1 Introduction

With the rapid development of high-density optical storage and the demand for wavelength-division-multiplexing communication networks, there is an urgent need for erbium-doped fiber amplifiers (EDFAs) with an intense and broad gain spectrum in the communication window at approximately 1.53 μm [1,2,3,4]. Silica-based EDFAs have drawn considerable attention due to their lower optical loss, excellent thermal stability, and chemical durability; however, the narrow gain spectrum (~ 35 nm) of these EDFAs limits the number of signal channels and restricts potential applications for broadband transmission [5,6,7]. To obtain an EDFA with a broader gain bandwidth, Er3+-doped tellurite, oxyfluoride, phosphate, and borate glasses have been synthesized, and the optical properties of these materials have been investigated [8,9,10,11]. By and large, the RE emission in glass host strongly depends on crystal-field effects, local environment where the ion is distributed, phonon energies, and refractive index of glass [9]. Among various host glasses, Er3+-doped borate glasses are superior due to their wider full width at half maximum (FWHM), which is more suitable for broadband signal amplifiers [12,13,14]. Furthermore, borate glasses exhibit additional advantages such as good rare-earth-ion solubility, a high refractive index, a large glass-forming region, and high phonon energy, which is convenient for mechanical processing and fiber drawing [15, 16].

The Er3+ ion is a rare earth ion with numerous energy levels; its different excitation energies lead to several emission phenomena such as 1-μm and 1.5-μm near-infrared emission and 2.8-μm mid-infrared emission. To maximize the opportunity for 1.5-μm-band fluorescence (corresponding to the Er3+:4I13/2 → 4I15/2 transition), the 4I11/2 → 4I13/2 transition can be accelerated by different approaches [17]. One desirable method is to adopt a glass with high phonon energy as the host, in which the 4I13/2 energy level can be populated by multi-phonon relaxation. This method is benefited by a high non-radiative relaxation rate for multi-phonon processes (≤ 1013 s−1) [18]. In particular, for borate glass hosts, the high slope efficiency of the 1.5-μm-band emission results in a higher multi-phonon relaxation rate than in other host glasses. Additionally, the 1.53-μm emission of Er3+ can be enhanced by the introduction of Yb3+ due to its large absorption cross-section at 980 nm, which increases the Er3+:4I13/2 population due to energy transfer (ET) from Yb3+ to Er3+ following a non-radiative transition from 4I11/2 to 4I13/2.

In this work, Er3+/Yb3+-codoped borate glasses were synthesized, and the glass structure and optical properties were investigated for potential application as a optical amplifier. The Judd–Ofelt parameters (Ω2, Ω4, Ω6, and Sed) were evaluated based on measured absorption spectra and the Judd–Ofelt theory, which is crucial for 1.53-μm-band signal gain of Er3+. Furthermore, the effect of ET on the 1.53-μm-band signal gain was investigated theoretically in Er3+/Yb3+-codoped borate glasses, which is beneficial to the signal-stimulated emission amplification.

2 Experimental

2.1 Glass preparation

Glass samples were synthesized by a conventional melt-quenching technology using high-purity powders (99.9%). The compositions of the as-prepared glass samples are 59.5% B2O3–15% WO3–20% ZnO–5% Y2O3–0.5Yb2O3 and (59.5 − x)% B2O3–15% WO3–20% ZnO–5% Y2O3–0.5Er2O3−x% Yb2O3 (x = 0, 0.5, 1.0, 2.0, and 5.0) in mol%, and the obtained glass samples are denoted as BY and BEY0–4 for clarity. Notably, the introduction of Y2O3 can increase the quenching concentration of Er3+ and Yb3+ ions and can enhance the linearity in the fiber [8]. Batches of 20.0 g of well-mixed original materials were weighed and fully melted in a corundum crucible at 900 °C–1100 °C for 20–30 min under a dry argon atmosphere. The obtained glass melts were casted in preheated brass molds, annealed at 300 °C–360 °C for 4–6 h, and then slowly cooled to room temperature. Finally, all of the glass samples were cut and polished for optical measurements.

2.2 Material characterization

The amorphous nature of the glass samples was confirmed using a D/Max-3C X-ray diffractometer (XRD) with Cu Kα radiation (1.5405 Å, 40 kV, 60 mA). The inner structure and phonon energy of our prepared borate glasses were investigated based on Raman spectra acquired using a high-resolution NRS-3300 laser Raman spectrophotometer (JASCO) system. Absorption spectra of the glass samples were measured using a Perkin-Elmer-Lambda 950 UV/Vis/NIR spectrophotometer in the wavelength range of 400–1700 nm. The photoluminescence (PL) spectra in the near-infrared region were recorded with an FLS920 spectrophotometer (Edinburgh Instruments, Livingston, UK) upon excitation of a 980-nm laser diode (LD) with a maximum power of 2 W. Fluorescence decay curves of Er3+ were recorded with light pulses from a 980-nm LD and a TDS1012 100-MHz oscilloscope.

