Sulfophosphate Glass Doped with Er³⁺ and TiO₂ Nanoparticles: Thermo-Optical Characterization by Photothermal Spectroscopy

Abstract

In this work, time-resolved thermal lens and beam deflection methods were applied to determine the thermo-optical properties of Er³⁺ doped sulfophosphate glass in which different concentrations of Titanium dioxide (TiO₂) nanoparticles (NPs) were embedded. Thermal diffusivity ($D$), thermal conductivity ($\kappa$), and the temperature coefficient of the optical path length ($ds/dT$) were determined as a function of NPs concentrations. Moreover, the growth of TiO₂ NPs inside the amorphous glass matrix was evidenced by Transmission Electron Microscopy (TEM) images as well as through optical effects such as refractive index change of the glass. The outcomes indicated relatively high values for $D$ and κ as well as a low $ds/dT$ as required for most optical components used for laser media. The addition of TiO₂ NPs with concentration of dopants up to 0.6 mol% improved the optical properties of the glass samples but did not affect its thermal properties. The results indicate that the enhanced optical and thermal performance of the proposed co-doped glass fits the quality standards for materials used in photonic devices.

1. Introduction

Phosphate based glasses doped with Lanthanide ions (Ln³⁺) have attracted great interest due to their thermo-optical properties and applicability in the development of photonics devices. These luminescent materials have been used for active media of solid-state lasers, LEDs, solar cells, and other photonics devices [1,2,3,4]. Among them, Erbium ion (Er³⁺)-doped glasses have been investigated for a wide range of applications including infrared and green solid-state lasers, broadband optical sources, and optical amplifiers [5,6]. Furthermore, Er³⁺ is a promising candidate for the frequency up-conversion due to its equally spaced long-lived excited states [7,8].

However, the design of optical devices needs quality control over all the physical processes which can affect its behaviour. In particular, the processes related to the nonradiative transitions are emphasized, because they can increase the heat deposited on the material and produce concentration quenching which reduces the inversion density, manifested by a rapid reduction of the fluorescence lifetime and luminescence quantum efficiency [9]. In the case of rare earth ion doping with high concentrations, non-radiative mechanisms of the energy transfer process reduce the lifetime of absorbed light in glass [10,11,12]. It can cause a narrowing of the absorption and emission band of the glass and consequently a luminescence quenching that can limit the use of rare earth ion-doped glasses in photonic applications [13].

Different routes are suggested to overcome the concentration quenching. Embedding metal or semiconductor nanoparticles in different rare earth ion-doped glasses could be offered as an approach to overcome the limitations related to the narrow optical band of rare earth ions at high concentration [14,15]. Over decades, several research efforts have been dedicated for determining the effects of noble metal NPs (Ag and Au) and TiO₂ semiconductor on the emission of various rare earth ions [16,17,18,19,20,21,22,23]. All these studies suggested that the metal NPs and TiO₂ semiconductors enabled intense local fields in the proximity of the Ln³⁺s. The subsequent energy transfer between them inside varied glass hosts improved the photoluminescence properties.

As mentioned, the optical properties of the glass materials may be accordingly engineered through the presence of nanoparticles to design a more efficient device. Co-doping with nanostructures has been comprehensively investigated to enhance the luminescent emission of rare earth ion-doped glass matrices [17,18,19]. Besides efficient optical and spectroscopic properties, thermal properties of the composite glass, including thermal conductivity ($\kappa$), thermal diffusivity ($D$) and and the temperature coefficient of the optical path length ($ds/dT$), may be also modified by NPs co-doping with Ln³⁺ ions [24,25,26].

Consequently, the measurement of the thermo-optical properties is of utmost importance given that laser-matter interaction results in thermal loading due to the nonradiative transitions which can increase the heat deposited on the material. This, in turn, produces a degradation of material performance. Efficient heat removal and the reduction of the thermal effects that are caused by the temperature gradients across the lasing material are obtainable by increasing the thermal diffusivity and conductivity. In addition, the temperature gradients set up in the material as a result of nonradiative relaxations can produce stress fractures, thus establishing the ultimate limit in average power attainable from the photonic material. Additional effects such as thermal lensing and birefringence adversely affect the beam quality [27]. The characterization of the thermo-optical properties of a material, therefore, is especially important for the optimization of photonic applications such as in high-power lasers, where unwanted thermal effects can cause extreme disruptions in laser action [27].

