy level and energy transfer diagram are given in Fig. 6(b). Upon the excitation of 808 nm LD, the ions at the 4 I9/2 ground state are excited to the (4F5/2, 4H9/2) level. Since the energy level gap between (4F5/2, 4H9/2) level and 4F3/2 level is small, the particles quickly transfer their energies to the 4F3/2 level through the non-radiative relaxation process. Then three emissions at 877 + 895, 1063 and 1333 nm are realized through the radiative relaxation process from the 4F3/2 level to the lower energy levels. It is worth noting that the emission around 890 nm is split into two parts that centered at 877 and 895 nm, respectively. This infrequent phenomenon perhaps relates to the specificity of the matrix glass. Fig. 7 shows the fluorescence decay curves of the 4F3/2 level in Nd3+-doped TMZ glass (λex = 808 nm, λem = 1063 nm). All the fitting degree of decay curves are higher than 99.9%, with the standard errors showing in Fig. 7. As can be seen, the fluorescence lifetimes of 1063 nm

3.6. Emission spectrum and fluorescence lifetime analysis Fig. 6(a) presents the emission spectra of Nd3+-doped 70TeO2 − 20MoO3 − 10ZnO glass with different doping concentrations. Three emission bands at 877 + 895, 1063 and 1333 nm are observed upon the excitation of 808 nm LD, corresponding to the Nd3+: 4 F3/2 → 4I9/2, 4F3/2 → 4I11/2 and 4F3/2 → 4I13/2 transitions, respectively. Among them, the 1063 nm emission is the sharpest and strongest one. Moreover, their intensities are enhanced with the increase of Nd3+ doping concentration consistently and reached a maximum value until the Nd2O3 doping concentration is 0.7 mol%. Then the emission 36

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Fig. 7. The fluorescence decay curves from 4F3/2 level of Nd3+-doped TMZ glass (λex = 808 nm, λem = 1063 nm).

are reduced with Nd2O3 content increased. It is interesting to note that the decay curves of Nd3+: 4F3/2 → 4I11/2 are almost double exponential even at low Nd3+ concentrations. This indicates that there is more than one attenuation mode of 4F3/2 → 4I11/2 transition in Nd3+-doped TMZ glass. It may be related to the high hydroxyl content or the effect of ligands in the TMZ glass [9,10,40,44]. 3.7. Absorption, emission cross-section and gain coefficient analysis The absorption and emission cross-section is one of the most key parameters for evaluating the laser performance of a material. They can be calculated by the Beer-Lambert equation and McCumber (MC) theory, as follows [45,46]:

σa (λ ) =

2.303OD (λ ) Nd

σeMC (λ ) = σa (λ )

Fig. 8. (a) Absorption and emission cross sections for Nd3+-doped TMZ glass. (b) Gain cross section of 4F3/2 → 4I11/2 transition for Nd3+-doped TMZ glass.

(1)

ZL hc ⎛ 1 1 exp ⎡ − ⎞⎤ ⎢ κB T ⎝ λZL ZU λ ⎠⎥ ⎦ ⎣ ⎜

laser materials. If the particles of Nd3+ are only distributed at the 4F3/2 and 4I11/2 levels, the gain coefficient can be calculated by the following Eq. [49]:

⎟

(2)

where σa is the absorption cross-section, σe is the stimulated emission cross-section, OD(λ) is the intensity of absorption spectrum, N is the ion concentration of Nd3+, d is the thickness of the glass sample. ZL/ZU is the partition function of the lower and upper levels (here namely the 4 I11/2 and 4F3/2 levels) tested at low temperature or can be approximately replaced by the ratio of the degeneracy of the upper and lower energy levels at high temperature. κB is the Boltzmann constant, T is the Kelvin temperature, and λZL = 1081 nm is the zero phonon line. In addition, σe can also be calculated by using the FuchtbauerLadenburg (FL) equation, as follows [45]:

σeFL (λ ) =

λ5β I (λ ) 8πcn2 τrad ∫ λI (λ ) dλ

G (λ ) = N [pσe (λ ) − (1 − p) σa (λ )]

(4)

where G(λ) is the gain coefficient from the upper level to the lower level at the wavelength λ. p is a reversal factor value from 0 to1, representing the ratio of upper-level populations to the totals. Fig. 8(b) shows the gain coefficient of the 4F3/2 → 4I11/2 transition for Nd3+doped TMZ glass. The laser output is available when p > .4 predicting that this glass system has a lower laser threshold. Finally, it is necessary to introduce the spectroscopic figure of merit (FOM), which is a prediction of the likelihood in low threshold operation. A large FOM value indicates a low laser threshold of the laser host. The equation of FOM is followed [50,51]:

