Positive influence of Ce3+ on effective transfer Yb3+:2F5/2 → Ho3+:5I6 in silica-germanate glass for mid-infrared applications

Tao Wang; Feifei Huang; Wenqian Cao; Yanyan Guo; Ruoshan Lei; Renguang Ye; Junjie Zhang; Shiqing Xu

doi:10.1364/OME.7.001084

1. Introduction

In last decades, extensive work has been done on the 2.0 μm laser materials driven by its wide applications in biomedicine, hazardous chemical detection, pollution monitoring and military system [1–4]. In particular, the trace gases with even ppm level can be detected because of various molecules (CO₂, CO, NO, SO₂) have strong rovibrational absorption lines in this ‘molecule fingerprint’ region of the electromagnetic spectrum. Tm³⁺ and Ho³⁺ are commonly chosen as fiber dopants to generate 2 μm laser due to Tm³⁺:³F₄→³H₆ and Ho³⁺:⁵I₇→⁵I₈ transitions, respectively. Ho³⁺ possesses longer radiative lifetime, longer-operating laser wavelength, higher emission cross section and broad emission band compared with Tm³⁺ [5–7]. However, there is no energy level in Ho³⁺ matching with the low cost and readily commercially available 800 or 980 nm laser diodes (LDs) [8,9], which limits its efficient laser operation. Therefore, some of the sensitizers such as Er³⁺, Yb³⁺, Tm³⁺ and Nd³⁺ with strong absorption bands in commercial LD at wavelength of 808 or 980 nm are taken into consideration to absorb and transfer pumping energy effectively. Up to now, investigations on the 2.0 μm emission from Er³⁺/Ho³⁺, Yb³⁺/Ho³⁺, Tm³⁺/Ho³⁺ co-doped and Er³⁺/Tm³⁺/Ho³⁺, Er³⁺/Yb³⁺/Ho³⁺ tri-doped have been performed in the glasses [10–14].

Among all the sensitizers, Yb³⁺ plays an important role due to its efficient absorption at 980 nm, and the simple energy level structure for Yb³⁺ (the ground state ²F_7/2 and excited state ²F_5/2) can avoid any undesirable excited state absorption [15,16]. However, strong upconversion (UC) emissions occurred in Yb³⁺/Ho³⁺ co-doping scheme, especially, when they are incorporated in a host matrix with relatively low phonon energies, leading to a dramatic reduction of the pumping efficiency for the 2.0 μm emission [8,17,18]. Thus, Ho³⁺ 2.0 μm emission intensity can be enhanced by developing an effective approach to minimize the UC process. Ce³⁺ has been proved as an ideal candidate in enhancing Er³⁺ 1.53 μm emission by reducing the UC emission when pumped by a 980 nm LD [19]. A small energy mismatch is found between the Er³⁺:⁴I_11/2→⁴I_13/2 and Ce³⁺:²F_7/2→²F_5/2 energy gap, so the cross relaxation (CR) process (Er³⁺:⁴I_11/2 + Ce³⁺:²F_5/2→Er³⁺:⁴I_13/2 + Ce³⁺:²F_7/2) between Er³⁺ and Ce³⁺ lead to a inhibition of the excited state absorption (ESA) and cooperative upconversion (CUC) processes which occur in Er³⁺:⁴I_11/2, both of them would further cause a population of Er³⁺:⁴F_7/2 and result in green UC fluorescence [20]. The energy gap between Ho³⁺:⁵I₆ and ⁵I₇ levels is similar to that between Er³⁺:⁴I_11/2 and ⁴I_13/2 levels, and the visible upconverted emissions are also occurred in Yb³⁺/Ho³⁺ co-doping under 980 nm LD due to the ESA and CUC processes, in which some of Ho³⁺ ions in ⁵I₆ were excited to higher manifolds (⁵S₂ + ⁵F₄) [8,17,18]. Hence, the incorporation of Ce³⁺ would reinforce the Ho³⁺ 2.0 μm emission intensity through CR process (Ho³⁺:⁵I₆ + Ce³⁺:²F_5/2→Ho³⁺:⁵I₇ + Ce³⁺:²F_7/2). In 2011, Tian et al. reported the 2.0 μm emission in Yb³⁺/Ho³⁺/Ce³⁺ tri-doped fluorophosphate glass under 980 nm LD [21]. In the next year, Tao et al. using Ce³⁺ as sensitize ion obtained an enhanced 2.0 μm emission in Yb³⁺/Ho³⁺/Ce³⁺ tri-doped tellurite glass [8], but it has not been reported in heavy metal oxide glass. In addition, the poor chemical durability, lower damage threshold, low thermal shock resistance in fluoride and tellurite glasses, which limit the stability and output power of fluoride and tellurite fiber lasers [22,23], and the effect of Ce³⁺ ion on Ho³⁺ 2.0 μm emission in fluorophosphate glass only resulting in a very weak enhancement.

