Mid-infrared (IR) wavelength lasers, particularly fiber lasers at around 3 μm, have been used in numerous applications in a wide range of fields including military affairs, eye-safe laser radar, and medical surgery^[1–4]. Because of the ${\mathrm{Er}}^{3+}\text{:}{}^4{\mathrm{I}}_{11/2}\to {}^4{\mathrm{I}}_{13/2}$ transition at 2.7 μm, ${\mathrm{Er}}^{3+}$-doped glass is especially attractive and has been investigated widely^[3–31]. To obtain high-power output and high mid-IR laser efficiency, an appropriate glass host is extremely important. An efficient glass host must satisfy several important factors, such as high IR transmittance, low hydroxyl group (i.e., OH) concentration, low phonon energy, good thermal stability, and high rare-earth solubility.

Fluoride glass^[3–10] presents low phonon energy and wide mid-IR transmittance. ${\mathrm{Er}}^{3+}$-doped fluoride glasses have been used to develop fiber lasers around 2.8 μm. For example, output power of 10 W level at 2.8 μm was demonstrated by a heavily ${\mathrm{Er}}^{3+}$-doped ${\mathrm{ZrF}}_4\text{-}{\mathrm{BaF}}_2\text{-}{\mathrm{LaF}}_3\text{-}{\mathrm{AlF}}_3\text{-}\mathrm{NaF}$ (ZBLAN) glass fiber laser in 1994^[6]. In 2009, Tokita et al. reported a liquid-cooled 24 W mid-IR ${\mathrm{Er}}^{3+}$: ZBLAN fiber laser^[9]. In 2011, Faucher et al. reported fabrication of a 20 W passively cooled, single-mode, all-fiber laser at 2.8 μm from a heavily ${\mathrm{Er}}^{3+}$-doped fluoride fiber^[10]. However, the glass transition temperature ($T_g$) of ZBLAN is as low as 267°C^[3], which means poor thermal stability. In addition, another disadvantage of ZBLAN is its poor chemical stability^[4], and it is readily corroded in the moist environment. All these drawbacks limit the scaling up of the output power in laser applications. Consequently, researchers must find a new kind of mid-IR glass with better thermal and chemical stability.

Besides fluoride glass, studies on oxide system glass, such as tellurite^[11], and germanate^[12,13] glasses have been carried out. These traditional oxide glasses can be prepared and fiberized easily as they offer good thermal durability and stable physicochemical properties. However, these glasses possess high intrinsic phonon energy; for example, germanate glass possesses a maximum phonon energy of $900{\mathrm{cm}}^{-1}$^[13], and tellurite glass possesses a maximum phonon energy of $750{\mathrm{cm}}^{-1}$^[15]. The multi-phonon relaxation rate depends on the maximum phonon energy of the host glass^[5]. Compared with fluoride glass ($500{\mathrm{cm}}^{-1}$)^[3–6], the high phonon energy increases multi-phonon relaxation rates in those glasses and reduces the quantum efficiency of lasers^[5].

To obtain an advantageous glass host with both low phonon energy and high thermal stability, oxyfluoride glasses are expected to feature good optical and thermal properties representing a compromise between pure fluoride and oxide glasses. These glasses, such as fluorosilicate^[16,17], fluorotellurite^[18–22], and fluorophosphate^[23,24], have been investigated over the last several years.

Gallium-based oxide glass possesses high thermal stability and relatively low phonon energy ($650–675{\mathrm{cm}}^{-1}$)^[32,33]; as such, this glass is a good candidate as glass host. In this work, a new kind of ${\mathrm{Er}}^{3+}$-doped fluorogallate glass is prepared. A certain amount of fluorides is useful to remove ${\mathrm{OH}}^{-}$ in the glass via the reaction ${\mathrm{F}}^{-}+{\mathrm{OH}}^{-}\to \mathrm{HF}\uparrow +{\mathrm{O}}^{2-}$. Upon 980 nm excitation, an intense mid-IR emission at around 2.71 μm is observed. A large fluorescence branching ratio $\beta$ (21.71%) and a maximum stimulated emission cross-section ${\sigma }_{\text{em}}$ of ${\mathrm{Er}}^{3+}\text{:}{}^4{\mathrm{I}}_{11/2}\to {}^4{\mathrm{I}}_{13/2}$ transition are obtained.

