Energy Transfer and Cross-Relaxation Induced Efficient 2.78 μm Emission in Er³⁺/Tm³⁺: PbF₂ mid-Infrared Laser Crystal

Abstract

An efficient enhancement of 2.78 μm emission from the transition of Er³⁺: ⁴I_11/2 → ⁴I_13/2 by Tm³⁺ introduction in the Er/Tm: PbF₂ crystal was grown by the Bridgman technique for the first time. The spectroscopic properties, energy transfer mechanism, and first-principles calculations of as-grown crystals were investigated in detail. The co-doped Tm³⁺ ion can offer an appropriate sensitization and deactivation effect for Er³⁺ ion at the same time in PbF₂ crystal under the pump of conventional 800 nm laser diodes (LDs). With the introduction of Tm³⁺ ion into the Er³⁺: PbF₂ crystal, the Er/Tm: PbF₂ crystal exhibited an enhancing 2.78 μm mid-infrared (MIR) emission. Furthermore, the cyclic energy transfer mechanism that contains several energy transfer processes and cross-relaxation processes was proposed, which would well achieve the population inversion between the Er³⁺: ⁴I_11/2 and Er³⁺: ⁴I_13/2 levels. First-principles calculations were performed to find that good performance originates from the uniform distribution of Er³⁺ and Tm³⁺ ions in PbF₂ crystal. This work will provide an avenue to design MIR laser materials with good performance.

1. Introduction

Over the past several decades, mid-infrared (MIR) solid-state lasers operating around 2.7–3 μm have received extensive attention for numerous applications in medicine surgery, communications, remote sensing, pollution monitoring, and military countermeasures, etc. [1,2,3,4,5]. Additionally, 2.7–3 μm lasers are suitable pump sources for longer wavelength mid-infrared or long-infrared (8–12 μm) laser applications utilizing the optical parametric oscillators [6,7].

Up to now, many kinds of rare-earth ions in favorable ~3 µm MIR emissions have been analyzed, such as erbium ion (Er³⁺): ⁴I_11/2 → ⁴I_13/2 [8], holmium ion (Ho³⁺): ⁵I₆ → ⁵I₇ [9], and dysprosium ion (Dy³⁺): ⁶H_13/2 → ⁶H_15/2 [10]. Among them, the Er³⁺ ion-doped single crystal has been deemed as the effective source for ~3 µm laser operation, benefiting from its abundant energy levels, such as GSGG [11], YSGG [12], YAP [13], Lu₂O₃ [14], GdScO₃ [15], SrF₂ crystals [16], NdVO₄ [17], InVO₄ crystals [18], etc. As investigated, the Er³⁺ ion can be directly pumped utilizing 808 or 980 nm commercial laser diodes (LDs) corresponding to Er³⁺ ion absorption transitions from ground state ⁴I_15/2 to ⁴I_9/2, ⁴I_11/2 levels, respectively. To take further advantage of this, a co-doping suitable sensitization ion having strong absorption around 980 nm or 800 nm would improve the absorption efficiency, such as Yb³⁺, Nd³⁺, or Tm³⁺ ions [19,20,21]. However, the fluorescence lifetime of the ⁴I_11/2 level (the upper) is fairly shorter than that of the ⁴I_13/2 level (the lower) of Er³⁺ ion, causing the possible termination of 2.7 μm mid-infrared emissions [22]. Therefore, the shortcoming of the intrinsic self-terminating “bottleneck” effect of Er³⁺ ion is important to consider. On one hand, the self-terminating “bottleneck” effect can be restrained by the energy transfer up-conversion (UC) process: 2 ⁴I_13/2 → ⁴I_15/2 + ⁴I_9/2, which needs heavy doping of Er³⁺ ion (>30 at.% ). The UC process can simultaneously depopulate the ⁴I_13/2 level and populate the ⁴I_11/2 level via non-radiative transition from ⁴I_9/2 to ⁴I_11/2 levels. However, excessive Er³⁺ doping concentrations will generate the inclusion defects in as-grown crystal and degenerate the crystal quality and thermal performance, which is not conducive to laser output efficiency [23,24]. On the other hand, we can focus attention on co-doping a suitable deactivation ion for Er³⁺ ion to suppress the self-terminating effect, such as Pr³⁺, Ho³⁺, Dy³⁺, or Tm³⁺ ions [25,26,27,28]. These deactivation ions can dramatically reduce the population of lower Er³⁺: ⁴I_13/2 levels, thereby achieving efficient 2.7 μm mid-infrared emission. Based on the above investigation, it is noteworthy that Tm³⁺ ion can simultaneously serve as sensitization and deactivation effects for Er³⁺ ion [29,30].

