2.0 μm Ultra Broadband Emission from Tm³⁺/Ho³⁺ Co-Doped Gallium Tellurite Glasses for Broadband Light Sources and Tunable Fiber Lasers

Abstract

A flat 2.0 μm ultra broadband emission with a full width at half maximum (FWHM) of 329 nm is achieved in 1 mol.% Tm₂O₃ and 0.05 mol.% Ho₂O₃ co-doped gallium tellurite glasses upon the excitation of an 808 nm laser diode. The influence of Tm³⁺ and Ho³⁺ contents on 2.0 μm spectroscopic properties of gallium tellurite glasses is minutely investigated by absorption spectra, emission spectra, and lifetime measurement. In addition, emission cross section and gain coefficient of Ho³⁺ ions at 2.0 μm are calculated, and the maximum values reach 8.2 × 10⁻²¹ cm² and 1.54 cm⁻¹, respectively. Moreover, forward and backward energy transfer probability between Tm³⁺ and Ho³⁺ ions are qualitatively evaluated by the extended spectral overlap method. Large ratio of the forward energy transfer from Tm³⁺ to Ho³⁺ to the backward one (19.7) and high forward energy transfer coefficient (6.22 × 10³⁹ cm⁶/s) are responsible for effective 2.0 μm emission from Ho³⁺ ions. These results manifest that Tm³⁺/Ho³⁺ co-doped gallium tellurite glass is suitable for potential applications of broadband light sources and tunable fiber lasers operating in eye-safe 2.0 µm spectral region.

1. Introduction

In the past few decades, numerous studies have gone into achieving high-brightness broadband light sources and tunable fiber lasers operating at eye-safe 2.0 μm wavelength range because of broad applications in the fields of urology, gas sensing, remote atmospheric monitoring, and material processing, and their use as an efficient pumping source for obtaining mid-infrared supercontinuum [1,2,3,4,5,6]. It is well known that Tm³⁺:³F₄ → ³H₆ and Ho³⁺:⁵I₇ → ⁵I₈ radiative transitions are the most efficient and feasible ways to generate 2.0 μm emission when they are doped into an appropriate host glass. Moreover, both transitions work in the three-level quantum scheme and hence respective emission bands are relatively broad, which allows to obtain broadband emission from 1.7 to 2.1 μm [4,7]. Tm³⁺ has an intense absorption band near 808 nm, which allows for the excitation of high-power and low-cost laser diode (LD). Another advantage of the pump scheme is the so-called “two-for-one” cross relaxation process (³H₄ + ³H₆ → 2³F₄) resulting in a quantum efficiency of near 200% [8]. Additionally, Tm³⁺:³F₄ → ³H₆ transition is one of the broadest luminescent transitions among rare earth ions and thus enables a fair degree of wavelength tenability [8]. Compared with Tm³⁺, the emission wavelength of Ho³⁺:⁵I₇ → ⁵I₈ transition generates ~200 nm redshift, which overlaps with a crucial atmospheric transmission window and leads to lower absorption in some nonlinear crystals (e.g., ZnGeP₂) for the generation of mid-infrared light [7,9]. Moreover, the lifetime of Ho³⁺:⁵I₇ energy level is longer than that of Tm³⁺:³F₄ energy level, which is beneficial to reduce the laser threshold and achieve higher pulse energy in a Q-switched mode [9]. However, Ho³⁺ cannot be promoted directly by commercially available 808 or 980 nm LD, owing to the inexistence of a suitable ground absorption band. Therefore, a Tm³⁺/Ho³⁺ co-doped system is developed to utilize direct commercial LD pumping [10,11,12]. In this case, Tm³⁺ plays the role of a sensitizer that efficiently absorbs pumping energy and then transfers a part of this energy to Ho³⁺, followed by the generation of 2.0 μm emission. This system can make the best use of an emission bandwidth of Tm³⁺ and Ho³⁺ near 2.0 μm so it is expected to achieve ultra broadband emission by adjusting Tm³⁺ and Ho³⁺ concentrations. In fact, a 303 nm tuning range from 1727 to 2030 nm has been obtained in Tm³⁺/Ho³⁺ co-doped silica fiber laser [13]. Compared with silica glass, tellurite glass is characterized by lower phonon energy (780 cm⁻¹), excellent infrared transmission range (up to 5 μm), higher rare earth ion solubility, and large refractive index (>1.95) [7,8,14]. It is worth mentioning that tellurite glass owns different structural units such as TeO₄, TeO_3+δ, and TeO₃, which creates a range of electro-static fields around a rare earth ion and thus leads to the spectral broadening [15]. Richards et al. found that the full width at half maximum (FWHM) of Tm³⁺:³F₄ → ³H₆ emission band in the tellurite glass (200 nm) was larger than that in ZBLAN glass (125 nm) and silica glass (150 nm), indicating that tellurite glass host can extend the tuning range for 2.0 μm fiber lasers [8]. Recently, our group reported gallium tellurite glasses with excellent glass-forming ability, thermal stability, and 2.0 μm spectra properties [16,17]. Moreover, with the addition of 9 mol.% BaF₂, the emission intensity near 1.8 μm was 1.6 times as large as the original while the lifetime became 1.7 times as long as the original [18]. These outstanding optical properties hearten us to further explore whether Tm³⁺/Ho³⁺ co-doped gallium tellurite glasses is appropriate for broadband light sources and tunable fiber lasers.