The investigated glass has the nominal composition $[35{\mathrm{Ga}}_2{\mathrm{O}}_3-45\mathrm{SrO}-10{\mathrm{BaF}}_2-10({\mathrm{LaF}}_3+{\mathrm{YF}}_3+{\mathrm{AlF}}_3)]+x{\mathrm{Er}}_2{\mathrm{O}}_3$ ($x=0$ and 5 mol. %, terms GaOF0 and GaOF5, respectively).

High-purity reagent grade chemicals were used as starting materials. The batches were weighed and dried in a vacuum dry chamber at 100°C for 1 h, and then transferred to a platinum crucible. Then the glass samples were melted at 1400°C in a furnace for 1 h and then poured into a preheated stainless steel mold. After annealing and optical polishing, a series of measurements were performed at room temperature. The refractive indices of the samples were measured by the prism minimum-deviation method, and the values for GaOF0 and GaOF5 are 1.7190 and 1.7394, respectively. Using distilled water as an immersion liquid, the densities were measured by Archimedes’ method. Characteristic temperatures were determined using a NETZSCH STA 409PC/PG instrument. IR transmission spectra were obtained by a Thermo Nicolet [Nexus Fourier-transform (FT) IR] spectrophotometer. Raman spectra were recorded with a Renishaw inVia Raman spectrometer using a 488 nm excitation line. A Perkin–Elmer Lambda 900 UV/visible/near-IR (NIR) spectrophotometer was used to measure absorption spectrum in the 250–1700 nm region. Emission spectra were measured by a Triax 550-type spectrometer (Jobin–Yvon) upon excitation at 980 nm.

The chemical durability of the GaOF5 sample was measured as follows. First, the weighed sample (W1) was placed in distilled water. The glass was then kept in a thermostatic water bath at 95°C for 24 h, after which the sample was cooled and dried in a drying box at 60°C for 4 h. Finally, the dry sample was weighed again (W2). The chemical durability of GaOF5 glass sample was evaluated in terms of the $\mathrm{\Delta }W$ value, which was calculated as follows^[21]$$\mathrm{\Delta }W=\frac{\mathrm{W}1-\mathrm{W}2}{\mathrm{W}1}\times 100\%.$$(1)

The $\mathrm{\Delta }W$ of GaOF5 is $75.0\mathrm{mg}/\mathrm{g}$; this value is approximately half of that of ZBLAN glass ($151.6\mathrm{mg}/\mathrm{g}$)^[21]. As a result, GaOF5 exhibits stronger resistance to water corrosion compared with ZBLAN glass.

The temperature of glass transition $T_g$ and temperature of onset crystallization peak $T_x$ are determined using a NETZSCH STA 409PC/PG differential scanning calorimeter at a heating rate of $10\mathrm{K}/\min$. A higher $T_g$ endows glass with good thermal stability at high pumping intensities^[31]. The difference between $T_g$ and $T_x$, $\mathrm{\Delta }T=T_x-T_g$, is frequently quoted as a rough indicator of thermal stability^[20,21]. A large $\mathrm{\Delta }T$ means strong inhibition to crystallization. Since fiber drawing has a reheating process and any crystallization during this process will enhance the scattering loss of the fiber, it is desirable for a glass to have $\mathrm{\Delta }T$ as large as possible. Terms $T_g$ and $\mathrm{\Delta }T$ of GaOF5 are 640°C and 150°C, respectively; these values are much higher than ZBLAN glass without ${\mathrm{Er}}^{3+}$ ($T_g\text{:}267°\mathrm{C}$, $\mathrm{\Delta }T\text{:}93°\mathrm{C}$)^[3]. Therefore, GaOF5 is probably more easily drawn into fibers than ZBLAN.