In recent years, fluoride crystals have attracted numerous attention in the field of mid-infrared lasers, such as the β-PbF₂ crystal [31]. The PbF₂ crystal exhibits its intrinsic advantages. The PbF₂ crystal has lower phonon energy (257 cm⁻¹), compared with GdLiF₄ (432 cm⁻¹), LiYF₄ (442 cm⁻¹), LuLiF₄ (400 cm⁻¹) and BaY₂F₈ (415 cm⁻¹) crystals [32,33,34]. Such low phonon energy is conducive to reducing the non-radiative transition probability and enhancing the spontaneous radiation transition probability between ⁴I_11/2 and ⁴I_13/2 levels of Er³⁺ ion [35]. Moreover, the PbF₂ crystal is optically transparent in the region of 0.25–15 μm, which is broader than other fluoride crystals, such as LiYF₄ (0.12–8.0 μm), BaY₂F₈ (0.2–9.5 μm), and KYF₄ (0.15–9.0 μm). Additionally, another issue to consider is the physical properties of the material. Some fluoride crystals have low thermal conductivity, such as CaF₂ and SrF₂. The PbF₂ crystal has high thermal conductivity (28 W/m/K) and stable mechanical and chemical properties [36,37]. Consequently, with these favorable characteristics, the PbF₂ crystal may be selected as a promising host material.

In this paper, Er: PbF₂, Tm: PbF₂, Er/Tm: PbF₂ crystals were successfully prepared by the Bridgman technique. The spectroscopic properties of prepared crystals were analyzed based on absorption spectra, emission spectra, and fluorescence decay curves. Compared with the Er: PbF₂ crystal, the Er/Tm co-doped PbF₂ crystal presents a larger 2.78 μm fluorescence emission intensity and higher fluorescence branching ratio. Moreover, theoretical calculations were performed to discover that the co-doping of the Tm³⁺ ion can make the Er³⁺ and Tm³⁺ ions more evenly distributed in PbF₂ crystals, which can effectively break the local clusters of the Er³⁺ in Er: PbF₂ crystal, thus ensuring efficient energy transfer between Er³⁺ and Tm³⁺ ions, and resulting in the enhancement of 2.78 μm MIR fluorescence emission.

2. Experimental Section

The 1.0 at.% Er: PbF₂, 0.5 at.% Tm: PbF₂, and 1.0 at.% Er/0.5 at.% Tm: PbF₂ crystals were grown by the conventional Bridgman method in an atmosphere of N₂ with intermediate molybdenum heating. The fluoride powders of the PbF₂ (99.999%), ErF₃ (99.999%), and TmF₃ (99.999%) were all raw materials. The raw materials were weighed and thoroughly mixed. The process of crystal growth was similar to our previous work [37]. The melt was homogenized in a covered graphite crucible in a high-temperature zone at 1000 °C for 8 h, and the crystal growth process was driven by lowering the graphite crucible at a speed of 0.5 mm/h. After the growth process was completed, the cooling rate of the crystal was 30 °C/cm–40 °C/h. The actual concentration of Er³⁺ and Tm³⁺ ions in the grown samples were measured utilizing inductively coupled plasma atomic emission spectrometry (ICP-AES). The concentrations of Er³⁺ and Tm³⁺ ions in dual-doped Er/Tm: PbF₂ crystal were 1.15 at.%, and 0.58 at.%, respectively. The concentration of Er³⁺ ion in the Er: PbF₂ crystal was 1.15 at.%, and the concentration of Tm³⁺ ion in the Tm: PbF₂ crystal was 0.59 at.%.

The crystalline structure of as-grown samples was observed utilizing D/max2550 X-ray diffraction (XRD) with Cu K_α radiation. The Perkin–Elmer UV-VIS-NIR spectrometer (Lambda 900) with a resolution of 1 nm was used to detect the absorption spectra of prepared samples in the range of 400–2200 nm. The emission spectra, up-conversion fluorescence spectra, and fluorescence decay curves were detected and recorded using the Edinburgh Instruments FLS920 and FSP920 spectrophotometers. The repetition frequency of the excitation pulse for measuring the fluorescence decay curves was set to 20 Hz, and the duration of the excitation pulses was 30s. All the measurements were performed at room temperature.