Because of its high sensitivity, photothermal spectrometry has been extensively used for characterization of a variety of samples [26,27,28,29,30,31]. In the past few years, thermal lens spectroscopy (TLS) as well as beam deflection spectroscopy (BDS) have been applied to evaluate the thermo-optical properties of transparent and opaque materials, including optical glasses [28,29,30].

In this work, the thermo-optical properties of sulfophosphate glass doped with 1mol% Er³⁺ as a function of the TiO₂ concentrations were studied. The thermo-optical properties of the samples were investigated using TLS and BDS techniques. Additional information was obtained by using thermal analysis (DTA), transmission electron microscopy (TEM), and UV-vis spectroscopy.

2. Theory

According to the TL model approach, developed by Shen et al. [31], the TLS signal S(z,t) is defined as the relative change of the light transmission T(z,t) through a small aperture in the presence of the excitation beam and T(0) is its initial value when the excitation beam is off:

$$\mathrm{S}\left(\mathrm{z},\mathrm{t}\right) = \frac{\mathrm{T}\left(\mathrm{z},\mathrm{t}\right) - \mathrm{T}\left(0\right)}{\mathrm{T}\left(0\right)}$$

(1)

In the situation of a small phase shift (<<0.2) and small aperture radius (<1 mm), the signal can be written as [31]:

$$\mathrm{S}\left(\mathrm{z},\mathrm{t}\right){ = \mathsf{\Theta }\tan }^{-1}\left\{\frac{4\mathrm{m}\left(\mathrm{z}\right)\mathsf{\nu }\left(\mathrm{z}\right)\mathrm{t}/{\mathrm{t}}_{\mathrm{c}}\left(\mathrm{z}\right)}{\left[1 + 2\mathrm{m}\left(\mathrm{z}\right) + \mathsf{\nu }{\left(\mathrm{z}\right)}^2\right]2\mathrm{t}/{\mathrm{t}}_{\mathrm{c}}\left(\mathrm{z}\right) + {\left[1 + 2\mathrm{m}\left(\mathrm{z}\right)\right]}^2{ + \mathsf{\nu }\left(\mathrm{z}\right)}^2}\right\},$$

(2)

where t_c is the characteristic time of TL $t_c = {\omega }_{0e}^2/4D$, and $\Theta$ is given by

$$\mathsf{\Theta } = \frac{{\mathrm{P}}_{\mathrm{e}}\mathsf{\alpha }\mathrm{l}}{{\mathsf{\lambda }}_{\mathrm{p}}\mathsf{\kappa }}\mathsf{\phi }\frac{\mathrm{ds}}{\mathrm{dT}}$$

(3)

In this equation, P_e represents the total excitation light power at the sample, α, $ds/dT$, and $\phi$ are the sample’s absorption coefficient, the temperature coefficient of the optical path, and the non-radiative quantum efficient, respectively. For non-fluorescent samples $\phi = 1$ and for luminescent samples it is <1.

Parameters $\kappa$ and $D$ are related through the density and heat capacity,

$$\mathsf{\kappa } = \mathsf{\rho }\mathrm{c} .\mathrm{D}$$

(4)

The parameter $m = {\left({\omega }_p/{\omega }_e\right)}^2$ indicates the mode-mismatching between the radii of excitation and probe beams and ν(z) is the geometrical factor defined as follows:

$$\mathsf{\nu }\left(\mathrm{z}\right) = \frac{\mathrm{z} -{ \mathrm{a}}_{\mathrm{p}}}{{\mathrm{z}}_{\mathrm{p}}} + \frac{{\mathrm{z}}_{\mathrm{p}}}{\mathrm{L} - \mathrm{z}}\left[1 + \frac{{\left(\mathrm{z} -{ \mathrm{a}}_{\mathrm{p}}\right)}^2}{{\mathrm{z}}_{\mathrm{p}}^2}\right],$$

(5)

where z is the position of the sample concerning the excitation beam waist. L is the distance from the sample to the detector, $a_p$, $z_p$ and ${\lambda }_p$ are the waist positions, Rayleigh parameter, and wavelength of the probe beam, respectively.