3 Results and discussion

3.1 Structural behavior

To investigate the structure of the prepared glass samples, the XRD patterns of Er3+ single+-doped and Yb3+/Er3+-codoped borate glass samples were obtained, as shown in Fig. 1. All of the XRD patterns are similar in shape and show broad humps, confirming the amorphous nature of the glass samples. Meanwhile, sharp diffraction peaks are not present in these patterns upon the introduction of Er3+ and Yb3+ ions, indicating that the Er3+ and Yb3+ ions are homogeneously distributed in the borate glass lattice.

Fig. 1
figure 1

XRD patterns of Er3+ single-doped and Er3+–Yb3+-codoped borate glasses

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To investigate the interior structure and maximum phonon energy of the glass structure, Raman measurements were carried out on Er3+ single-doped and Er3+/Yb3+-codoped borate glass samples. Figure 2 shows the Raman spectra of Er3+ single-doped (BEY0) and Er3+/Yb3+-codoped (BEY3) samples for comparison. The profiles exhibit similar shapes, with two well-defined bands located at 270 and 780 cm−1. The band at 270 cm−1 is attributed to stretching vibrations of O–B–O in the [BO4] units, while the second band at 780 cm−1 originates from bending vibrations of the B–O–B bond in the [BO3] units [19, 20]. The maximum phonon energy of our borate glass is approximately 800 cm−1 according to the Raman spectra, which accelerates the depopulation of the Er3+:4I11/2 to 4I13/2 level through multi-phonon relaxation, thus increasing the 1.53-μm emission intensity.

Fig. 2
figure 2

Raman spectra of Er3+ single-doped and Er3+–Yb3+-codoped borate glasses

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3.2 Absorption spectra and Judd–Ofelt analysis

Absorption spectra of the glass samples were recorded for a wavelength range of 400–1700 nm. As an example, the absorption spectra of a Yb3+-doped sample with 1.0% mol Yb3+ (BY), an Er3+-doped sample with 1.0% mol Er3+ (BEY0), and an Er3+–Yb3+-codoped sample with 1.0% mol Er3+ and 1.0% mol Yb3+ (BEY1) are presented in Fig. 3. In the absorption spectrum of the Yb3+-doped sample, there is only one broad absorption peak located at 980 nm, which is assigned to the Yb3+:2F7/2–2F5/2 transition. In contrast, the Er3+-doped sample exhibits inhomogeneous absorption peaks located at 406, 451, 490, 520, 542, 650, 792, 980, and 1532 nm. These peaks are ascribed to transitions from the ground state 4I15/2 of Er3+ to each excited state. The absorption spectrum of the Er3+–Yb3+-codoped sample is similar to that of the Er3+-doped sample, although the peak at 980 nm is broader and more intense due to the overlap of the Yb3+:2F7/2-2F5/2 and Er3+:4I15/2–4I11/2 transitions. In addition, the corresponding absorption cross section increases from 3.18 × 10−21 to 2.93 × 10−20 cm2 [21]. The shapes of the BEY2–4 absorption spectra are similar to that of BEY1 except for the intensity of the 980-nm peak, which increases with increasing Yb3+ concentration.

Fig. 3
figure 3

Absorption spectra of Yb3+, Er3+ single-doped, and Er3+–Yb3+-codoped borate glasses

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The Judd–Ofelt theory provides an important theoretical method for investigating the optical properties of RE-doped glasses. Based on a least-square fit [22] to the absorption spectra, the three Judd–Ofelt intensity parameters [(Ωt = 2, 4, 6)] of our prepared borate glasses were determined, as listed in Table 1.

Table 1 Judd–Ofelt intensity parameters [Ωt (t = 2, 4, 6)] and spectral line intensities (Sed) for the 4I13/2 4I15/2 transition of Er3+ in BEYx (x = 0, 1, 2, 3) glass samples
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These three intensity parameters are associated with the ligand structure of the glass matrix; for instance, Ω2 is associated with the ligand symmetry, and Ω6 is related to the covalency of the metal–ligand bond, which increases with decreasing covalency of the Er–O bond [23]. Because ZnO and WO3 are excellent glass formers, when these components are introduced into the glass system, more non-bridge oxygen ions coordinate with the cations in the glass, as compared with Er3+ and Yb3+ ions. Consequently, the lower covalency of the Er–O and Yb–O bonds leads to a higher Ω6 value, which then increases with increasing Yb3+ concentration. According to the report of Tanabe [24], the fluorescence emissions of Er3+, including emissions due to transitions from various excited energy levels to the ground state 4I15/2, are primarily attributed to the electric-dipole transition. To acquire a broader and more intense fluorescence emission spectrum of Er3+ ions, one feasible method is to increase the spectral line strength (Sed) of the electric-dipole transition. Here, the Sed value for the electric-dipole transition is calculated from the following equation based on the three intensity parameters:

$$S_{{{\text{ed}}}} \, \left[ {{}^{4}{\text{I}}_{13/2} \to {}^{4}{\text{I}}_{15/2} } \right] = 0.0188\varOmega_{2} + 0.1176\varOmega_{4} + 1.4617\varOmega_{6} ].$$