In this investigation, we systematically study the effect of Tm³⁺ and Ho³⁺ concentrations on 2.0 μm spectroscopic properties of gallium tellurite glasses by absorption spectra, emission spectra, and lifetime measurement. A flat ultra broadband emission at 2.0 μm with FWHM of 329 nm is demonstrated by adjusting doping concentration. Furthermore, emission cross section and gain coefficient of Ho³⁺:⁵I₇ → ⁵I₈ transition are evaluated based on absorption spectra and emission spectra. Additionally, forward and backward energy transfer probabilities between Tm³⁺ and Ho³⁺ ions are qualitatively discussed by the extended spectral overlap method.

2. Materials and Methods

Gallium tellurite glasses with different nominal compositions of (81-x)TeO₂-10Ga₂O₃-9BaF₂-xTm₂O₃ (x = 0, 0.5, 1, 1.5, and 2), (80-y)TeO₂-10Ga₂O₃-9BaF₂-1Tm₂O₃-yHo₂O₃ (y = 0.05, 0.1, 0.15, 0.3, and 0.5), and 80.5TeO₂-10Ga₂O₃-9BaF₂-0.5Ho₂O₃ were prepared by standard melt-quenching method. A series of samples were labeled as TGBT-x (x = 0, 0.5, 1, 1.5, and 2), TGBTH-y (y = 0, 0.05, 0.1, 0.15, 0.3, and 0.5), and TGBH-0.5, respectively. Batches of 20 g mixtures by weighing and mixing high-purity reagents (99.99% minimum) were placed in the alumina crucible and melted in an electric furnace at ~950 °C for 30 min. The molten glasses were poured into a preheated cylindrical graphite mold, followed by annealing in the muffle furnace at 330 °C for 2 h, and then cooled down slowly to room temperature. The annealed samples were optically polished into Φ15 mm × 1.5 mm cylinders for subsequent measurements.

Absorption spectra of samples were obtained by UV/VIS/NIR double beam spectrophotometer (Perkin-Elmer Lambda 900, Waltham, MA, USA) in the wavelength range from 350 to 2200 nm. The fluorescence spectra were recorded with a computer-controlled Omni 5015i spectrometer (Zolix, Beijing, China) under the excitation of an 808 nm LD. The fluorescence signal was collected by InAs detector equipped with a choppe and lock-in amplifier. In addition, the luminescence decay curves of Tm³⁺ and Ho³⁺ were recorded by a digital oscilloscope (TDS3012C, Tektronix, OR, USA) after the samples were pumped with 808 nm pulse laser controlled by a function generator (TFG3051C, Tektronix, OR, USA). The pulse duration was 22.5 ms. All of the measurements were carried out at room temperature.