The Raman spectrum of the host glass is shown in Fig. 1. Peaks are located at 254, 518, and $671{\mathrm{cm}}^{-1}$. The low-frequency peaks at $254{\mathrm{cm}}^{-1}$ affirms the collective modes of local structures and heavy-metal vibrational modes^[32]. The band at $671{\mathrm{cm}}^{-1}$ is attributed to the stretching vibration of nonbridging oxygen in [${\mathrm{GaO}}_4$] tetrahedral^[32,33] and the band at $518{\mathrm{cm}}^{-1}$ can be attributed to Ga-O-Ga bond vibrations between two [${\mathrm{GaO}}_4$] tetrahedra^[33]. The maximum phonon energy of GaOF0 is $671{\mathrm{cm}}^{-1}$, which is lower than those of some glass systems, such as germanate ($900{\mathrm{cm}}^{-1}$)^[13], tellurite ($750{\mathrm{cm}}^{-1}$)^[15], and fluorotellurite ($700{\mathrm{cm}}^{-1}$)^[22]. The energy gap between the ${\mathrm{Er}}^{3+}\text{:}{}^4{\mathrm{I}}_{11/2}\to {}^4{\mathrm{I}}_{13/2}$ transition is approximately $3680{\mathrm{cm}}^{-1}$, which is over 5 times the maximum phonon energy of our glass. Thus, nonradiative relaxation induced by multi-phonon excitation ($W_{\mathrm{mp}}$) is minimal, and its effects on laser performance may be ignored^[5,16].

Figure 2 shows the transmittance spectrum of 1 mm thick GaOF0 which is used to determine the IR cutoff wavelength and OH absorption of the glass. The IR cutoff wavelength is the wavelength which the transmission of a 1 mm thick sample is 10%^[34]. The IR cutting edge of GaOF0 glass extends to 6.8 μm, which indicates that the investigated glass is a good kind of mid-IR material. The ${\mathrm{OH}}^{-}$ concentration in the glass can be expressed by^[7]$${\alpha }_{\mathrm{OH}}=\ln (T/T_0)/l,$$(2)where $l$ is the thickness of the sample; $T$ and $T_0$ are the incident and transmitted intensities, respectively. The calculated absorption coefficient ${\alpha }_{\mathrm{OH}}$ at 3.14 μm is $0.07{\mathrm{cm}}^{-1}$. In general, the OH absorption band extends from 2500 to $3800{\mathrm{cm}}^{-1}$ because of fundamental stretching vibrations of the OH groups; this region involves the energy gap of ${\mathrm{Er}}^{3+}\text{:}{}^4{\mathrm{I}}_{11/2}\to {}^4{\mathrm{I}}_{13/2}$ ($\sim 3680{\mathrm{cm}}^{-1}$). Therefore, decreasing OH contents can enhance the 2.7 μm emission. The OH in GaOF glass may be further decreased if the melting conditions are improved. Additional studies on OH removal in this glass will be carried out in the future.

Figure 3 shows the absorption spectrum of GaOF5 sample at room temperature. The shape and peak position of each transition are very similar to those in other ${\mathrm{Er}}^{3+}$-doped glasses^[3–31]. Absorption bands corresponding to transitions beginning from the ground state ${}^4{\mathrm{I}}_{15/2}$ to the high levels ${}^4{\mathrm{I}}_{13/2}$, ${}^4{\mathrm{I}}_{11/2}$, ${}^4{\mathrm{I}}_{9/2}$, ${}^4{\mathrm{F}}_{9/2}$, ${}^2{\mathrm{S}}_{3/2}$, ${}^2{\mathrm{H}}_{11/2}$, ${}^4{\mathrm{F}}_{7/2}$, ${}^4{\mathrm{F}}_{5/2}$, ${}^4{\mathrm{F}}_{3/2}$, ${}^2{\mathrm{H}}_{9/2}$, ${}^4{\mathrm{G}}_{11/2}$, and ${}^4{\mathrm{G}}_{9/2}$ are labeled. The relative absorption at around 980 nm indicates that the glass can be excited efficiently by a 980 nm laser diode (LD). The inset of Fig. 3 shows the intense 2.71 μm emission spectrum of GaOF5 upon excitation at 980 nm.