For the particular configuration of well-focused excitation beam and highly collimated probe beam the TL signal, under steady-state condition, reaches its maximum value and the Equation (2) can be expressed by [32]:

$${\mathrm{S}}_{\max } = \frac{\mathsf{\pi }}{2}\mathsf{\Theta }.$$

(6)

3. Experimental Part

3.1. Preparation of the Samples

Seven sulfophosphate glass samples coded by PMZExTiO₂ with the composition of (60-x) P₂O₅-20MgO-20ZnSO₄.7H₂O-1Er₂O₃- xTiO₂ were synthesized by the melt quenching method. Where xTiO₂ nanoparticles (x = 0.0, 0.1, 0.2, 0.3, 0.4, 0.5 and 0.6 mol %) were added to the nominal composition and co-doped with the 1mol% rare earth ion Er₂O₃. The raw powders were first mixed and then were melted in a crucible at 1200 °C for one hour and then were annealed at 300 °C for 3 h. The synthesized glasses were cut and polished for characterization and optical measurements. The energy dispersive X-ray (EDX) spectrum of the glass sample PMZ0.5Er is shown in Figure 1. It indicates the presence of all the elements in the host glass matrix.

3.2. Methodology

The presence of TiO₂ NPs inside the glass matrix was demonstrated by operating a Zeiss LEO906 TEM imaging system. To enhance TEM imaging the well-powdered sample was dispersed in methanol using an ultrasonic bath for 15 min. ImageJ software was used to obtain the size distribution of the TiO₂ NPs.

The thermal analysis of the prepared glasses was performed using a Pyris Diamond (TG-DTA, Japan) with a rate of 10 °C/min. The samples were heated from room temperature to 900 °C under a N₂ atmosphere with a rate of flow of 20 mL/min. UV-Vis-NIR absorption spectra were measured in a range from 330 nm to 1100 nm using a scanning spectrophotometer (model Shimadzu UV-3101 PC). The optical band gap energy was obtained through Tauc’s plots for direct $\left(E_{opt}^{dir}\right)$ and indirect $\left(E_{opt}^{indir}\right)$ transitions using the optical absorption spectra [33]. The refractive indices (n) of the samples were calculated using Dimitrov and Sakka expression [34].

Glass mass density, $\rho \left(g.c{m}^{-3}\right)$ was determined through the Archimedes method using toluene as an immersed medium, where the density of toluene is ${\rho }^{\prime }$ = 0.8669 g.cm⁻³. All measurements were performed at room temperature.

For TL measurement we first measure the TLS signal amplitude, followed by the fitting of the corresponding amplitude as a function of time using Equation (2). In the fitting process, $\Theta$ and D are considered as adjustable parameters. Utilizing the fitted value of $D$, we can calculate $\kappa$ of the measured sample using Equation (4) and the measured glass mass density. Moreover, to determine $ds/dT$, the maximum TL signal $S_{max}$ is first measured for different excitation powers, and then the phase amplitude $\Theta$ is calculated using Equation (6). Equation (3) can be normalized with the absorbed power of the excitation beam as follows:

$$\frac{\mathsf{\Theta }}{{\mathrm{P}}_{\mathrm{abs}}} = \mathrm{C}\mathsf{\phi } , \mathrm{C} = \frac{1}{{\mathsf{\lambda }}_{\mathrm{p}}\mathsf{\kappa }}\frac{\mathrm{ds}}{\mathrm{dT}}$$

(7)

The excitation power absorbed by the sample $P_{abs} = P_e\alpha l$ can be obtained directly using the Beer law $P_{abs} = P_e\left(1-exp\left(-\alpha l\right)\right)$. Finally, by linear fitting of the obtained phase shift versus the absorbed pump power, the slope C is measured from which $ds/dT$ can be obtained.