This equation indicates that Sed primarily depends on the Judd–Ofelt intensity parameter Ω6, which has the largest weighted coefficient of 1.4617. For our prepared borate glasses, the calculated Ω6 value is larger than that of other glasses in the literature [25, 26], resulting in a larger Sed. Therefore, a broader and more intense 1.5-μm emission from Er3+ ions is acquired. Note that the calculated results of J–O theory for BEY0–3 (with Yb3+ doping concentrations are 0, 1.0, 2.0, and 4.0 mol%, respectively) is credible according to the previous reports [27, 28]. However, with the concentration of Yb3+ increasing to 10.0 mol% in BEY4, the impurities of rare earth ions may reduce the accuracy of the calculation result of J–O theory. Consequently, the J–O parameters of BEY4 have not quantitatively calculated and not listed in Table 1.

3.3 1.53-μm fluorescence

Figure 4 shows the 1.53-μm fluorescence emission spectrum of the Er3+-doped sample (BEY0) in the wavelength range of 1400–1700 nm, as measured under 980-nm excitation. The spectrum shows a broad emission peak at 1.53-μm, and the fluorescence full width at half maximum (FWHM) reaches 82 nm, which is larger than that of tellurite (53 and 64 nm) [8, 27], germanate [29], silicate (40 nm) [6, 7], oxyfluoride (63 nm) [9], and phosphate [10] glasses. Note that all samples possess the same FWHM since the Er3+ concentration is fixed to be 1.0 mol%, while the emission intensity increases to 166.7% in Yb3+/Er3+-codoped glass sample (BEY4) due to the ET process. The larger FWHM value is attributed to the internal structure of borate glass, which consists of [BO3] trigonal pyramid and [BeO4] trigonal bi-pyramid units. As ZnO and Y2O3 are incorporated into the two types of networks, the glasses exhibit different types of dopant sites with varying spatial distributions and ligand fields, which increases the disorder degree of the glass host and further leads to an inhomogeneously broadened emission spectrum [26]. Additionally, the greater FWHM also arises from the high phonon energy of the borate glass, which promotes rapid non-radiative relaxation from 4I11/2 to 4I13/2 in Er3+ ions by a multi-phonon process. Furthermore, the 1.53-μm emission intensity increasing in Yb3+/Er3+-codoped glass samples is ascribed to the ET between Yb3+ and Er3+ ions, during which more Er3+ ions at the 4I13/2 level join the 1.53-μm-band-stimulated emission due to the efficient absorption of pump photons by Yb3+ ions.

Fig. 4
figure 4

The emission spectrum of the Er3+-doped borate glass in the wavelength range of 1400–1700 nm upon 980 nm excitation

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3.4 Energy transfer mechanism

To elucidate the ET from Yb3+ to Er3+, Fig. 5 displays emission spectra of Er3+ single-doped (BEY0) and Er3+-Yb3+-codoped samples (BEY1–4) upon 980-nm excitation; in this case, the Er3+:4I11/2 and Yb3+:2F5/2 energy levels are both populated. For the Er3+ single-doped and Er3+–Yb3+-codoped samples, the Er3+:4I15/2 → 4I11/2 emissions exhibit similar peak positions (1532 nm) and FWHM values (82 nm), although the emission intensity increases substantially with increasing Yb3+ concentration. Because the Er3+ concentration is fixed at 1.0 mol%, the introduction of Yb3+ increases the optical absorption at 980 nm, as shown in Fig. 3. Therefore, the population of Er3+:4I11/2 is enhanced by the ET from Yb3+:2F5/2 to Er3+:4I11/2. Consequently, the Er3+:4I13/2 → 4I15/2 emission intensity (1532 nm) increases due to the non-radiative transition of 4I11/2 → 4I13/2 in Er3+. The ET from Yb3+ to Er3+ is further verified under 890-nm excitation, where only Yb3+ is excited to the 2F5/2 energy level. The increased Er3+:4I13/2 → 4I15/2 emission (1532 nm) and decreased Yb3+ 980-nm emission confirm the occurrence of ET from Yb3+ to Er3+, as shown in Fig. 6.