3. Calculation Method

In the framework of density functional theory, VASP codes and the plane-wave basis set method were used for calculation [38,39]. The mutual interactions were described by the projector augmented-wave pseudopotential with an exchange-correlation function (Perdew–Burke–Ernzerhof form) [40,41]. The cut-off was set at 550 eV and a 1 × 1 × 1 Gamma k-grid was used to guarantee the relaxation accuracy of 10⁻⁵ eV and 0.01 eVÅ⁻¹ within a 2 × 2 × 2 supercell, respectively. The spin polarization was included in the calculations. According to the method reported previously [42], the formation energy (∆E) and cluster symbols were obtained. It is pointed that the energy correction of the PbF₂ crystal was different from that of CaF₂, SrF₂, and BaF₂ crystals. For a 2 × 2 × 2 supercell with a net charge, the calculated value in PbF₂ crystal was 0.069 eV.

4. Results and Discussion

4.1. Crystal Structure Analysis

Figure 1 shows the XRD patterns and refined XRD patterns of the Er: PbF₂, Tm: PbF₂, Er/Tm: PbF₂ crystals, and the JCPDS standard card of the PbF₂ crystal (nos. 06-2051) [37]. The residuals of refinements (fit profiles shown in Figure 1) of Er: PbF₂, Tm: PbF₂, Er/Tm: PbF₂ crystals were 9.61%, 7.71%, 10.17%, respectively. It is obvious that no clear shift in the phase diffraction peaks was observed and all XRD curves were well matched with the standard card of the β-PbF₂ crystalline phase (nos. 06-2051). The results demonstrate successful co-doping of Er³⁺ and Tm³⁺ ions in PbF₂ crystal without phase transitions.

4.2. First-Principles Calculations

Based on the first-principal calculations, the cluster structure of Tm³⁺ and Er³⁺ ions were simulated to research the change of local structures of doping ions in PbF₂ crystal. The possible thermodynamically stable Er³⁺ and Tm³⁺ centers in PbF₂ crystals are shown in Figure 2a,b. It is clear to see that there are 9 different types of centers in each Tm: PbF₂ and Er: PbF₂ crystals. In particular, only the 3₁|0|8|4₁-C center in the Tm: PbF₂ crystal varies from the 2₁|0|6|3₁ center in the Er: PbF₂ crystal, and the other eight different types of centers in the Tm: PbF₂ crystal are the same as the Er: PbF₂ crystal. Moreover, Figure 2c shows the formation energy of Er³⁺ and Tm³⁺ versus the number of Er³⁺ and Tm³⁺ ions within a cluster, respectively. It can be seen that the slope of Er³⁺ clusters in PbF₂ crystal is −0.988 eV, which is almost the same as the slope of Tm³⁺ clusters in the PbF₂ crystal (−1.003 eV). These results indicate that the clustering characteristics of Er³⁺ and Tm³⁺ ions in PbF₂ crystal are almost consistent. This phenomenon agreed well with the approximately equal segregator coefficients of Er³⁺ (1.15) and Tm³⁺ (1.16) in the Er/Tm: PbF₂ crystal mentioned above, which may be owing to the slightly different ion radii between Er³⁺ (88.1 pm) and Tm³⁺ (86.9 pm) ions. That is to say, it can be considered that the Er³⁺ and Tm³⁺ ions replace Pb²⁺ ions with equal probability when they are co-doped in PbF₂ crystal, which makes the Er³⁺ and Tm³⁺ ions more evenly distributed in the PbF₂ crystal. The results suggest that the efficient energy transfer between Er³⁺ and Tm³⁺ ions can be guaranteed due to the uniform distribution of Er³⁺ and Tm³⁺ ions, and result in the enhancing of 2.78 μm MIR fluorescence emission in the ensuing discussion.

