The effect of MnCO₃ on the gain coefficient for the ⁴I_13/2 → ⁴I_15/2 transition of Er³⁺ ions and near-infrared emission bandwidth flatness of Er³⁺/Tm³⁺/Yb³⁺ co-doped barium zinc silicate glasses

Abstract

The roles of Mn²⁺ ions in the MnCO₃ compound, leading to the formation of an Mn²⁺–Yb³⁺ dimer and affecting the gain coefficient for the ⁴I_13/2 → ⁴I_15/2 transition of Er³⁺ ions and near-infrared (NIR) emission bandwidth flatness of Er³⁺/Tm³⁺/Yb³⁺ co-doped in SiO₂–ZnO–BaO (SZB) barium zinc silicate glasses, were investigated in this work. The composition of all elements from the original raw materials that exist in the host glasses was determined using energy-dispersive X-ray spectroscopy (EDS). Under the excitation of a 980 nm laser diode (LD), the NIR emission of Er³⁺/Tm³⁺/Yb³⁺-co-doped SZB glasses produced a bandwidth of about 430 nm covering the O, E, and C bands. The effects of Mn²⁺ ions and the Mn²⁺–Yb³⁺ dimer on the gain coefficient for the ⁴I_13/2 → ⁴I_15/2 transition of Er³⁺ ions and bandwidth flatness of NIR emission of Er³⁺/Tm³⁺-co-doped and Er³⁺/Tm³⁺/Yb³⁺-co-doped SZB glasses were also assigned. The optimal molar concentration of Mn²⁺ ions was determined such that the NIR bandwidth flatness of Er³⁺/Tm³⁺/Yb³⁺-co-doped SZB glasses was the flattest. In addition, the role of Mn²⁺ ions in reducing the gain coefficient for the ⁴I_13/2 → ⁴I_15/2 transition of Er³⁺ ions was also calculated and discussed.

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1. Introduction

The near-infrared (NIR) emission spectra of rare earth ions (REIs), such as Pr³⁺, Er³⁺, Tm³⁺, and Ho³⁺ ions, in the wavelength range from ∼1200 to 2000 nm with the coverage of long-band (L-band), ultra-band (U-band), and (L + U)-bands have been of interest to researchers due to their expected applications in optical amplifiers and fibre lasers.^1–3 The NIR emission spectra of the Er³⁺-doped peak at about 1545 nm and of the Tm³⁺-doped peak at about 1769 nm, corresponding to ⁴I_13/2 → ⁴I_15/2 (ref. 4) and ³F₄ → ³H₆ transitions, respectively, have been widely investigated because of their typical applications in an erbium-doped fiber amplifier (EDFA)^5,6 and a thulium-doped fiber amplifier (TDFA).⁷ While Er³⁺ ions can be directly excited by commercial wavelengths of both 808 nm LD and 980 nm LD,^1,5,6,8 Tm³⁺ ions can only be directly excited by the wavelength of an 808 nm LD but not by a 980 nm LD.^9,10 Therefore, for the NIR emission spectra of Tm³⁺-doped and Er³⁺/Tm³⁺-co-doped glasses using a commercial wavelength 980 nm LD for excitation, Yb³⁺ ions are often introduced as a sensitizer or for a cooperative energy transfer (CET) process through dimers/trimers such as a Yb³⁺–Yb³⁺ dimer,¹¹ Cr³⁺–Yb³⁺ dimer,¹² Mn²⁺–Yb³⁺ dimer,^13,14 or Mn²⁺–Mn²⁺–Yb³⁺ trimer^4,15 for direct excitation by the commercial wavelength of a 980 nm LD.¹⁶ Among the dimers, the Mn²⁺–Yb³⁺ dimer formed by transition metal ions Mn²⁺ and Yb³⁺ ions is commonly used for the CET process of NIR emission spectra of Tm³⁺ doped or Er³⁺/Tm³⁺ co-doped in host glasses.^13,14,17 In addition to expanding the NIR spectral bandwidth for REIs, recent studies have also focused on investigating and finding solutions to flatten the NIR spectral bandwidth of these REIs to optimize the obtained NIR spectral bandwidth for optical applications.^18–22 In our previous studies,^23,24 we investigated, calculated, and reported solutions to widen the bandwidth as well as to enhance the near-infrared bandwidth flatness of Tm³⁺-doped, Ho³⁺-doped, Tm³⁺/Ho³⁺-co-doped, and Ho³⁺/Tm³⁺/Yb³⁺-co-doped glasses.^19,23 The obtained results indicated that the NIR bandwidth flatness of Tm³⁺-doped, Ho³⁺-doped, Tm³⁺/Ho³⁺-co-doped, and Ho³⁺/Tm³⁺/Yb³⁺co-doped glasses was significantly improved by the presence of Mn²⁺ ions and an Mn²⁺–Yb³⁺ dimer in the host glasses.^13,14,23