Meanwhile, the luminescence of Ho³⁺ is easily quenched by the rapid multiphonon effect when it is incorporated in traditional oxide glasses due to their high phonon energies (e.g., 1500 cm⁻¹ for silica) [17,24]. So the suitable host is as important as the luminescent ions, when considering the gain media to be used in fiber lasers, both good mechanical properties and a high gain are required [25]. Silica-germanate glass combines the merits of relatively low maximum phonon energy and higher refraction index of germanate glass and low cost together with higher thermal stability of silicate glass [26,27]. In 2015, Wei et al. reported broadband 2.0 μm fluorescence in Er³⁺/ Ho³⁺ co-doped germanosilicate glass [28]. In this work, we report the sensitization effect of Ce³⁺ ions on Yb³⁺/Ho³⁺ co-doped silica-germanate glass. The Judd-Ofelt intensity parameters, transition and radiative probabilities, absorption and stimulated emission cross sections were calculated and discussed. In addition, the microparameters of the energy transfer processes were calculated.

2. Experimental

The compositions of silica-germanate glasses were 35SiO₂-35GeO₂-20 Ga₂O₃-5BaO-5Li₂O-1Yb₂O₃-1Ho₂O₃-XCeF₃ (X = 0, 0.1, 0.25, 0.5 denoted as YHC0, YHC0.1, YHC0.25 and YHC0.5, respectively). Meanwhile, the 1 mol% Ho³⁺ singly doped silica-germanate glass was prepared and denoted as H. High-purity of SiO₂, GeO₂, Ga₂O₃, BaO, Li₂CO₃, Yb₂O₃, Ho₂O₃ and CeF₃ powders were used as raw materials. Batches of raw materials (15 g) were well-mixed and melted in a platinum crucible in a Si-Mo resistance electric furnace at 1480 °C for 40 min. Then, they were quenched on preheated stainless steel plate and annealed near the temperature of glass transition for 2 h before they were cooled to room temperature. The annealed samples were finally cut and optically polished to the size of 10 mm × 10 mm × 1 mm for the optical property measurements.

The densities of samples were tested via the Archimedes principle using distilled water as the immersion medium with error of ± 0.001 g/cm³. Refractive indexes were measured by the prism minimum deviation method at the wavelength of 1053 nm with error limit of ± 0.05%. The visible UC (500–800 nm) fluorescence spectra were obtained with a TRIAX550 spectrofluorimeter upon the excitation of 980 nm LD. Absorption spectra were obtained using a PerkinElmer Lambda 900UV-VIS-NIR spectrophotometer in the range of 300~2200 nm with a resolution of 1 nm. Fluorescence spectra from 1000~2200 nm were tested with a computer-controlled Triax 320 type spectrometer excited by a 980 nm LD. All the measurements were carried out at room temperature.

3. Results and discussion

3.1 Absorption spectra and Judd-Ofelt analysis

Figure 1 shows the absorption spectra of Ho³⁺ singly doped, Yb³⁺/Ho³⁺ co-doped and Yb³⁺/Ho³⁺/Ce³⁺ tri-doped silica-germanate in the wavelength region of 300~2200 nm. The absorption bands corresponding to the transitions starting from Yb³⁺:²F_7/2 ground state to ²F_5/2 and the Ho³⁺:⁵I₈ ground state to the higher levels ⁵I₇, ⁵I₆, ⁵F₅, (⁵F₄, ⁵S₂), (⁵G₆, ⁵F₁) and ⁵G₅ are labeled. It can be seen from Fig. 1 that the addition of Ce³⁺ ions into the glass matrix results in a red-shift of the UV-side absorption edge, and this is assigned to the 4f→5d transition in Ce³⁺ ions which causes a broad absorption around 400–500 nm [29,30].