4.3. Absorption Spectroscopy

The illustrations in Figure 3 shows the photos of Er/Tm: PbF₂, Er: PbF₂, Tm: PbF₂ crystals and their cut and polished crystal pieces; their sizes are also marked, respectively. It can be seen that all the crystal pieces are transparent and have no inclusions. Figure 3 illustrates the room temperature absorption spectra of Er: PbF₂, Tm: PbF₂, and Er/Tm: PbF₂ crystals ranging from 400 nm to 2200 nm. Clearly, the typical absorption bands centered at approximately 417, 451, 486, 521, 541, 650, 802, 975, and 1509 nm in the Er: PbF₂ crystal originated from the transitions from the ground state ⁴I_15/2 level to upper-lying ²H_9/2, ⁴F_5/2,_3/2, ⁴F_7/2, ²H_11/2, ⁴S_3/2, ⁴F_9/2, ⁴I_9/2, ⁴I_11/2 and ⁴I_13/2 levels of Er³⁺ ion, respectively [37]. While in the Tm: PbF₂ crystal mainly five absorption bands of Tm³⁺ ion are labeled, the absorption peaks centered at round 464, 680, 792, 1211, and 1618 nm are in accord with the transitions from ground state ³H₆ level to upper-lying ¹G₄, ³F₂,₃, ³H₄, ³H₅ and ³F₄ levels, respectively. Obviously, the huge absorption band centered at around 792 nm in the range of 750–830 nm corresponding to Tm³⁺: ³H₆ → ³H₄ transition well coincides with the wavelength of 808 nm AlGaAs LD pumping. The absorption bands in the Er/Tm: PbF₂ crystal are altogether composed of the transitions of Er³⁺ and Tm³⁺ ions discussed above, indicating the successful introduction of both Er³⁺ and Tm³⁺ ions. Strong overlap between the Tm³⁺: ³H₆ → ³H₄ absorption transition and the Er³⁺: ⁴I_15/2 → ⁴I_9/2 absorption transition can be seen in the Er/Tm: PbF₂ crystal. The absorption overlap indicates that a possible nonradiative energy transfer process Tm³⁺: ³H₄ → Er³⁺: ⁴I_9/2 would effectively occur for enhancing the absorption efficiency of Er³⁺ ion ~800 nm. Therefore, benefiting from the broad absorption band of Tm³⁺ ion centered at around LD pump wavelength and the possibility for energy transfer, the Tm³⁺ ion can act as a suitable sensitizer for Er³⁺ ion in the Er/Tm dual-doped PbF₂ crystal.

For demonstrating the sensitization effect of Tm³⁺ ion for Er³⁺ ion via the Tm³⁺: ³H₄ → Er³⁺: ⁴I_9/2 energy transfer transition, the lifetimes of Tm³⁺: ³H₄ level in the Tm³⁺ single-doped and Er/Tm dual-doped PbF₂ crystals were measured and shown in Figure 4a,b, respectively. The decay curves were measured under the condition of 1.47 μm emission (Tm³⁺: ³H₄ → ³F₄) and 800 nm excitation (Tm³⁺: ³H₆ → ³H₄) and were all well fitted by single-exponential behavior. As shown in Figure 4a, the measured lifetime of the Tm³⁺: ³H₄ manifold is 1.67 ms in the Tm: PbF₂ crystal, while the lifetime is 0.54 ms in the Er/Tm: PbF₂ crystal shown in Figure 4b. The remarkable decreasing lifetime in the Er/Tm: PbF₂ crystal indicates the effective sensitization effect of the Tm³⁺ ion. The energy transfer efficiency from Tm³⁺: ³H₄ to Er³⁺: ⁴I_9/2 level can be calculated by the following equation: η_ET1 = 1 − τ_Er/Tm/τ_Tm, where τ_Er/Tm and τ_Tm are the lifetimes of Tm³⁺: ³H₄ level in Tm: PbF₂, Er/Tm: PbF₂ crystals, respectively. The high value of η_ET1 (67.66%) confirms that the Tm³⁺ ion has a significant influence on Er³⁺: ⁴I_9/2 level in PbF₂ crystal, and can effectively act as a sensitizer for Er³⁺ ion for enhancing ~2.7 μm MIR emission.