3.3. Photothermal Spectroscopy Setups

The experimental setup used for TL measurement is shown schematically in Figure 2. The excitation laser (MGL-III-532-100, UltraLasers) emits at 532 nm wavelength and is modulated at 2 Hz using a signal generator (RIGOL DG1022, RIGOL Technologies, Inc., Beaverton, OR 97008, USA). Its output power is regulated by the neutral density filter (NDF) (NDC 50S-3, Thorlabs). The beam is collimated and then focused into a spot of 30 µm diameter in the sample by a set of lenses L3, L4, L5 with 30 mm, 100 mm, 150 mm focal lengths (LB1757-A, LB1676-A, LB1437-A, Thorlabs), respectively. The TL effect is probed by a He-Ne laser (632.8 nm, 3 mW, 05-UR-111, Melles Griot) beam which was collimated to a size of 4 mm in diameter by a set of lenses L1 and L2 with 40 mm and 150 mm focal lengths (LB1757-A, LB1437-A, Thorlabs, respectively). Both beams are directed collinearly through the sample using a set of turning mirrors M1, M2, M3 (BB1-E02, Thorlabs) and a dichroic mirror DM (DMSP605, Thorlabs). The probe beam intensity changes resulting from the TL effect are detected by the Si detector (PDA 36A-EC, Thorlabs) equipped with a 0.5 mm diameter pinhole. The TL signal is recorded directly using a digital oscilloscope (RIGOL DS1102E, RIGOL Technologies, Inc.).

The experimental setup used for BDS is shown schematically in Figure 3. The excitation laser (MGL-III-532-100, UltraLasers) emits at 532 nm wavelength and is modulated at 13 Hz by a signal generator (RIGOL DG1022, RIGOL Technologies, Inc.). The examined sample is illuminated by the intensity-modulated light beam with 50 mW output power which is directed by the turning mirror (M) BB1-E02, Thorlabs) to impinge on the sample perpendicularly to its surface. The beam is collimated and then focused onto a spot of 30 µm diameter in the sample by a set of lenses L4, L5, L6 with 40 mm, 100 mm, 150 mm focal lengths (LB1757-A, LB1676-A, LB1757-A, Thorlabs), respectively. The lens L6 and the mirror M are placed on an XYZ translation stage to move the excitation beam in the y-direction with a 12.5 µm step. The sample is also placed on a 3D translation stage (Thorlabs) to vary its position in x, y, and z-direction and to optimize the experimental configuration. The absorbed energy induces temperature oscillations inside the sample as well as in its surroundings, which are probed by a second laser (He-Ne, 3 mW, 05-UR-111, Melles Griot) emitting at 632.8 nm. This beam is collimated and then focused into a spot of 30 µm diameter over the sample by a set of lenses L1, L2, L3 with 40 mm, 100 mm, 150 mm focal lengths (LB1757-A, LB1676-A, LB1757-A, Thorlabs), respectively. The interaction of the probe beam with the temperature oscillations over the sample results in probe beam deflections, which are detected by a quadrant photodiode (QP) (PDQ80A, Thorlabs) equipped with an interference filter (IF) (632.8 nm CWL, Thorlabs) and connected to the lock-in amplifier (Stanford Research System, Model SR5 10). To optimize the experimental set-up the probe beam is carefully aligned close to the sample surface, just to skim it. There is a linear relation between the phase of the transverse component of the perpendicular deflection and the pump to probe offset y at a given frequency f. $D$ can be calculated from the slope $m = -\sqrt{\pi f/D}$ [35].

4. Results and Discussion

4.1. Transmission Electron Microscopy (TEM)

TEM imaging was used to confirm the presence of the TiO₂ NPs doped in the glass matrix. Figure 4 shows the TEM image of a PMZE0.6T glass sample which reveals the presence of spherical TiO₂ NPs. ImageJ software was used to obtain the TiO₂ NPs size distribution from the TEM image. The histogram of the size distribution which is presented in the inset of the Figure 4 was fitted with the well-known Gaussian function. The majority of size values are between ~20 to 50 nm in diameter, but there are some NPs also observed with diameters between 60 to 70 nm.