Following the positive results described above, in this work, we continue to examine and report the effects of Mn²⁺ ions and Mn²⁺–Yb³⁺ dimers on the gain coefficient for the ⁴I_13/2 → ⁴I_15/2 transition of Er³⁺ ions and NIR emission bandwidth flatness of Er³⁺/Tm³⁺/Yb³⁺-co-doped barium zinc silicate glasses with the aim of clarifying the roles of Mn²⁺ ions in the MnCO₃ compound in the formation of an Mn²⁺–Yb³⁺ dimer. Remarkably, we have attempted to determine not only the optimal BFN_NIR emission of Er³⁺/Tm³⁺/Yb³⁺-co-doped SZB glasses but also the optimal molar concentration of Mn²⁺ ions in the MnCO₃ compound such that the BFN_NIR emission of Er³⁺/Tm³⁺/Yb³⁺-co-doped SZB glasses is a maximum. In addition, the role of Mn²⁺ ions in the MnCO₃ compound in reducing the gain coefficient for the ⁴I_13/2 → ⁴I_15/2 transition of Er³⁺ ions was also examined. The obtained results are able to guide the selection of more optimal materials for EDFA and TDFA optical amplifiers.

2. Experimental details

2.1. Materials

In this experiment, the glass materials are fabricated by the conventional melting method. All the raw materials consisting of SiO₂, ZnO, BaO, TiO₂, MnCO₃, Er₂O₃, Tm₂O₃, and Yb₂O₃ used in this study are laboratory reagents with high purity (99.99%). The abbreviations, chemical compositions, and detailed molar ratios are listed in Table 1.

Table 1 Detailed chemical composition and concentration ratios of SiO₂–ZnO–BaO–TiO₂–Er₂O₃–Tm₂O₃–MnCO₃–Yb₂O₃ barium zinc silicate glasses

Name of glass sample	Details of composition and molar concentration (in mol%)
	SiO2	ZnO	BaO	TiO2	Er2O3	Tm2O3	MnCO3	Yb2O3
SZB-2Mn2Yb	45	26	17	8	0	0	2	2
SZB-0.5Er	45	26	20.5	8	0.5	0	0	0
SZB-1Tm	45	26	20	8	0	1	0	0
SZB-0.5Er2Yb	45	26	18.5	8	0.5	0	0	2
SZB-0.5Er2Yb2Mn	45	26	16.5	8	0.5	0	2	2
SZB-0.5Er2Yb2.5Mn	45	26	16	8	0.5	0	2.5	2
SZB-0.5Er2Yb3Mn	45	26	15.5	8	0.5	0	3	2
SZB-0.5Er2Yb3.5Mn	45	26	15	8	0.5	0	3.5	2
SZB-0.5Er2Yb4Mn	45	26	14.5	8	0.5	0	4	2
SZB-1Tm2Yb	45	26	18	8	0	1	0	2
SZB-1Tm2Yb2Mn	45	26	16	8	0	1	2	2
SZB-1Tm2Yb2.5Mn	45	26	15.5	8	0	1	2.5	2
SZB-1Tm2Yb3Mn	45	26	15	8	0	1	3	2
SZB-1Tm2Yb3.5Mn	45	26	14.5	8	0	1	3.5	2
SZB-1Tm2Yb4Mn	45	26	14	8	0	1	4	2
SZB-0.5Er1Tm2Yb	45	26	17.5	8	0.5	1	0	2
SZB-0.5Er21TmYb2Mn	45	26	15.5	8	0.5	1	2	2
SZB-0.5Er1Tm2Yb2.5Mn	45	26	15	8	0.5	1	2.5	2
SZB-0.5Er1Tm2Yb3Mn	45	26	14.5	8	0.5	1	3	2
SZB-0.5Er1Tm2Yb3.5Mn	45	26	14	8	0.5	1	3.5	2
SZB-0.5Er1Tm2Yb4Mn	45	26	13.5	8	0.5	1	4	2