Based on Judd–Ofelt (J–O) theory^[35], the parameters ${\mathrm{\Omega }}_t$ of ${\mathrm{Er}}^{3+}$-doped glass can be calculated from a least-squares fit procedure to the integrated absorption bonds. The root-mean square error deviation of the intensity parameters is within $0.34\times {10}^{-6}$. This characteristic indicates the validity of J–O theory for predicting the spectral intensities of ${\mathrm{Er}}^{3+}$ and obtaining reliable calculations. As is shown in Table 1, ${\mathrm{\Omega }}_2$ in present glass is higher than that of ZBLAN, but lower than those of other glasses. In general, ${\mathrm{\Omega }}_2$ is associated with the covalency and asymmetry of the ligand field around the ${\mathrm{Er}}^{3+}$ ions^[19]. This behavior suggests that the asymmetry of the site occupied by ${\mathrm{Er}}^{3+}$ and the covalency in fluorogallate glass are higher than those of ZBLAN, but lower than those of other glasses. Terms ${\mathrm{\Omega }}_4$ and ${\mathrm{\Omega }}_6$ are related to the rigidity and 6-s electron density of the ${\mathrm{Er}}^{3+}$. As a spectroscopic quality factor, ${\mathrm{\Omega }}_4/{\mathrm{\Omega }}_6$ usually indicates the lasing efficiency of the laser transition of ${\mathrm{Er}}^{3+}$ in the host glass^[19]. The relatively high ${\mathrm{\Omega }}_4/{\mathrm{\Omega }}_6$ value of the present glass will benefit the radiative transition (Table 1), which means a strong stimulated emission can be induced^[19].

The spontaneous transition probability ($A$) and fluorescence branching ratio ($\beta$) of the transition ${\mathrm{Er}}^{3+}\text{:}{}^4{\mathrm{I}}_{11/2}\to {}^4{\mathrm{I}}_{13/2}$ in various glasses are also listed in Table 1. The corresponding values for the GaOF5 are $25.89{\mathrm{s}}^{-1}$ and 21.71%, respectively. Compared with other glasses, GaOF5 has a relatively higher fluorescence branching ratio. The branching ratio is a critical parameter in laser design because it characterizes the possibility of attaining stimulated emission from specific transitions.

Based on Fuchtbauer–Ladenburg theory^[19], the stimulated emission cross section ${\sigma }_{\text{em}}$ can be determined from the emission spectrum $${\sigma }_{\text{em}}(\lambda )=\frac{{\lambda }_p^4{A}_{\text{rad}}}{8\mathrm{\pi }\mathrm{c}{n}^2}\times \frac{\lambda I(\lambda )}{\int \lambda I(\lambda )\mathrm{d}\lambda }.$$(3)

The absorption cross-section (${\sigma }_{\text{abs}}$) can be calculated using the McCumber equation^[19]$${\sigma }_{\text{abs}}(\lambda )={\sigma }_{\text{em}}(Z_U/Z_L)\exp [(-\epsilon -\mathrm{h}\mathrm{c}{\lambda }^{-1})/\mathrm{k}T],$$(4)where ${\lambda }_p$ is the peak fluorescence wavelength, $A_{\text{rad}}$ is the spontaneous transition probability, $I(\lambda )$ is the fluorescence spectra intensity, and $n$ and c are the refractive index and light velocity in vacuum, respectively. Term $\epsilon$ is the net free energy required to excite one ${\mathrm{Er}}^{3+}$ ion from the ${}^4{\mathrm{I}}_{13/2}$ to ${}^4{\mathrm{I}}_{11/2}$ state at the temperature $T$, and k and h are the Boltzmann’s and Planck’s constants, respectively. Terms $Z_U$ and $Z_L$ are the partition functions of the lower and upper manifolds, respectively.