3. Results and Discussion

3.1. Absorption Spectra

Figure 1 shows the absorption spectra of Tm³⁺ singly doped, Ho³⁺ singly doped, and Tm³⁺/Ho³⁺ co-doped gallium tellurite glasses in the 350–2200 nm range. The typical absorption bands assigned to the transitions from the ground state to higher excited states of Tm³⁺ and Ho³⁺ are marked in the figure. For Tm³⁺ singly doped glass, there are five absorption bands centered at 473, 687, 794, 1214, and 1700 nm, which are corresponding to respective transitions from the ³H₆ ground state to the higher energy levels ¹G₄, ³F₂,₃, ³H₄, ³H₅, and ³F₄. For Ho³⁺ singly doped glass, eight absorption peaks located at 418, 450, 486, 538, 644, 892, 1154, and 1952 nm appear, which are assigned to respective transitions from the ⁵I₈ ground state to the higher energy levels ⁵G₅, ⁵G₆ + ⁵F₁, ⁵F₃, ⁵F₄ + ⁵S₂, ⁵F₅, ⁵I₅, ⁵I_6, and ⁵I₇. Energy levels above ¹G₄ energy level of Tm³⁺ and ⁵G₅ energy level of Ho³⁺are not clearly observed due to strong intrinsic bandgap absorption in the host glass. In addition, the peak positions of each absorption band for the Tm³⁺/Ho³⁺ co-doped glass sample are very similar to those reported previously from other host glasses [7,19,20]. It is worth noting that there is a strong absorption band centered at 794 nm from Tm³⁺:³H₆ → ³H₄ transition, which indicates that the commercial high-power 808 nm LD can act as an effective pump source for Tm³⁺ singly doped and Tm³⁺/Ho³⁺ co-doped samples. The inset of Figure 1 presents the integral absorption intensity at 538 nm as a function of Ho₂O₃ concentration. Good linear dependence on concentration reveals that Ho³⁺ ions are homogeneously distributed in the present gallium tellurite glasses and the concentration is in accord with the nominal value [21].

3.2. Fluorescence Spectra and Energy Transfer Mechanism

To study the effect of Tm³⁺ concentration on the 2.0 μm emission property and determine its optimum concentration, the fluorescence spectra of Tm³⁺ singly doped samples with different content pumped by 800 nm LD were measured, as shown in Figure 2. There is no emission band in the host glass without containing Tm³⁺. However, the spectra are characterized by an intense emission peak at 1808 nm resulting from ³F₄ → ³H₆ transition along with a very weak emission band near 1488 nm corresponding to ³H₄ → ³F₄ transition when Tm³⁺ ions are doped in the host glass. Moreover, with the increment of Tm³⁺ concentration, 1.8 μm emission is stronger until the concentration of Tm₂O₃ reaches 1 mol.%, which can be accounted for by the enhancement of cross-relaxation process (³H₄ + ³H₆ → 2³F₄) due to shortening the distance among neighboring Tm³⁺ ions. Then, the emission intensity decreases gradually with further increasing the concentration, which may ascribe to the concentration quenching phenomenon. The inset of Figure 2 shows that fluorescence intensity near 1488 nm is gradually reduced with increasing Tm₂O₃ concentration from 0.5 to 2 mol.%, which reveals that the cross-relaxation process becomes more significant and is in favor of the enhancement of 1.8 μm emission. Therefore, the optimum concentration of Tm₂O₃ is 1 mol.% in view of the 1.8 μm emission intensity.