4.4. Emission Spectra and Emission Cross-Sections

For further clarifying the energy transfer mechanism between Tm³⁺ and Er³⁺ ions, the emission spectra of Er/Tm: PbF₂, Er: PbF₂ samples in the range of 1400–1700 nm, and Er/Tm: PbF₂, Tm: PbF₂ samples in the 1700–2200 nm region are shown in Figure 5a,b, respectively. The test parameters of the luminescence performance of the prepared samples, such as pump power and slits, are uniformed. As shown in Figure 5a, compared with the Er: PbF₂ crystal the emission intensity centered at around 1.55 μm corresponding to the Er³⁺: ⁴I_13/2 → ⁴I_15/2 transition in the Er/Tm: PbF₂ crystal weakened sharply, at almost ten times lower. The result shows that the introduction of Tm³⁺ ion would significantly reduce the population of the Er³⁺: ⁴I_13/2 energy level, thereby enhancing the ~2.7 μm mid-infrared emission and reversely weakening the 1.55 μm infrared emission. This depopulation of Er³⁺: ⁴I_13/2 energy level is mainly attributed to the deactivation effect of Tm³⁺ ions via energy transfer process: Er³⁺: ⁴I_13/2 → Tm³⁺: ³F₄ in Er/Tm: PbF₂ crystal. As the deactivation energy transfer process occurs, the population on the Tm³⁺: ³F₄ level would increase, thereby enhancing the 1.91 μm emission (Tm³⁺: ³F₄ → ³H₆ transition) in the Er/Tm: PbF₂ crystal, but it is actually weakened (shown in Figure 5b). The 1.91 μm emission intensity of the Tm³⁺ ion in Er/Tm: PbF₂ crystal is nearly three times lower than that in the Tm³⁺ single doped PbF₂ crystal. This result is mainly assigned to the cross-relaxation (CR) process between Tm³⁺ and Er³⁺ ions (Tm³⁺: ³F₄ + Er³⁺: ⁴I_13/2 → Tm³⁺: ³H₄ + Er³⁺: ⁴I_15/2), bringing about the depopulation of the Tm³⁺: ³F₄ level and Er³⁺: ⁴I_13/2 level. Therefore, the reduced emission intensity of 1.55 μm of Er³⁺ ion and 1.91 μm of Tm³⁺ ion both would depopulate the ions on the Er³⁺: ⁴I_13/2 level, which is beneficial to enhance ~2.7 μm MIR emission. More importantly, as shown in Figure 6, the emission intensity of the Er/Tm: PbF₂ crystal centered at around 2.7 μm in the 2500–3100 nm region is remarkably larger than that of the Er: PbF₂ crystal, confirming that the efficient enhanced ~2.7 μm emission is achieved in the Er/Tm: PbF₂ designed crystal. To further confirm the prospects of Er: PbF₂, Er/Tm: PbF₂ crystals as the mid-infrared luminescent material in laser applications, the 2.78 μm emission cross-sections are subsequently calculated according to the Fuchtbauere–Ladenburg theory [43]:

$${\sigma }_{\mathrm{em}}(\lambda )=\frac{A\beta {\lambda }^{5}I(\lambda )}{8\pi c{n}^2{\displaystyle \int \lambda I(\lambda )d\lambda }}$$

(1)

where λ denotes the wavelength of fluorescence spectrum, I (λ) is the intensity of emission spectrum at λ, $I(\lambda )/{\displaystyle \int \lambda }I(\lambda )\mathrm{d}\lambda$ is the normalized line shape function of the emission spectrum of prepared crystal, n is the refractive index of PbF₂ crystal, c is the speed of light in a vacuum, β is the fluorescence branching ratio of ⁴I_11/2 → ⁴I_13/2 transition, and A is the spontaneous emission probability. The value of β for ~2.7 μm mid-infrared emission in Er: PbF₂ is calculated to be 14.9%, and in the Er/Tm: PbF₂ crystal is calculated to be 20.24%. The maximum emission cross-section of the Er/Tm: PbF₂ crystal is calculated to be 0.63 × 10⁻²⁰ cm² at 2780 nm, which is almost twice that of the Er: PbF₂ crystal (0.32 × 10⁻²⁰ cm²). Moreover, as shown in

Table 1. MIR emission cross-sections σ_em, and lifetimes of ⁴I_11/2, ⁴I_{13/ 2} levels of Er/Tm: PbF₂, Er: PbF₂ crystals compared with other Er³⁺-doped crystals.