The stimulated emission cross section and absorption cross section spectra obtained for GaOF5 are shown in Fig. 4(a), and the maximum value of ${\sigma }_{\text{em}}$ is $1.04\times {10}^{-20}{\mathrm{cm}}^2$. Compared with other glasses listed in Table 1, GaOF5 has a high emission cross section, which could provide high gain for a laser medium^[37].

Based on ${\sigma }_{\text{em}}$ and ${\sigma }_{\text{abs}}$, the wavelength dependence of net gain can be calculated^[7] as a function of population inversion of the upper laser level to determine the gain property qualitatively $$G(\lambda )=P·{\sigma }_{\text{em}}(\lambda )-(1-P)·{\sigma }_{\text{abs}}(\lambda ),$$(5)where $P$ is the population inversion parameter, and ${\sigma }_{\text{em}}$ and ${\sigma }_{\text{abs}}$ are the emission and absorption cross section, respectively. The gain cross section of GaOF5 as a function of population inversion is shown in Fig. 4(b). A positive gain is achieved when $P>0.5$, close to the case in ZBLAN glass^[38], which implies that a low pumping threshold could be achieved during ${\mathrm{Er}}^{3+}\text{:}{}^4{\mathrm{I}}_{11/2}\to {}^4{\mathrm{I}}_{13/2}$ laser operation.

As usual, the experimental lifetime (${\tau }_{\text{exp}}$) in the glass is lower than the calculated value (${\tau }_{\text{rad}}$) based on the J–O theory and the deviation is due to the nonradiative decay rates. Term ${\tau }_{\text{exp}}$ can be defined as^[39]$$\frac{1}{{\tau }_{\exp }}=\frac{1}{{\tau }_{\text{rad}}}+W_{\mathrm{mp}}+W_{\mathrm{cq}}+W_{\text{et}}+W_{\mathrm{OH}},$$(6)where the terms $W_{\mathrm{mp}}$, $W_{\mathrm{cq}}$, $W_{\text{et}}$, and $W_{\mathrm{OH}}$ denote the nonradiative decay rates corresponding to the multiphonon relaxation, concentration quenching, energy transfer to another doping impurity, and hydroxyl groups, respectively.

As we have previously analyzed in this work, the multiphonon relaxation for ${\mathrm{Er}}^{3+}\text{:}{}^4{\mathrm{I}}_{11/2}\to {}^4{\mathrm{I}}_{13/2}$ transition is minimal because of the low maximum phonon energy. Therefore, the $W_{\mathrm{mp}}$ can be ignored. All the starting materials are high-purity reagent-grade chemicals, so $W_{\text{et}}$ induced by the impurity can also be neglected in the present glass. The intense emission at 2.71 μm means low concentration effects in the present glass which means that $W_{\text{cq}}$ is very small.

Hydroxyl groups play a dominate role in the nonradiative decay process for 2.7 μm emission. We consider that the main nonradiative decay in our glass is due to $W_{\mathrm{OH}}$, and it will be further decreased if we improve the melting condition. Then the deviation between ${\tau }_{\exp }$ and ${\tau }_{\text{rad}}$ will be small. The quantum efficiency $\eta$, which is defined as the ratio of ${\tau }_{\exp }$ and ${\tau }_{\text{rad}}$, will be expected to be a high value.

In conclusion, a new kind of ${\mathrm{Er}}^{3+}$-doped fluorogallate glass with low maximum phonon energy is prepared. Compared with fluoride glass, the proposed glass possesses better chemical stability, higher $T_g$ (640°C) and larger $\mathrm{\Delta }T$ (150°C), and all of these characteristics are suitable for the fabrication of high-power laser fiber. A large fluorescence branching ratio ($\beta =21.71\%$) and stimulated emission cross-section (${\sigma }_{\text{em}}=1.04\times {10}^{-20}{\mathrm{cm}}^2$) at 2.71 μm are obtained by J–O theory. In addition, the nonradiative relaxation at 2.7 μm in the glass is also discussed. The results suggest that the proposed glass might be considered as a promising material for mid-IR high-power fiber lasers.