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2.2. Experimental methods

Approximately 12 g of the mixtures of raw materials were weighed for each glass sample using an electronic analytical balance. After being finely ground using an onyx mortar and pestle, these mixtures were compressed into a platinum crucible and were then heated in a German-manufactured Nabertherm electric furnace at 1580 °C for a continuous period of 50 minutes, under an air atmosphere.²³ In the process of fabrication of the host glass and the glass doped with rare earth elements, the raw material mixtures after fine grinding are often heated at a temperature that is equal to or greater than the glass transition temperature of the raw materials, (abbreviated T_g). This temperature T_g is related to the melting point temperature of the materials (T_m) through the expression .^24,25 In the experiment in this study, the SiO₂, ZnO, TiO₂, BaO, Er₂O₃, Tm₂O₃, and Yb₂O₃ raw material mixtures have melting points greater than 1580 °C. However, we chose the material melting temperature of 1580 °C²³ at which these material mixtures are melted enough to form glasses.^23,24 In the next step, the melted mixtures were poured into a mold and quenched on the surface of a stainless steel plate to form the raw glass. To increase the mechanical strength and remove thermal strain from the raw glass, all raw glass samples were annealed at ∼500 °C for a continuous period of 12 hours.^17,19,23,26 The glass samples used for optical measurements were cut to a size of ∼10 mm × 10 mm × 2 mm. The edges and surfaces of these glass samples were then thoroughly polished.

The EDS spectrum was carried out using field emission scanning electron microscopy (FE-SEM), with a Jeol JSM-6510LV. Optical transmittance spectra of the glass within the wavelength range of 350 to 2000 nm were carried out using a Hitachi U-4100 UV/VIS/NIR spectrophotometer. NIR emission spectra of the glass within the wavelength range of 1300 to 2100 nm were measured using a Zolix SBP300 spectrophotometer with an InGaAs detector under excitation by a 980 nm LD. Optical transmittance and NIR emission spectra measurements as well as EDS analysis of the glass samples were performed at ambient temperature.^17,19

3. Results and discussion

3.1. EDS analysis

To determine whether the elements in the original raw material still exist in the glass materials after fabrication, we conducted an EDS analysis for the SZB-0.5Er1Tm2Yb2Mn glass sample, and the analyzed results within the energy range from 0 to 10 keV are plotted in Fig. 1. The energy levels of each element are listed in detail in Table 2. The obtained results of the EDS spectrum analysis of the SZB-0.5Er1Tm2Yb2Mn glass sample confirmed that the C, Ti, O, Ba, Zn, Si, Mn, Tm, Er, and Yb elements were still present in the SiO₂–ZnO–BaO–TiO₂–Er₂O₃–Tm₂O₃–MnCO₃–Yb₂O₃ glass matrix.^27,28 It should be noted that the Mn element has many different valence states, including +2, +3, +4, +5, +6, and +7 valences. When the MnCO₃ compound is introduced into the host glasses, the Mn element exists almost exclusively in the Mn 2p1 and Mn 2p3 valence states and this was investigated through XPS analysis and reported in a previous study.¹⁷ Following the results achieved on the behavior of the MnCO₃ compound doped into barium zinc silicate glasses, the goal of this work is mainly to focus on investigating the role of Mn²⁺ ions in the MnCO₃ compound for combining to form an Mn²⁺–Yb³⁺ dimer and transferring energy to Er³⁺ and Tm³⁺ ions to enhance the NIR emission intensity of Er³⁺/Tm³⁺/Yb³⁺-co-doped barium zinc silicate glasses under 980 nm LD excitation.

Fig. 1 EDS spectral analysis of the SZB-0.5Er1Tm2Yb2Mn glass sample.

Table 2 Details of the energy levels of the elements in the EDS spectral analysis

Energy	Element
	C	Ti	O	Ba	Zn	Si	Mn	Er	Tm	Yb
Lα (keV)	0.278	0.452	0.526	0.971	1.012	1.741	0.638	1.405	7.179	1.521
Kα (keV)		4.509		4.466	8.629		5.895	6.946		7.415

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3.2. Optical transmittance spectra