Fig. 5
figure 5

The emission spectra of Er3+ single-doped and Er3+–Yb3+-codoped borate glasses upon 980 nm excitation

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Fig. 6
figure 6

Emission spectra for Yb3+, Er3+ ions in Er3+–Yb3+-codoped borate glasses under 890 nm emission

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To provide further evidence for ET from Yb3+ to Er3+, Fig. 7 presents decay curves for the Yb3+ single-doped (BY) and Er3+–Yb3+-codoped (BEY1) samples. To avoid interference from Er3+:4I13/2 → 4I15/2 emission, the decay curves are recorded under 980-nm excitation and monitored by 1020-nm emission. The curve for the Yb3+ single-doped sample (BY) displays a nearly single-exponential decay, and then deviates from that with Yb3+ concentration increasing for the Er3+–Yb3+-codoped sample (BEY4). In general, the lifetime values of Yb3+ increase with Yb3+ concentration increasing due to the radiation trapping effect for Yb3+ single-doped samples [30]. However, the decay of the Yb3+:2F5/2 level in the codoped sample (BEY4) is faster than in the single-doped sample (BY). The decreased lifetime for the Er3+–Yb3+-codoped sample is attributed to the ET from Yb3+:2F5/2 to Er3+:4I13/2. The ETE for transfer from Yb3+ to Er3+ is given by the following formula:

$$\eta_{{{\text{Yb}} {-} {\text{Er}}}} = 1 - \frac{{\int {I_{{x\% \;{\text{Yb}}}} {\text{d}}t} }}{{\int {I_{{0\% \;{\text{Yb}}}} {\text{d}}t} }} = 1 - \frac{{\tau_{{x\% \;{\text{Yb}}}} }}{{\tau_{{x\% \;{\text{Yb}}}} }},$$
Fig. 7
figure 7

Donor fluorescence decay curves for Yb3+ single-doped and Er3+–Yb3+-codoped borate glasses under 980 nm excitation and monitored by 1020 nm emission

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where I represents the emission intensity and x% Yb represents the doped concentration of Yb3+ in the Er3+–Yb3+-codoped samples. τ and ETE are plotted for various Yb3+ concentrations in Fig. 8. As the Yb3+ concentration increases from 1.0 to 10.0 mol%, the lifetime decreases from 180 to 60 μs, and the ETE increases rapidly from 13.8% to 66.7%. These changes occur because the distance between Yb3+ and Er3+ decreases, thus facilitating the ET, as the Yb3+ concentration increases.

Fig. 8
figure 8

The decay lifetimes of Yb3+: 1020 nm emission and ETE between Yb3+ and Er3+ as a function of Yb3+ concentrations

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To illustrate the mechanism of ET between the Er3+ and Yb3+ ions, Fig. 9 provides an energy diagram of Er3+ and Yb3+. The Yb3+:2F5/2 energy level matches well with the Er3+:4I11/2 energy level, enabling effective ET from Yb3+:2F5/2 to Er3+:4I11/2. Under 980-nm excitation, the 4I11/2 state of the Er3+ ions is populated due to ET from Yb3+ ions, as indicated by Yb3+:2F5/2 + 4I15/2 → Yb3+:2F7/2 + Er3+:4I11/2. The phonons populated in the 4I11/2 state subsequently relax to the 4I13/2 state, leading to fluorescence emission at 1532 nm. This ET process is assumed to be dominant due to the large absorption cross-section of Yb3+ at 980 nm. As the Yb3+ concentration increases, the population of the Er3+:4I11/2 state is enhanced, and the ETE from Yb3+ to Er3+ is also improved.

Fig. 9
figure 9

Energy level diagram of Er3+ and Yb3+ ions in borate glasses, relevant transitions, and the energy transfer route between Yb3+ and Er3+ ions in borate glass

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4 Conclusions

Er3+/Yb3+-codoped borate glasses with a composition of (59.5 − x)% B2O3–15% WO3–20% ZnO–5% Y2O3–0.5Er2O3–x% Yb2O3 (x = 0, 0.5, 1.0, 2.0, and 5.0) were synthesized by a conventional melt-quenching method. The prepared glasses displayed larger Judd–Ofelt intensity parameters (Ω6 and Sed) than other previously studied glasses. Moreover, the Er3+ single-doped glasses exhibited broad 1.53-μm emission, with the FWHM reaching 82 nm. Upon the introduction of Yb3+ into the glass host, the 1.53-μm emission intensity increased significantly due to ET, as indicated by Yb3+:2F5/2 + 4I15/2 → Yb3+:2F7/2 + Er3+:4I11/2 under 980-nm excitation. The ET from Yb3+ to Er3+ was further evidenced by the decay lifetimes of Yb3+: 1020-nm emission under 980-nm excitation, and the ETE was observed to reach 66.7%. These results indicate that Er3+/Yb3+-codoped borate glass is an excellent gain medium suitable for broadband and high-gain EDFA, which is benefited from codoping of Yb3+ ions and high phonon energy glass matrix.