Figure 3 presents the fluorescence decay traces of Tm³⁺:³F₄ energy level monitored at 1808 nm in TGBT-x glass samples. It is found that the fluorescence lifetime of ³F₄ energy level decreases monotonically from 1.42 to 0.24 ms with the increment of Tm₂O₃ concentration from 0.5 to 2 mol.%, which may be due to the enhancement of energy transfer probability toward unidentified impurities in samples such as OH⁻ groups. In addition, the fluorescence decay curves are well fitted by single-exponential and R² is above 0.999, indicating that the radiative decay process is prominent compared with the nonradiative decay process, benefitted from low maximum phonton energy and the presence of BaF₂. A similar single-exponential phenomenon has been observed in Tm³⁺-doped heavy metal gallate glasses and tellurite glasses [22,23].

In the case where the concentration of Tm₂O₃ was 1 mol.%, the influence of Ho³⁺ concentration on 2.0 μm emission property of Tm³⁺/Ho³⁺ co-doped glass samples was further investigated. Figure 4 exhibits the fluorescence spectra of Tm³⁺/Ho³⁺ co-doped TGBTH-y samples in the range from 1400 to 2200 nm under the excitation of 808 nm LD. It is noted that two emission bands from Tm³⁺ centered at 1488 and 1808 nm appear in TGBTH-y samples, while a new double peak at 2.0 μm arises, originating from Ho³⁺:⁵I₇ → ⁵I₈ transition, with the incorporation of Ho³⁺ ions. With gradually enhancing Ho₂O₃ from 0 to 0.5 mol.%, 1.8 μm emission intensity reduces and 2.0 μm emission intensity increases while 1488 nm peak intensity is almost constant, which is ascribed to the presence of an effective energy transfer process from Tm³⁺:³F₄ to Ho³⁺:⁵I₇ energy level and thus makes their intensity values approximately equal. The inset of Figure 4 shows Ho₂O₃ concentration dependence of the largest emission bandwidth, defined as full width at half maximum (FWHM), in TGBTH-y samples. It is found that FWHM increases from 193 to 329 nm with the addition of 0.05 mol.% Ho₂O₃ and then decreases gradually to 152 nm with further boosting Ho₂O₃ concentration to 0.5 mol.%. It is worth mentioning that a flat ultra broadband 2.0 μm emission with FWHM of 329 nm is achieved in 1 mol.% Tm₂O₃ and 0.05 mol.% Ho₂O₃ co-doped gallium tellurite glasses, which is due to energy transfer process from Tm³⁺:³F₄ to Ho³⁺:⁵I₇ energy level and partial overlap of Tm³⁺:³F₄ → ³H₆ and Ho³⁺:⁵I₇ → ⁵I₈ transitions. The value is larger than that of Tm³⁺/Ho³⁺ co-doped silicate-germanate glass (231.5 nm) [20] and silicate glass (189 nm) [24] and is slightly lower than that of Yb³⁺/Tm³⁺/Ho³⁺ triply doped gallo-germanate glass (343 nm) [25]. Larger FWHM will provide a better opportunity to achieve broad amplified spontaneous emission (ASE) sources and tunable fiber lasers [4,7]. In addition, the dependence of Ho³⁺:⁵I₇ lifetime on Ho₂O₃ concentration is presented in Figure 5. It is noted that the fluorescence lifetime of Ho³⁺:⁵I₇ energy level is gradually prolonged from 1.46 to 2.08 ms with increasing Ho₂O₃ concentration from 0.05 to 0.3 mol.% because of improved energy transfer from Tm³⁺:³F₄ to Ho³⁺:⁵I₇ energy level. However, with further increasing the concentration, the lifetime begins to decrease due to the effect of concentration quenching. The relationship between the lifetime and doping concentration is very similar to that reported previously in Tm³⁺/Ho³⁺ co-doped silicate and tellurite glasses [24,26].