In Fig. 2(A), optical transmittance spectra of the SZB-0.5Er, SZB-0.5Er2Yb2Mn, SZB-1Tm, and SZB-1Tm2Yb2Mn glass samples are shown in curves (a), (b), (c) and (d), respectively. Curve (a) shows the optical transmittance spectra of the Er³⁺-doped sample in which seven optical transmittance bands can be observed corresponding to the ⁴I_15/2 → ⁴G_11/2, -⁴F_7/2, -²H_11/2, -⁴S_3/2, -⁴F_9/2, -⁴I_11/2 and -⁴I_13/2 transitions of Er³⁺ ions.^29,30 Curve (b) shows the optical transmittance spectrum of the Er³⁺/Yb³⁺/Mn²⁺-co-doped sample in which nine optical transmittance bands can be observed, among which, one corresponds to the ⁶A_1g → ⁴T_1g transition of Mn²⁺ ions,^13,14,17 one corresponds to the ²F_7/2 → ²F_5/2 transition of Yb³⁺ ions,^27,28 and the remaining seven correspond to the ⁴I_15/2 → ⁴G_11/2, -⁴F_7/2, -²H_11/2, -⁴S_3/2, -⁴F_9/2, -⁴I_11/2 and -⁴I_13/2 transitions of Er³⁺ ions.^30,31 Curve (c) shows the optical transmittance spectra of the Tm³⁺-doped in SZB-1Tm glass sample in which five optical transmittance bands can be observed corresponding to the ³H₆ → ¹G₄, -³F_2,3, -³H₄, -³H₅, and -³F₄ transitions of Tm³⁺ ions. Curve (d) shows the optical transmittance spectra of the Tm³⁺/Yb³⁺/Mn²⁺ co-doped in SZB-1Tm2Yb2Mn glass sample in which seven optical transmittance bands can be observed, among which, one corresponds to the ⁶A_1g → ⁴T_1g transition of Mn²⁺ ions,^13,14,17 one corresponds to the ²F_7/2 → ²F_5/2 transition of Yb³⁺ ions,^27,28,31 and the remaining five optical transmittance bands correspond to the ³H₆ → ¹G₄, -³F_2,3, -³H₄, -³H₅, and -³F₄ transitions of Tm³⁺ ions.^27,28

Fig. 2 (A) Optical transmittance spectra of the SZB-0.5Er, SZB-0.5Er2Yb2Mn, SZB-1Tm, and SZB-1Tm2Yb2Mn glass samples. (B) Optical transmittance spectra of the SZB-2Mn2Yb, SZB-0.5Er1Tm2Yb, and SZB-0.5Er1Tm2Yb2Mn glass samples.

To more clearly observe the optical transmittance spectra of Er³⁺, Mn²⁺, and Yb³⁺ ions, we measured and further analyzed the optical transmittance spectra of the SZB-2Mn2Yb, SZB-0.5Er1Tm2Yb, and SZB-0.5Er1Tm2Yb2Mn glass samples. The analyzed results of these optical transmittance spectra are plotted in Fig. 2(B). The obtained results displayed in curve (c) of Fig. 2(B) indicate that we can also observe all nine optical transmittance bands corresponding to ⁶A_1g → ⁴T_1g of Mn²⁺ ions, ²F_7/2 → ²F_5/2 of Yb³⁺ ions,^{4,11,13,14,17} and the ⁴I_15/2 → ⁴G_11/2, -⁴F_7/2, -²H_11/2, -⁴S_3/2, -⁴F_9/2, -⁴I_11/2, -⁴I_13/2 transitions of Er³⁺ ions,^4,30,31 similar to the analysis above. Interestingly, the analyzed results reveal that the transmittance spectrum of the SZB-0.5Er1Tm2Yb2Mn glass samples containing Mn²⁺ components in the wavelength region of ∼380–900 nm was decreased whereas the optical transmittance spectrum in the wavelength region of ∼900–2000 nm was increased compared to SZB-0.5Er1Tm2Yb glass samples without Mn²⁺ components. Also from the results displayed in Fig. 2(B), it can be seen that the optical transmittance spectrum of the SZB-2Mn2Yb glass sample within the wavelength range ∼1000–2000 nm is higher than that of the SZB-0.5Er1Tm2Yb or SZB0.5Er1Tm2Yb2Mn glass samples. For the SZB-0.5Er1Tm2Yb and SZB0.5Er1Tm2Yb2Mn glass samples, in addition to the Mn²⁺ and Yb³⁺ components, there are also Er³⁺ and Tm³⁺ components with absorption peaks at about 1230 nm and 1542 nm in the wavelength range ∼1000 to 2000 nm, corresponding to the ³H₆ → ³H₅ transition of Tm³⁺ ions and the ⁴I_15/2 → ⁴I_13/2 transition of Er³⁺ ions, respectively. Part of the excitation energy is thus absorbed in the wavelength region from ∼1000 to 2000 nm, which does not occur for the SZB-2Mn2Yb glass sample. This is the reason why the transmittance spectrum of the SZB-2Mn2Yb sample is higher than those of the other glass samples.