4.2. Thermal Characterization

Figure 5 shows the DTA curve of the studied glasses which compares the glass transition, the crystallization, and the melting temperatures in the presence of TiO₂ NPs and without NPs. The observation of a broad endothermic hump corresponds to the glass transition temperature (T_g), the exothermic peak is assigned to the crystallization temperature (T_c), and the other endothermic peak is attributed to the melting temperature (T_m). Previous studies showed that the growth of NPs happens when the glass viscosity attains values sufficient to promote the diffusion of NPs [36,37]. If the annealing temperature is higher than the glass transition temperature, the crystallization may happen during heat treatment. In this study, the temperature of annealing is less than the glass transition temperature (>400 °C) so crystallization does not occur as has been shown by X-Ray Diffraction (XRD) patterns [19].

The results demonstrate that the introduction of TiO₂ NPs causes an increase in the temperature of T_g, T_c, and T_m. For instance, T_g was obtained at around 405 °C and 418 °C for glass sample without TiO₂ NPs (PMZE0.0T) and glass sample containing 0.2 mol% TiO₂ NPs (PMZE0.2T), respectively. In this manner, T_c increased from 625 °C to 696 °C and T_m increased from 840 °C to 898 °C for the sample containing TiO₂ NPs. Moreover, the difference between crystallization and transition temperature (T_c − T_g) is 220 °C and 278 °C for glass samples with and without TiO₂ NPs, respectively.

4.3. Optical Properties

Figure 6a,b shows the UV-Vis-NIR absorption spectra of the glass matrix doped with Er³⁺ (PMZE0.0T) and co-doped with TiO₂ NPs (PMZE0.4T) in the range of 330–1100 nm as well as SPR absorption band of TiO₂ NPs in glass (PMZ0.4T), respectively. In the absorption measurements the reference sample was the glass matrix without Er3+ or TiO₂ NPs We named it as PMZ which it is presented in the Figure 6a. The observed peaks in this range are attributed to the transition of Er³⁺ ion from the ground state (⁴I_15/2) to the different excited states as presented in the figure. The results demonstrate that co-doping of Er³⁺-doped glass with TiO₂ NPs has no significant effect on the intensity or position of the absorption peaks. The presence of the NPs leads to a surface plasmon resonance (SPR) absorption peak observed around 437 nm. The SPR related effects of TiO₂ NPs in the glass matrices have been reported in our previous works [18,19,20].

Optical Band Gap and Refractive Index

Figure 7 shows the optical band gap energies for direct $\left(E_{opt}^{dir}\right)$ and indirect $\left(E_{opt}^{indir}\right)$ transitions as well as refractive index (n) of the samples versus the varied mol% of TiO₂ NPs doping into the glass matrix. By addition of TiO₂ NPs concentration the optical band gap of the samples was decreased which can be attributed to the formation of more non-bridging oxygen groups than bridging oxygen groups in the glass [38]. The number of localized electrons would be increased as a result of the formation of more non-bridging oxygen groups, and these may behave like donor centres in the glass network, causing redshift of the absorption edge. Therefore, the electron transfer from the valence band to the conduction band may have happened at lower energy as the concentration of TiO₂ NPs was increased [38]. The refractive index of the studied glass samples has an incrementing trend by adding TiO₂ NPs, as illustrated in the figure.

4.4. TLS Measurements

The values for $D$ of the samples were measured using the TLS and BDS. Figure 8 presents the TLS signal as a function of time obtained by irradiating the 0.2 mol % doped glass sample with P_e = 53 mW. In the studied samples, the increase of the TLS signal reveals the convergence of the probe beam as a result of the induced TL effect, so in this material $ds/dT$> 0 according to Equation (3). The solid curve in the figure is the best fit to the experimental data (circles) using Equation (2), in which the parameters $\Theta$ and $D$ were adjustable and the other variables were assigned well-known experimental values.$D$ was found directly from the fitting procedure. The BDS slope method was also applied for the measurement of $D$ similarly as shown for PMZE + 0.6TiO₂ in Figure 9. The value of $D$ was obtained from the slope [35].