According to above-mentioned results, the concerned energy transfer mechanisms in Tm³⁺/Ho³⁺ co-doped gallium tellurite glasses are shown in Figure 6 with the help of the simplified energy level diagram of Tm³⁺and Ho³⁺. When samples are excited by 808 nm LD, Tm³⁺ ions are initially motivated from the ³H₆ ground state to the ³H₄ excited state. Then, a small part of Tm³⁺ ions on the ³H₄ excited state decay radiatively to the ³F₄ energy level, emitting fluorescence at 1488 nm, while the majority of ions return nonradiatively to the ³F₄ energy level by muliphonon relaxation process and effective cross-relaxation process (CR) between two nearby Tm³⁺ ions (³H₄ + ³H₆ → 2³F₄). Tm³⁺ ions on the ³F₄ state return radiatively to the ground state, producing 1.8 μm photon. On the other hand, they excite Ho³⁺:⁵I₈ energy level to the ⁵I₇ energy level via energy transfer process between two adjacent Tm³⁺ and Ho³⁺ ions (Tm³⁺:³F₄+Ho³⁺:⁵I₈ → Tm³⁺:³H₆+Ho³⁺:⁵I₇). Finally, strong 2.0 μm emission from Ho³⁺ is observed by Ho³⁺:⁵I₇ → ⁵I₈ transition. It is worth noting that based on absorption spectra, the energy gap between ³H₄ → ³F₄ and ³H₆ → ³F₄ transitions is about 830 cm⁻¹, indicating that the cross-relaxation process has nonresonant character and only one or two phonons are demanded to bridge the energy gap because the maximum phonon energy of this gallium tellurite glass is nearly 787 cm⁻¹ [18].

3.3. Gain Properties and Energy Transfer Coefficients between Tm³⁺ and Ho³⁺ Ions

To evaluate the gain properties of Tm³⁺/Ho³⁺ co-doped gallium tellurite glasses, absorption and emission cross sections of Tm³⁺ and Ho³⁺ ions, corresponding to Tm³⁺:³H₆↔³F₄ and Ho³⁺:⁵I₈↔⁵I₇ transitions, were determined by McCumber theory [27], as shown in Figure 7a. It is noted that the peak absorption cross section (σ_a) of Ho³⁺ is 5.6 × 10⁻²¹ cm² at 1952 nm, which is higher than that of germanate glass (4.6 × 10⁻²¹ cm²) [28], lead silicate glass (3.9 × 10⁻²¹ cm²) [29], and silicate-germanate glass (2.8 × 10⁻²¹ cm²) [30]. Furthermore, the corresponding peak emission cross section (σ_e) reaches 8.2 × 10⁻²¹ cm² at 2042 nm, which is higher than that of germanate glass (5.2 × 10⁻²¹ cm²) [28], lead silicate glass (4.2 × 10⁻²¹ cm²) [29], silicate-germanate glass (4.8 × 10⁻²¹ cm²) [30], and tellurite glass (6.7 × 10⁻²¹ cm²) [19], indicating that high laser gain can be achieved in the fiber prepared by the present glass. After absorption and emission cross sections of Ho³⁺ ions were obtained and it was assumed that Ho³⁺ ions are only in either the ⁵I₇ or ⁵I₈ energy level, the gain coefficient G(λ) near 2.0 µm was computed by the expression to estimate the gain property qualitatively [31].

$$G(\lambda )=N[p{\sigma }_e-(1-p){\sigma }_a]$$

(1)

where N stands for the total population of Ho³⁺ ions and p represents the population inversion defined as the ratio between the population at the ⁵I₇ energy level and the total population. Figure 7b describes the effect of ⁵I₇ → ⁵I₈ transition wavelength on the gain coefficient in gallium tellurite glasses when p increases from 0 to 1 in steps of 0.2. It is found that the position of maximum gain moves toward shorter wavelength when p increases, which is a typical feature of the quasi-three-level system. Furthermore, positive gain coefficient occurs when p equals 0.2, revealing a low pumping threshold. In addition, the maximum gain coefficient reaches 1.54 cm⁻¹ at 2048 nm, which is larger than that of lead silicate glass (0.89 cm⁻¹) [32], germanate-tellurite glass (0.27 cm⁻¹) [33], and tellurite glass (0.37 cm⁻¹) [19]. It is worth noting that overlay area between Tm³⁺ emission and Ho³⁺ absorption cross sections is much larger than that between Ho³⁺ emission and Tm³⁺ absorption cross sections, meaning that the forward energy transfer probability from Tm³⁺:³F₄ to Ho³⁺:⁵I₇ energy level is more efficient than the backward one. In order to evaluate forward and backward energy transfer probabilities between Tm³⁺ and Ho³⁺ ions qualitatively, a method proposed by Miyakawa and Dexter was adopted [34]. The probability rate of energy transfer from Tm³⁺ to Ho³⁺ can be computed by the following formula [34]:

$$W_{D-A}=(\frac{2\pi }{\hslash }){\left|H_{DA}\right|}^2{S}_{DA}^N$$

(2)

where $\left|H_{DA}\right|$ represents the matrix element of the perturbation Hamilton between initial and final states in the energy transfer process, $S_{DA}^N$ stands for the overlap integral between the m-phonon emission sideband of donor ions (D referring to Tm³⁺ here) and the k-phonon absorption sideband of acceptor ions (A referring to Ho³⁺ here), and N (N = m + k) denotes the total phonons in the energy transfer process. Subsequently, Tarelho et al. propose a method to determine the spectral sideband based on calculated emission and absorption cross sections for rare earth (RE) ions, as described by the following equations [35]:

$${\sigma }_e^D{}_{(\mathrm{m}-\mathrm{phonons})}={\sigma }_e^D({\lambda }_m^{+})\approx \frac{S_0^m{e}^{-S_0}}{m!}{(\overline{n}+1)}^m{\sigma }_e^D{}_{(\exp t)}(E-m\hslash w_0)$$

(3)

$${\sigma }_a^A{}_{(\mathrm{k}-\mathrm{phonons})}={\sigma }_a^A({\lambda }_k^{-})\approx \frac{S_0^k{e}^{-S_0}}{k!}{(\overline{n})}^k{\sigma }_a^A{}_{(\exp t)}(E+k\hslash w_0)$$

(4)

where S₀ represents the Huang-Rhys factor with the value of 0.31 for RE³⁺ ions, $\hslash {\omega }_0$ stands for the phonon energy of the host, and $\overline{n}=1/(e^{\hslash w_0/k_{B}T}-1)$ is the average occupancy of phonon mode at temperature T. In addition, ${\lambda }_m^{+}=1/(1/\lambda -m\hslash w_0)$ and ${\lambda }_k^{-}=1/(1/\lambda +k\hslash w_0)$ signify the wavelengths of Tm³⁺ with m-phonon emission and Ho³⁺ with k-phonon absorption, respectively. If we neglect the k-phonon annihilation process and just consider the m-phonon creation process, forward (D → A) and backward (A → D) energy transfer coefficients can be estimated by the following equations [35].

$$C_{D-A}=\frac{6c{g}_{low}^D}{{(2\pi )}^4{n}^2{g}_{up}^D}{\displaystyle \sum _{N=0}^{\infty }{\displaystyle \sum _{k=0}^N{P}_{(N-k)}^{+}}}{P}_k^{-}{P}_k^{+}{\displaystyle \int {\sigma }_e^D}({\lambda }_N^{+}){\sigma }_a^A(\lambda )d\lambda$$

(5)

$$C_{A-D}=\frac{6c{g}_{low}^A}{{(2\pi )}^4{n}^2{g}_{up}^A}{\displaystyle \sum _{N=0}^{\infty }{\displaystyle \sum _{k=0}^N{P}_{(N-k)}^{-}}}{P}_k^{-}{P}_k^{+}{\displaystyle \int {\sigma }_e^A}({\lambda }_N^{-}){\sigma }_a^D(\lambda )d\lambda$$

(6)

$$P_{(N-k)}^{+}\cong \exp [-(2\overline{n}+1)S_0]\frac{S_0^{(N-k)}}{(N-k)!}{(\overline{n}+1)}^{(N-k)}$$