3.3. NIR emission spectra

NIR emission spectra of the SZB-0.5Er2YbxMn (x = 0, 2, 2.5, 3, 3.5, and 4 mol%) glass samples under 980 nm LD excitation are plotted in Fig. 3. For the SZB-0.5Er2Yb glass sample, the NIR emission of Er³⁺/Yb³⁺-co-doped peaks at ∼1542 nm corresponds to the ⁴I_13/2 → ⁴I_15/2 transition of Er³⁺. With the increased concentrations of the MnCO₃ compound from 2 up to 4 mol%, the NIR emission intensity of the Er³⁺/Yb³⁺-co-doped peaks at ∼1542 nm was significantly increased. Moreover, the NIR emission peak of Er³⁺ tends to split and shift the peaks by Δλ = 1553 − 1542 nm = 11 nm. The main reason for the increase in NIR emission intensity of Er³⁺/Yb³⁺-co-doped peaks at ∼1542 nm can be attributed to the combination between Yb³⁺ and Mn²⁺ ions in the MnCO₃ compound leading to the formation of Mn²⁺–Yb³⁺ dimers^13,32 contributing to the energy transfer (ET) to the ⁴I_13/2 → ⁴I_15/2 transition of Er³⁺ ions.^13,23 The formation of an Mn²⁺–Yb³⁺ dimer can be interpreted with the result shown in Fig. 3, where the Er³⁺ and Yb³⁺ concentrations are unchanged when the concentration of the MnCO₃ compound increases from 2 up to 4 mol%, and the NIR emission intensity of the Er³⁺/Yb³⁺-co-doped peaks at ∼1542 nm under the excitation of 980 nm LD was significantly increased. However, the Mn²⁺ ions cannot receive the direct excitation of the 980 nm LD, proving that Mn²⁺ ions combine with the Yb³⁺ ions to form an Mn²⁺–Yb³⁺ dimer,^13,23 and therefore, the Mn²⁺–Yb³⁺ dimers receive the excitation of the 980 nm LD and transfer energy from the Mn²⁺–Yb³⁺ dimer to the ⁴I_13/2 → ⁴I_15/2 transition of Er³⁺ ions.^13,23 The addition of MnCO₃ compound into the host glass efficiently promotes not only the formation of the Mn²⁺–Yb³⁺ dimer but also contributes to breaking of the O–Zn, Si–O, Si–O–Si, Zn–O–Zn, and Si–O–Zn bonds,³³ subsequently creating new non-bridging oxygens (NBOs), like Mn–O, Mn–Si, Si–O–Mn, Mn–O–Mn, and Mn–O–Zn bonds.^34,35 Therefore, we believe that the presence of Mn²⁺ ions in the MnCO₃ compound contributed to shifting the NIR emission peak at the ⁴I_13/2 → ⁴I_15/2 transition of Er³⁺ ions.

Fig. 3 NIR emission spectra of the SZB-0.5Er2YbxMn (x = 0, 2, 2.5, 3, 3.5, and 4 mol%) glass samples.

We also investigated the effects of Mn²⁺ on the NIR emission bandwidth flatness (NIR_EBF) parameter of Er³⁺/Yb³⁺ co-doped in SZB glasses. The NIR_EBF parameter of Er³⁺/Yb³⁺ co-doped in SZB glasses can be calculated based on the NIR emission spectra of Er³⁺/Yb³⁺ co-doped in SZB glasses with the following formula:^19,23

where I(n) is the NIR emission intensity of Er³⁺/Yb³⁺ co-doped in SZB glasses within the analytical data range n of the NIR emission wavelength N.^19,23 NIR_EBF takes a value from 0 to 1.^19,23 The value of NIR_EBF is equal to 1 when all values of I(n) are equal.^19,23 The NIR_EBF calculated results of Er³⁺/Yb³⁺ co-doped in SZB glasses displayed in Fig. 4 show that with increasing concentrations of Mn²⁺ ions, the NIR_EBF of Er³⁺/Yb³⁺ co-doped in SZB glasses gradually decreased.

Fig. 4 Relationship between NIR spectra flatness of the SZB-0.5Er2YbxMn (x = 0, 2, 2.5, 3, 3.5, and 4 mol%) glass samples and molar concentration of Mn²⁺ ions.