Crystal	σem	τ(4I11/2)	τ(4I13/2)	τ(4I11/2)/τ(4I13/2)	Ref.
	(10−20 cm2)	(ms)	(ms)	(%)
1.0 at.% /0.5 at.% Er/Tm: PbF2	0.63@2780nm	6.91 ± 0.01	3.14 ± 0.01	220.06	[This work]
1 at.% Er: PbF2	0.32@2780nm	6.03 ± 0.01	12.06 ± 0.05	50.00	[This work]
10 at.% Er:BaLaGa3O7	7.34@2714nm	0.72	7.99	9.01	[44]
10 at.% Er:CaLaGa3O7	17.9@2702nm	0.77	8.41	9.16	[45]
8 at.%Er:LuAl3(BO3)4	8.60@3170nm	2.10	2.54	82.68	[46]
7 at.% Er:Y2O3	1.41@2723nm	2.95	17.57	16.79	[47]
10 at.% Er:SrGdGa3O7	[email protected]μm	1.10	4.48	24.55	[24]
5at.% Er:YAP	9.00@2792nm	0.85	7.30	11.64	[13]
7 at.% Er:Lu2O3	1.10@2730nm	1.10	4.30	25.58	[14]
5 at.% Er:GdScO3	0.93@2720nm	2.24	4.57	49.02	[15]
4 at.% Er:SrF2	0.78@2727nm	9.56	15.06	63.48	[16]
4 at.% Er:CaF2	0.65@2720nm	5.98	9.94	60.16

, this higher stimulated emission cross-section in the Er/Tm: PbF₂ crystal possibly coincides well with the higher fluorescence branching ratio β (20.24%) of the Er³⁺: ⁴I_11/2 → ⁴I_13/2 transition. A higher emission cross-section is more favorable in achieving high performance of MIR laser operation. These results are related to the more uniform distribution of Er³⁺ and Tm³⁺ ions in PbF₂ crystal after the co-doping of Tm³⁺ ions, which is consistent with the theoretical calculation results. Furthermore, it is pointed out that the enhancing of 2.78 μm MIR fluorescence emission is more dependent on the efficient energy transfer between Er³⁺ and Tm³⁺ ions, which comes from the uniform distribution of doped ions.

4.5. Energy Transfer Mechanism between Tm³⁺ and Er³⁺ Ions

Based on spectroscopic results discussed above, the simplified energy level scheme and electron transitions of the Er³⁺/Tm³⁺ co-doped PbF₂ crystal are presented in Figure 7. The cyclic related processes of the Tm³⁺ and Er³⁺ ions in the crystal under optical excitation are as follows: cross-relaxation, energy transfer between Tm³⁺ and Er³⁺ ions, and multiphonon relaxation. The main two ET (namely ET1, ET2) and three CR (namely CR1, CR2, CR3) processes are listed as follows:

ET 1: Tm³⁺: ³H₄ + Er³⁺: ⁴I_15/2 → Tm³⁺: ³H₆ + Er³⁺: ⁴I_9/2;

ET 2: Er³⁺: ⁴I_13/2 + Tm³⁺: ³H₆ → Er³⁺: ⁴I_15/2 + Tm³⁺: ³F₄;

CR 1: Tm³⁺: ³F₄ + Er³⁺: ⁴I_13/2 → Tm³⁺: ³H₆ + Er³⁺: ⁴I_9/2;

CR 2: Tm³⁺: ³F₄ + Er³⁺: ⁴I_13/2 → Tm³⁺: ³H₄ + Er³⁺: ⁴I_15/2;

CR 3: 2Er³⁺: ⁴I_13/2 → Er³⁺: ⁴I_15/2 + Er³⁺: ⁴I_9/2.