(3)

where I(λ) is the emission intensity, τrad is the radiative lifetime. Since the Nd3+: 4F3/2 → 4I11/2 is not a transition from an excited state to a ground state, the absorption cross section cannot be calculated by the absorption spectrum and the MC formula. Therefore, the “reverse method” is adopted in this work and the calculation results are shown in Fig. 8(a). It can be seen that the maximum value of σa and σe are 1.04 ± 0.03 × 10−20 cm2 and 3.12 ± 0.09 × 10−20 cm2, respectively. The errors were obtained by averaging the calculation of Nd3+doped TMZ glass with different doping concentrations. Compared with other glass systems we can found that the maximum values of σe in this work is larger than the germanate [8] and borate glass [47] while slightly lower than those traditional zinc‑sodium-tellurite (TZN) [48] and phosphate glasses (N31) [41]. Therefore, the investigated TMZ glass system has a great potential application for a diode-pump 1.06 μm laser. The gain coefficient is another important parameter for RE-doped

FOM = σe τeff

(5)

where τeff is the experimental lifetime. The calculation shows that the value of FOM is 6.01 × 10−24 s·cm2, which is greater than that of Nd3+-doped TeO2 − ZnO glass [42], TeO2 − Nb2O5− Al2O3 (TNAN) glass [43], TeO2 − WO3 − Y2O3 (TWY) glass [52] and germanate glass [8] but slightly smaller than borate glass [47]. It means that Nd3+doped TMZ glass may have a low threshold power in 1.06 μm lasers. The peak emission wavelength (λp), σa, FOM and theoretical fluorescence lifetime (τrad) of the present glass and other typical glass systems are summarized in Table 6. The results show that Nd3+-doped TMZ glass has the advantages of large emission cross-section, high spectroscopic figure of merit and long radiative lifetime. At the same time, the σa, FOM and τrad of Nd3+-doped TMZ glass are comparable with two commercial laser glasses, namely N31 and N41 from Shanghai Institute of Optics and Fine Mechanics (SIOM), indicating a feasibility of laser 37

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Table 6 The comparison of radiative properties for 4F3/2 → 4I11/2 transition in different Nd3+-doped glasses. Glass

λp (nm)

σeFL (10−20 cm2)

FOM (10−24 s·cm2)

τrad (μs)

TMZ TZN [42] TNAN [43] TWY [52] Germanate [8] Borate [47] N31 [41] N41 [41]

1063 1062 1062 1061 1054 1067 1053 1053

3.12 ± 0.09 4.27 3.38 2.70 2.09 2.00 3.8 3.9

6.01 ± 0.18 4.44 < 5 4.06 4.56 6.98 − −

376.1 104 148 229 349.8 − 348 351

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operation from this new glass. Overall, the TMZ glass system exhibit significant advantages over TeO2 − ZnO glass not only on vitrification and physical properties but also in NIR luminescence due to the addition of MoO3. TMZ glass has low phonon energy, high RE solubility, excellent thermal stability and optical properties, which are beneficial for other rare-earth-doping such as Tm3+ and Ho3+ for 2 μm emission or Er3+ ion for 1.5 μm and 2.7 μm emissions. Therefore, there are reasons to believe that efficient near- and mid-infrared luminescence or laser could be achieved in the TMZ glass system by different RE ions doping. 4. Conclusion In summary, a new TeO2−MoO3−ZnO tellurite glass system is explored towards the potential applications of laser materials and fiber lasers. Owing to the predicted glass-forming region through the “thermodynamic method”, the experimental glass-forming region of the TMZ glass is conveniently determined by some few sets of experiment. The addition of MoO3 significantly improves the vitrification, thermal and optical properties of the glass. The favorable spectroscopic parameters such as high radiative transition probabilities, branching ratios, stimulated emission cross-section, gain coefficient and FOM for Nd3+: 4 F3/2 → 4I11/2 transition indicate that the Nd3+-doped TMZ glass might have potential application prospects in high power 1.06 μm laser materials. Acknowledgements This work was financially supported by the National Natural Science Foundation of China (Grant Nos. U1601205 and 51802098), NSAF (Grant No. U1830203), National Postdoctoral Program for Innovative Talents of China (No. BX20180099), Fundamental Research Funds for the Central Universities, SCUT (No. 2018MS74), China Postdoctoral Science Foundation (No. 2018 M643073) and Local Innovative and Research Teams Project of Guangdong Pearl River Talents Program (2017BT01X137). References [1] R.S. Conroy, T. Lake, G.J. Friel, A.J. Kemp, B.D. Sinclair, Opt. Lett. 23 (1998) 457–459. [2] L. Bolundut, L. Pop, M. Bosca, N. Tothazan, G. Borodi, E. Culea, P. Pascutta, R. Stefan, J. Alloy. Compd. 692 (2017) 934–940. [3] T. Taira, A. Mukai, Y. Nozawa, T. Kobayashi, Opt. Lett. 16 (1991) 1955–1957.

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