Similarly, the NIR emission spectra of SZB-1Tm2YbxMn (x = 0, 2, 2.5, 3, 3.5, and 4 mol%) glass samples under excitation of 980 nm LD are plotted in Fig. 5 and indicate that the NIR emission of the Tm³⁺/Yb³⁺-co-doped sample has two peaks at about ∼1457 and ∼1801 nm, corresponding to the ³H₄ → ³F₄ and ³F₄ → ³H₆ transitions of Tm³⁺ ions.^36,37 Along with the increase in MnCO₃ concentration from 2 up to 4 mol%, the NIR emission intensity of Tm³⁺/Yb³⁺-co-doped peaks at ∼1457 and ∼1801 nm was also significantly increased. This result is due to the ET processes from the Mn²⁺–Yb³⁺ dimer to the ³H₄ → ³F₄ and ³F₄ → ³H₆ transitions of Tm³⁺ ions.¹⁷

Fig. 5 NIR emission spectra of the SZB-1Tm2YbxMn (x = 0, 2, 2.5, 3, 3.5, and 4 mol%) glass samples.

Formula (1) continued to be used to calculate the NIR_EBF spectra of Tm³⁺/Yb³⁺-co-doped samples when the molar concentration of the MnCO₃ compound increases from 0 up to 4 mol% and the results of the calculation are shown in the insert to Fig. 5. These results show that the NIR_EBF spectra of the Tm³⁺/Yb³⁺-co-doped sample reached the optimal value of 0.668 when the molar concentration of the MnCO₃ compound was 2 mol%. Energy levels of Er³⁺, Tm³⁺, Yb³⁺ ions, the Mn²⁺–Yb³⁺ dimer and mechanisms of the ET_I (I = 1, 2, 3, 4, and 5) processes in the SZB glass system are shown in Fig. 6. Mechanisms of the ET_I (I = 1, 2, 3, 4, and 5) processes between the Mn²⁺–Yb³⁺ dimer with Er³⁺, Tm³⁺ ions were also reported and discussed in detail in our previous studies.^17,26 These ET_I (I = 1, 2, 3, 4, and 5) processes can be described in detail in the form of the following equations:

ET₁: ²F_5/2(Yb³⁺) + ³H₅(Tm³⁺) → ²F_7/2(Yb³⁺) + ³H₆(Tm³⁺).¹⁷

ET₂: |²F_5/2, ⁶A₁〉(Mn²⁺–Yb³⁺) + ³H₅(Tm³⁺) → |²F_7/2, ⁶A₁〉(Mn²⁺–Yb³⁺) + ³H₆(Tm³⁺).¹⁷

ET₃: |²F_5/2, ⁶A₁〉(Mn²⁺–Yb³⁺) + ⁴I_11/2(Er³⁺) → |²F_7/2, ⁶A₁〉(Mn²⁺–Yb³⁺) + ⁴I_15/2(Er³⁺).^17,23

ET₄: ²F_5/2(Yb³⁺) + ⁴I_11/2(Er³⁺) → ²F_7/2(Yb³⁺) + ⁴I_15/2(Er³⁺).²⁶

ET₅: |²F_7/2, ⁴T₂〉(Mn²⁺–Yb³⁺) + ¹G₄(Tm³⁺) → |²F_7/2, ⁶A₁〉(Mn²⁺–Yb³⁺) + ³H₆(Tm³⁺).^17,23

Fig. 6 Energy levels of Er³⁺, Tm³⁺, Yb³⁺, Mn²⁺–Yb³⁺ dimer and mechanisms of ET_I (I = 1, 2, 3, 4, and 5) processes in the SZB glass system.