As discussed, the Tm³⁺: ³H₄ → ³H₆ transition is resonant with the Er³⁺: ⁴I_15/2 → ⁴I_9/2 transition in the Er/Tm: PbF₂ crystal. Therefore, after the crystal is excited to the Tm³⁺: ³H₄ level by a pump of 800 nm LD, ET1 process Tm³⁺: ³H₄ → Er³⁺: ⁴I_9/2 would occur. Ions in the Er³⁺: ⁴I_9/2 level decay non-radiatively to the lower Er³⁺: ⁴I_11/2 level, and then decay radiatively to the Er³⁺: ⁴I_13/2 level and emit 2.78 μm mid-infrared light. Ions in the Er³⁺: ⁴I_13/2 level continue to decay radiatively to the ground state Er³⁺: ⁴I_15/2 level and emit 1.55 μm infrared light. Similarly, the Er³⁺: ⁴I_13/2 → ⁴I_15/2 transition is resonant with the Tm³⁺: ³H₆ → ³F₄ transition, and the ET2 process from Er³⁺: ⁴I_13/2 to Tm³⁺: ³F₄ level takes place. The ET2 process would reduce the population of the lower level of Er³⁺: ⁴I_13/2, thereby enhancing the 2.78 μm emission and weakening the 1.55 μm emission, as shown in Figure 5a and Figure 6. Meantime, the energy transfer up-conversion (UC) CR3 process (Er³⁺: 2⁴I_13/2 → ⁴I_15/2 + ⁴I_9/2) in the crystal can also populate the Er³⁺: ⁴I_11/2 level and depopulate the Er³⁺: ⁴I_13/2 level. Additionally, ions in the Tm³⁺: ³F₄ level decay radiatively to the ³H₆ level and emit 1.91 μm emission. The subsequent CR1 populates the Er³⁺: ⁴I_9/2 level, and then the Er³⁺: ⁴I_11/2 level is populated through the nonradiative decay from the ⁴I_9/2 level to the ⁴I_11/2 level, increasing the population ratio of ⁴I_11/2/⁴I_13/2 levels. Moreover, the ions in the Tm³⁺: ³F₄ energy level will also absorb energy and jump to the upper Tm³⁺: ³H₄ energy level due to Stark level splitting, and then the CR2 process described above occurs_. The CR2 process can simultaneously reduce the population Er³⁺: ⁴I_13/2, Tm³⁺: ³F₄ levels, to achieve 2.78 μm emission enhancement and 1.91 μm emission reduction, as shown in Figure 5b and Figure 6. The CR2 process also brings about the increasing population of the Tm³⁺: ³H₄ level. Besides emitting 1.47 μm light via the Tm³⁺: ³H₄ → ³F₄ transition_, ions in the Tm³⁺: ³H₄ level can populate the Er³⁺: ⁴I_9/2 level via ET1 process, resulting in further enhancement of the sensitization effect. To prove the CR2 process, the UC emission spectra of Er: PbF₂ and Er/Tm: PbF₂ crystals are shown in Figure 8 under 980 nm excitation. Clearly, as shown in Figure 7, under 980 nm NIR light excitation, the electrons in the ground level ⁴I_15/2 can be excited to the intermediate level ⁴I_11/2, and the electrons in the ⁴I_11/2 level sequentially populate the ⁴F_7/2 level (⁴I_15/2 → ⁴I_11/2 → ⁴F_7/2). Additionally, then, the multiple nonradiative multi-phonon relaxation in the ⁴F_7/2 state in turn populate the lower ²H_11/2, ⁴S_3/2, ⁴F_9/2, and ⁴I_9/2 levels, which would produce 800 nm light via the process: ⁴I_9/2 → ⁴I_15/2. It is clear to see that the UC emission intensity of the Er/Tm: PbF₂ crystal is at least two times larger than that of the Er: PbF₂ crystal at around 800 nm. Obviously, Tm³⁺ ions have no absorption band matching the 980 nm excitation (shown in Figure 3). This enhancing UC emissions phenomenon is possibly assigned to the CR2 and ET1 mechanism processes illustrated in Figure 7. To summarize, the ET1, ET2, CR1, CR2, CR3 processes all have significant effects on narrowing the lifetime gap of upper-lying Er³⁺: ⁴I_11/2 and lower-lying Er³⁺: ⁴I_13/2 levels or even achieving population conversion of these two levels, thereby obtaining efficient enhanced 2.78 μm emission.