Figure 10 shows the linear behaviour of the phase shift $\Theta$ and the absorbed excitation power (P_e), as expected by Equation (3), for the 0.4 mol% doped sample. For that purpose, we fixed the modulation frequency as f = 0.5 Hz to establish a stationary situation where $S_{max}$ could be achieved according to Equation (6). The linear trend of phase shift versus the pump beam power was verified for all samples thus demonstrating the validity of Equation (3) and assuring that nonlinear effects such as absorption saturation or Auger upconversion (excited ion-ion energy transfer) were not observed in the investigated pump intensity range [26,39]. From the slope of the plot shown in Figure 10 and using Equation (7), $ds/dT$ was calculated. For the glass samples used here, excited at 532 nm the florescence was negligible, therefore $\phi \approx 1$. The reported emission spectrum of the sulfophosphate glass doped by TiO₂ NPs illustrates that these glass structures have two main emission peaks at 552 nm and 620 nm under 449 nm excitation wavelength [19].

The same analysis as mentioned above was performed for all samples and the resulting values of $D$, $\kappa$ and $ds/dT$, obtained from three independent measurements, are shown in

Table 1. Thermal properties of the PMZE + xTiO₂ samples.

Sample	$\mathit{D}\left[{10}^{-3}{\mathbf{cm}}^{-2}{\mathbf{s}}^{-1}\right]$	$\mathsf{\rho c}[\mathbf{J} {\mathbf{cm}}^{-3}{\mathbf{K}}^{-1}]$ (±0.01)	$\mathit{\kappa }\left[{10}^{-3}{\mathbf{Wcm}}^{-1}{\mathbf{K}}^{-1}\right]$	$\mathbf{C}=\left(\frac{1}{{\mathit{\lambda }}_{\mathit{p}}\mathit{\kappa }}\right).\frac{\mathit{d}\mathit{s}}{\mathit{d}\mathit{T}}\left[{\mathbf{W}}^{-1}\right]$	$\mathit{d}\mathit{s}/\mathit{d}\mathit{T}[{10}^{-6} {\mathbf{K}}^{-1}]$
PMZE0.0T	3.10 ± 0.05	1.95	6.05 ± 0.36	9.63	3.70 ± 0.10
PMZE0.1T	3.33 ± 0.05	1.96	6.53 ± 0.10	7.76	3.20 ± 0.02
PMZE0.2T	3.39 ± 0.10	2.00	6.78 ± 0.20	7.84	3.36 ± 0.05
PMZE0.3T	3.54 ± 0.15	2.03	7.18 ± 0.30	6.84	3.11 ± 0.08
PMZE0.4T	3.58 ± 0.16	2.05	7.34 ± 0.34	7.49	3.51 ± 0.09
PMZE0.5T	3.61 ± 0.12	2.08	7.51 ± 0.24	7.20	3.41 ± 0.08
PMZE0.6T	3.65 ± 0.13	2.10	7.66 ± 0.26	5.82	2.80 ± 0.05

. The reported values for $D$ and $\kappa$ are the average between the results achieved by the two independent techniques. These values slightly increase with concentration of NPs. This result is supported by the fact that the values of $D$ and $\kappa$ of TiO₂ are higher than $D$ and $\kappa$ in the basic matrix PMZE0.0T. The maximum value of the $D$ for the samples presented in this work is $D = 3.65\times {10}^{-3}\left(c{m}^2/s\right)$, which represents a relatively high value, as required for applications in high power photonic devices, when compared to other similarly doped phosphate glass samples [40].