To achieve one of the main goals of this study, we investigated the effects of Mn²⁺ ions in the MnCO₃ compound on the NIR_EBF spectra of Er³⁺/Tm³⁺/Yb³⁺-co-doped SZB glasses. We kept the molar compositions of the Er³⁺/Tm³⁺/Yb³⁺-co-doped sample to 0.5Er³⁺/1Tm³⁺/2Yb³⁺, and changed the molar composition of the MnCO₃ compound from 2 up to 4 mol%. As shown in Fig. 7, the NIR emission spectra of SZB-0.5Er1Tm2YbxMn (x = 0, 2, 2.5, 3, 3.5, and 4 mol%) glass samples under excitation by a 980 nm LD reveal that when the molar concentration of the MnCO₃ compound increases from 2 up to 4 mol%, the NIR emission intensity of the Er³⁺/Tm³⁺/Yb³⁺-co-doped peaks at ∼1553 and ∼1801 nm also strongly increases. This result may be due to Mn²⁺–Yb³⁺ dimers being formed during the excitation by 980 nm LD, with the energies from Mn²⁺ ions and Mn²⁺–Yb³⁺ dimers simultaneously transferred to Er³⁺ and Tm³⁺ ions. The NIR emission spectra of Er³⁺/Tm³⁺/Yb³⁺ co-doped in the SZB-0.5Er1Tm2YbxMn (x = 0, 2, 2.5, 3, 3.5, and 4 mol%) glass under 980 nm LD excitation created an NIR bandwidth of ∼430 nm. The NIR_EBF spectra of the Er³⁺/Tm³⁺/Yb³⁺-co-doped samples were determined when the molar concentration of Mn²⁺ ions in the MnCO₃ compound increased from 2 up to 4 mol% using formula (1). The results of the calculation of the NIR_EBF value, given in Fig. 8, showed that the NIR_EBF spectra of the Er³⁺/Tm³⁺/Yb³⁺-co-doped sample reached the optimal value of 0.849 when the molar concentration of Mn²⁺ ions in the MnCO₃ compound was 3.5 mol%.

Fig. 7 NIR emission spectra of the SZB-0.5Er1Tm2YbxMn (x = 0, 2, 2.5, 3, 3.5, and 4 mol%) glass samples.

Fig. 8 The relationship between the molar concentration of Mn²⁺ ions and NIR_EBF parameter of the SZB-0.5Er1Tm2YbxMn (x = 0, 2, 2.5, 3, 3.5, and 4 mol%) glass samples.

3.4. Cross-section and gain coefficient study

To evaluate the influence of Mn²⁺ ions in the MnCO₃ compound on the gain coefficient of Er³⁺ (G_Er(λ)), we first investigated and calculated the absorption cross-section σ_abs(λ) and emission cross-section σ_ems(λ) for the ⁴I_13/2 → ⁴I_15/2 transition of Er³⁺ ions in the SZB glasses based on McCumber's theory.^6,38,39 The value of σ_abs(λ) is calculated from the absorbance spectrum according to the following formula:^6,38,39in which A(λ) is the absorbance spectrum; λ is the wavelength; C is the concentration of Er³⁺ ions; and d is the thickness of the SZB glass samples, where the glass sample in this study has a thickness of d = 2 mm.^6,38 The absorbance spectrum A(λ) can be calculated from the transmittance spectrum T(λ) according to the formula:^40,41

A(λ) = −log₁₀ T(λ) = 2 − log₁₀(% T(λ)), (3)

where % T(λ) is the transmittance spectrum (measured as a percentage) determined from the experimental results in Fig. 2(A) and (B).

The value of σ_ems(λ) is thus determined in relation to the value of σ_abs(λ) as follows:^6,39

where Z_U and Z_L are the partition functions of the upper and lower manifolds, respectively; T is the temperature; h is Planck's constant, k is Boltzmann's constant; c is the speed of light; λ is the photon wavelength; λ_UL the wavelength corresponding to the transition between the bottom of the excited (upper) state manifold and the bottom of the ground (lower) state manifold.^6,35,36 The value of σ_abs(λ) for the ⁴I_15/2 → ⁴I_13/2 transition and of σ_ems(λ) for the ⁴I_13/2 → ⁴I_15/2 transition of Er³⁺ ions are determined as shown in Fig. 9. The gain coefficient G(λ) for transitions of the REIs in the glass samples can be determined with the following formula:^6,38,39

G(λ) = C·[P·σ_ems(λ) − (1 − P)·σ_abs(λ)], (5)

in which P is the population inversion and P = 0–1 stands for the ratio between the number of REIs in the excited state to the total number of REIs.

Fig. 9 Absorption and emission cross-sections of the SZB-0.5Er glass sample.