4.6. Fluorescence Decay Curves and Fluorescence Lifetimes

For further demonstrating the energy interaction mechanism between Er³⁺ and Tm³⁺ ions, the time-resolved decay curves of the Er³⁺ ion 2.78 μm (⁴I_11/2 → ⁴I_13/2) and 1.55 μm (⁴I_13/2 → ⁴I_13/2) fluorescence emission for the Er/Tm: PbF₂ and Er: PbF₂ crystals were measured and shown in Figure 9. The lifetimes of ⁴I_13/2 levels were measured under the conditions of 1.55 μm emission (⁴I_13/2 → ⁴I_15/2) and 1.49 μm excitation (⁴I_15/2 → ⁴I_13/2). The decay curves of the Er³⁺: ⁴I_11/2 and Er³⁺: ⁴I_13/2 levels are well fitted with single-exponential behavior. As shown in Figure 9a,b, the measured lifetime of the upper-lying ⁴I_11/2 level in the Er/Tm: PbF₂ crystal (6.91 ms) is 14.6% longer compared with the Er: PbF₂ crystal (6.03 ms), which is assigned to the sensitization effect of the Tm³⁺ ion on the upper-lying Er³⁺: ⁴I_11/2 level. Moreover, as shown in Figure 9c,d, the measured lifetime of the lower-lying ⁴I_13/2 level in the Er/Tm: PbF₂ crystal is 3.14 ms, which is 73.96% shorter compared with the Er: PbF₂ crystal (12.06 ms). This remarkable decrease of the lifetime of lower-lying ⁴I_13/2 level denotes that Tm³⁺ ions can dramatically depopulate the Er³⁺: ⁴I_13/2 level via ET2, CR1, CR2, CR3 processes, thereby enhancing the 2.78 μm emission in PbF₂ crystals. The ET2, CR1, CR2, CR3 processes all have significant effects on narrowing the lifetime gap of upper-lying Er³⁺: ⁴I_11/2 and lower-lying Er³⁺: ⁴I_13/2 levels or even achieving population conversion of these two levels. Besides, the energy transfer efficiency η_ET2 was calculated to be 73.96%, confirming the efficient deactivation effect of the Tm³⁺ ion for the Er³⁺ ion. Furthermore, Table 1 shows the lifetimes of ⁴I_11/2, ⁴I_{13/ 2} levels of Er/Tm: PbF₂, Er: PbF₂ crystals, and other Er³⁺ doped laser crystals. The shorter fluorescence lifetime of ⁴I_13/2 lower level induces the longer fluorescence lifetime ratio τ(⁴I_11/2)/τ(⁴I_13/2). The fluorescence lifetime ratio τ(⁴I_11/2)/τ(⁴I_13/2) in Er/Tm: PbF₂ crystal is 220.06%, which is dramatically larger than that of the Er: PbF₂ crystal (50.00%) and other Er³⁺ doped crystals. The remarkably enhanced τ(⁴I_11/2)/τ(⁴I_13/2) ratio in Er/Tm: PbF₂ crystal is favorable for achieving efficient laser operation ~2.7 µm. As a consequence, the introduction of Tm³⁺ ions can simultaneously act as sensitization and deactivation ions for the Er³⁺ ion, thereby enhancing 2.78 μm mid-infrared emission and reducing the laser threshold of 2.78 μm luminescence.

5. Conclusions

In summary, Er³⁺: PbF₂, Tm³⁺: PbF₂, and Er³⁺/Tm³⁺: PbF₂ crystals were prepared successfully by the Bridgman technique. An efficient enhanced 2.78 μm emission was obtained in the Er/Tm: PbF₂ crystal for the first time, and the proposed energy transfer mechanism of the Er/Tm: PbF₂ crystal was systematically investigated. The theoretical calculations were performed to discover that the co-doping of Tm³⁺ ions can make the Er³⁺ and Tm³⁺ ions more evenly distributed in PbF₂ crystals, which can effectively break the local clusters of Er³⁺ in Er: PbF₂ crystal, thus ensuring efficient energy transfer between Er³⁺ and Tm³⁺ ions, and resulting in the enhancing of 2.78 μm MIR fluorescence emission. The cyclic energy transfer mechanism contains several energy transfer processes and cross-relaxation processes, which all have significant effects on narrowing the lifetime gap of upper-lying Er³⁺: ⁴I_11/2 and lower-lying Er³⁺: ⁴I_13/2 levels or even achieving population conversion of these two levels. As proved, the Tm³⁺ ion can simultaneously act as an appropriate sensitized and deactivated ion for the Er³⁺ ion in the PbF₂ crystal. Compared with the Er³⁺ single-doped crystal, the Er³⁺/Tm³⁺ co-doped PbF₂ crystal has the larger 2.78 μm mid-infrared fluorescence emission intensity, higher fluorescence branching ratio (20.24%), and higher stimulated emission cross-section (0.63 ×10⁻²⁰ cm²), corresponding to Er³⁺: ⁴I_11/2 → ⁴I_13/2 transition. Therefore, the introduction of Tm³⁺ ions is favorable for achieving efficient enhanced 2.78 μm emission in the Er/Tm: PbF₂ crystal, which can become a promising material for low threshold, and high-efficiency mid-infrared laser applications under the pump of a conventional 800 nm LD.