In many photonic devices such as laser systems, heat removal is critical to avoid thermal lensing and other deleterious effects on the device application induced by the temperature gradient. The most important physical parameter for heat removal capability of the material is $\kappa$ which was calculated using the obtained $D$ values of the samples as depicted in Equation (4). In calculations, we used the reported literature value of the heat capacity (c) for the phosphate glass $c = 0.73 J.g^{-1}.K^{-1}$ [40,41], and the measured mass density of the samples using the Archimedes method. The proportionality factor of $\kappa$ and $D$, $\rho$, showed increasing values between $1.95-2.10 \left(J/c{m}^3.K\right)$ versus the concentration of TiO₂ NPs. The results indicate that $\kappa$ also increases with the concentration of NPs giving a maximum value of $\kappa = 7.66\times {10}^{-3}\left(W/cm.K\right)$, as shown in Table 1. The studied glass samples exhibited relatively high values of $D$ and $\kappa$ as required for applications in high power photonic devices.

The value of $C = \Theta /P_{abs}$ for undoped glass was $C = 4.9 \left(1/W\right)$. This coefficient shows a decrease by adding TiO₂ NPs into the glass matrix, as shown in Table 1. The minimum averaged value $C = 5.82\left(1/W\right)$ was obtained for the doped samples. The constant C is a very interesting factor that depends on the glass matrix properties and the ratio between $ds/dT$ and $\kappa$. The thermo-optical parameter $ds/dT$ is associated with the deviation of the laser beam inside the material and the thermal lensing effect. This coefficient also decreases with NPs concentration, and thus its minimum value was determined to be $ds/dT = 2.8\times {10}^{-6}\left(1/K\right)$ which is a relatively low value when compared to other reported values for ceramics, crystals, and glasses [42]. The decreasing trend of $ds/dT$ in TiO₂ doped glass samples confirms that the thermal properties of the glass matrix were improved by the presence of TiO₂ NPs. The low $ds/dT$ value together with high $\kappa$ makes the glass matrix an excellent nearly “athermal” material with potential application in devices that require minimum optical distortion. The properties of some glasses are listed in

Table 2. Thermo-optical properties of some known glasses.

Glass Matrix	Dopants	$\mathit{D}\left[{10}^{-3}{\mathbf{cm}}^2{\mathbf{s}}^{-1}\right]$	$\mathit{\kappa }\left[{10}^{-3}{\mathbf{Wcm}}^{-1}{\mathbf{K}}^{-1}\right]$	$\mathit{d}\mathit{s}/\mathit{d}\mathit{T}[{10}^{-6} {\mathbf{K}}^{-1}]$	Reference
PMZ0.6T	Er3+ + TiO2	3.65 ± 0.13	7.66 ± 0.26	2.80 ± 0.05	Current work
PZABP	Yb3+ + ZnTe NC	2.6 ± 0.3	3.4 ± 0.4	1.0 ± 0.6	[25]
LG760	Nd3+	2.6	5.4	-	[41]
YAlB	Nd3+	4.1	10.6	6.9	[42]
TBZLN	Tm3+	3.01	2.5	1.5	[43]

for comparison. It is clear that the values of $D$ and $\kappa$ are higher compared to other reported values in well-known glasses. Specifically, the glass matrix investigated here shows higher values of $D$ and $\kappa$ in comparison to nanocrystal doped (PZABP), commercial (LG760) phosphate, and TBZLN glasses. While the obtained value of ds/dT is slightly higher than other compared glasses, it is much smaller than aluminoborate (YAIB) glasses.

5. Conclusions

The effect of doping with TiO₂ NPs on the thermo-optical properties of phosphate glass was investigated. TiO₂ NPs were inserted in the Er³⁺ doped sulfophosphate glass matrix and their presence was investigated by TEM and also demonstrated by the changes of the optical band gap and refractive index of the glass samples. The obtained values of $D$ and $\kappa$, are relatively high, and $ds/dT$ comparable with other reported values in similar glasses, thus demonstrating that this material can be used for applications in photonic devices. The doped samples demonstrated an increase in the values of $D$ and $\kappa$ with an increase in the amount of NPs, which is very important for applications where rapid heat removal is important. Finally, the results demonstrate the ability of photothermal spectroscopy, including TLS and BDS techniques, to achieve accurate measurements.