Formulae (2)–(5) are used to determine the values of σ_abs(λ), σ_ems(λ), and G_Er(λ), respectively, for the ⁴I_13/2 → ⁴I_15/2 transition of Er³⁺ ions in the SZB-0.5Er glass sample. The values of G_Er(λ) were calculated and are shown in Fig. 10. We can observe that the G_Er(λ) value becomes positive in the range wavelength of ∼1500–1600 nm for cases where P is equal to 0.5 to 1. When P is greater than 0.6, the NIR emission of the Er³⁺-doped SZB-0.5Er glass sample exhibits a flat net gain covering the L-, U-, and (L + U)-bands.⁶ At the same time, the G_Er(λ) value is found to be about 0.38, corresponding to P = 1. Similarly, we also used formulae (2)–(5) to determine the values of σ_abs(λ), σ_ems(λ), and G_{Er_Mn}(λ), respectively, for the ⁴I_13/2 → ⁴I_15/2 transition of Er³⁺ ions in the SZB-0.5Er2Yb2Mn glass sample. The values of σ_abs(λ) and σ_ems(λ) of the SZB-0.5Er2Yb2Mn glass sample are shown in Fig. 11 and the values of G_{Er_Mn}(λ) for the ⁴I_13/2 → ⁴I_15/2 transition of Er³⁺ ions in the SZB-0.5Er2Yb2Mn glass sample are shown in Fig. 12. Comparison of the results in Fig. 10 and 12 shows that with the existence of Mn²⁺ ions in the SZB-0.5Er2Yb2Mn glass sample, the value of G_{Er_Mn}(λ) for the ⁴I_13/2 → ⁴I_15/2 transition of Er³⁺ ions was significantly reduced. The value of G_{Er_Mn}(λ) is found to be about 0.21 corresponding to P = 1. These G_{Er_Mn}(λ) and G_Er(λ) calculation results showed that in the presence of Mn²⁺ ions and an Mn²⁺–Yb³⁺ dimer, the broadband NIR emission of the ⁴I_13/2 → ⁴I_15/2 transition of Er³⁺ ions in this study can be utilized for optical amplifiers. The γ_G ratio between G_{Er_Mn}(λ) and G_Er(λ) is determined as follows:

Fig. 10 Gain coefficient for the ⁴I_13/2 → ⁴I_15/2 transition of Er³⁺ ions in the SZB-0.5Er glass sample.

Fig. 11 Absorption and emission cross-sections of the SZB-0.5Er2Yb2Mn glass sample.

Fig. 12 Gain coefficient for the ⁴I_13/2 → ⁴I_15/2 transition of Er³⁺ ions in the SZB-0.5Er2Yb2Mn glass sample.

Based on the above results and analyses, we can confirm that in the presence of Mn²⁺ ions, the NIR bandwidth flatness of Er³⁺ ions was improved, but the gain coefficient for the ⁴I_13/2 → ⁴I_15/2 transition of Er³⁺ ions was significantly reduced. Therefore, depending on the specificity of the application in the optical amplifier, we should choose the type of SZB glass material with or without the Mn²⁺ component to suit the specific applications.

4. Conclusions

In this work, the effects of Mn²⁺ ions in the MnCO₃ compound leading to the formation of an Mn²⁺–Yb³⁺ dimer and affecting the gain coefficient for the ⁴I_13/2 → ⁴I_15/2 transition of Er³⁺ ions and the NIR_EBF value of Er³⁺-doped and Er³⁺/Tm³⁺/Yb³⁺-co-doped barium zinc silicate glasses under 980 nm LD excitation were investigated. A broadband NIR emission of Er³⁺/Tm³⁺/Yb³⁺-co-doped barium zinc silicate glasses with an FWHM of ∼430 nm was observed. The roles of Mn²⁺ ions in the MnCO₃ compound led to the formation of an Mn²⁺–Yb³⁺ dimer and contributed to a significant increase in the NIR_EBF value of Er³⁺-doped and Er³⁺/Tm³⁺/Yb³⁺-co-doped barium zinc silicate within the NIR wavelength range of 1600–2200 nm. The NIR_EBF value of Er³⁺/Tm³⁺/Yb³⁺-co-doped SZB glasses obtained at 0.849 corresponds to the molar concentration of MnCO₃ compound of 3.5 mol%. However, the presence of Mn²⁺ ions in the SZB glass composition also led to a significant decrease in the gain coefficient for the ⁴I_13/2 → ⁴I_15/2 transition of Er³⁺ ions. The results obtained in this study will be able to guide the selection of glass material compositions for applications in optical amplifiers in the future.

Conflicts of interest

There are no conflicts of interest to declare.

Acknowledgements

This research was supported by Project of the TNU-University of Sciences in Vietnam under Grant number CS2023-TN06-10. The corresponding author (Ho Kim Dan) would like to express his gratitude to Van Lang University.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3ra06348h

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