(7)

$$P_k^{-}\cong \exp [-2\overline{n}{S}_0]\frac{S_0^k}{k!}{(\overline{n})}^k$$

(8)

where $g_{low}^D$ ($g_{low}^A$) and $g_{up}^D$ ($g_{up}^A$) stand for the degeneracies of the respective lower and upper states of the donor (acceptor), respectively. In addition, $P_{(N-k)}^{+}$ and $P_k^{-}$ represent the probability of (N-k)-phonon emission by the donor and k-phonon absorption by the acceptor, respectively. Based on above equations, forward and backward energy transfer coefficients between Tm³⁺ and Ho³⁺ ions were obtained and are listed in

Table 1. Energy transfer parameters between Tm³⁺ and Ho³⁺ in TGBTH-y sample.

Energy Transfer	N( Number of Phonons) (% Phonon Assisted)		Energy Transfer Coefficient (cm6/s)
Tm3+ → Tm3+(migration) (3F4 + 3H6 → 3H6 + 3F4)	0	1	8.98 × 10−39
	99.86	0.16
Tm3+ → Ho3+ (direct transfer) (3F4 → 5I7)	0	1	6.22 × 10−39
	94.95	5.05
Ho3+ → Tm3+ (back transfer) (5I7 → 3F4)	0	1	3.16 × 10−40
	99.32	0.68

. It is noted that the energy transfer coefficient of Tm³⁺ → Tm³⁺ migration is the largest due to the largest overlapping area, as shown in Figure 7a. Additionally, the ratio of forward to back energy transfer coefficient (C_Tm-Ho/C_Ho-Tm) reaches 19.7, indicating that the forward energy transfer from Tm³⁺ to Ho³⁺ is more effective than the backward one and thus ensures to achieve a strong 2.0 μm emission from Ho³⁺. Comparing the percentage of each phonon participation, one can observe that both energy transfer processes between Tm³⁺ and Ho³⁺ are almost resonant energy transfer with non-phonon creation or annihilation. It is worth mentioning that the forward energy transfer coefficient from Tm³⁺:³F₄ to Ho³⁺:⁵I₇ energy level (6.22 × 10³⁹ cm⁶/s) in the present glass is larger than that of germinate-tellurite glass (1.42 × 10³⁹ cm⁶/s) [33] and silicate-germanate glass (3.39 × 10³⁹ cm⁶/s) [20]. Therefore, Tm³⁺/Ho³⁺ co-doped gallium tellurite glass with FWHM of 329 nm, larger emission cross section, and high C_Tm-Ho is a promising candidate for mid-infrared tunable fiber lasers.

4. Conclusions

In brief, dependence of Tm³⁺ and Ho³⁺ concentrations on 2.0 μm spectroscopic properties of Tm³⁺/Ho³⁺ co-doped gallium tellurite glasses under an 808 nm excitation is studied in detail. A flat ultra broadband emission at 2.0 μm with FWHM of 329 nm is achieved in gallium tellurite glasses co-doped with 1 mol.% Tm₂O₃ and 0.05 mol.% Ho₂O₃, benefitting from efficient energy transfer process from Tm³⁺:³F₄ to Ho³⁺:⁵I₇ energy level and partial overlap of Tm³⁺:³F₄ → ³H₆ and Ho³⁺:⁵I₇ → ⁵I₈ transitions. Furthermore, the present glass shows a long lifetime of Ho³⁺:⁵I₇ energy level (2.08 ms), high emission cross section (8.2 × 10⁻²¹ cm²), and gain coefficient (1.54 cm⁻¹) near 2.0 μm. Additionally, forward and backward energy transfer probabilities between Tm³⁺ and Ho³⁺ ions are qualitatively calculated by the extended spectral overlap method. Larger C_Tm-Ho/C_Ho-Tm (19.7) and high forward energy transfer coefficient (6.22 × 10³⁹ cm⁶/s) ensure effective 2.0 μm emission. Consequently, these results indicate that this gallium tellurite glass is a very prospective candidate in constructing broadband light sources and tunable fiber lasers operating in eye-safe 2.0 µm spectral range.