Fig. 1 Absorption spectra of H, YHC0 and YHC0.1 glasses.

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Based on the absorption spectrum of Ho³⁺ and J–O theory [31,32], J–O intensity parameters have been calculated in order to investigate the local environment around Ho³⁺ ions. Details of the theory and method have been well described earlier [33–35]. Table 1 shows the values measured (f_mea) and calculated (f_cal) oscillator strengths of sample (H) and other reported glass systems. Good agreement between f_mea and f_cal can be observed, and the small root mean square deviation δ_rms of 0.82 × 10⁻⁶, which further indicates the reliability and validity of the calculated J-O intensity parameters. In addition, it can be noticed that the oscillator strengths of silica-germanate glass are higher than those of silicate [36] and germanate [34] glasses in Table 1. It results from the different ligand field environment around Ho³⁺ ions [14]. What’s more, the transition of ⁵I₈→⁵F₁ + ⁵G₆ possesses the highest oscillator strength called hypersensitive transition (HST), which is sensitive to minor changes of local environment around Ho³⁺ ions and affects the J-O intensity parameters that characterize the optical properties of the system [35,37]. J–O parameters were obtained for further estimation of the difference of ligand field in glasses below.

Table 1. Measured (f_mea) and calculated (f_cal) oscillator strengths of H sample and compared with other systems.

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The J-O intensity parameters Ω_λ (λ = 2, 4, 6) of Ho³⁺ ions in various glass hosts are listed in Table 2. Previous studies have proved that parameters Ω₂ is closely related to the covalency parameter through the nephelauxetic effect and is strongly dependent on the local environments of Ho³⁺ ions [13]. It can be obtained that the Ω₂ value of Ho³⁺ doped sample (H) is larger than those of fluoride and fluorophosphate glasses [38,39] but lower than those of silicate and germanate glasses [40,41], which can be explained by the higher polarizability of O^2- ions than F^- ions. It is illustrated that the silica-germanate glass possesses lower polarizability and covalency. Meanwhile, the Ω₆ parameter is a vibronic dependent parameter, related to the rigidity and the viscosity of the host glass and the radio of Ω₄/Ω₆ determines the spectroscopy quality of the materials [42,43]. The prepared sample (H) possesses highest Ω₄/Ω₆ value as shown in Table 2. The larger Ω₄/Ω₆ value means the higher lasing efficiency for the laser transition of Ho³⁺ ions in a given matrix. Therefore, the largest Ω₄/Ω₆ value of H indicates that it is a great matrix for 2.0 μm emission [44].

Table 2. J–O intensity parameters Ω_λ (λ = 2, 4, 6) ( × 10⁻²⁰ cm²) of Ho³⁺ ions in various glass hosts.

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The radiative properties of Ho³⁺ in silica-germanate glass such as radiative transition probability (A_rad), fluorescence branching ratios (β) and radiative lifetimes (τ_rad) calculated based on J-O intensity parameters are listed in Table 3. High spontaneous transition probability is beneficial for high gain and more opportunity to achieve laser action [43]. It is found that the A_rad of Ho³⁺:⁵I₇→⁵I₈ transition is 85.89 s⁻¹ of the prepared sample, which is larger than those of fluorophosphate (73.54 s⁻¹) [39], silicate (78.71s⁻¹) [40] and germanate glasses (70.15 s⁻¹) [41].

Table 3. The calculated radiative transition probability (A_rad), fluorescence branching ratios (β) and radiative lifetimes (τ_rad) of Ho³⁺ ions for different transitions.

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3.2 Fluorescence spectra and energy transfer mechanism

The fluorescence spectra of the YHC (0, 0.1, 0.25, 0.5) glasses in the wavelength of 1050 to 2200 nm pumped at 980 nm are shown in Fig. 2. Because of the Ho³⁺:⁵I₆→⁵I₈ transition, the 1.2 μm emission is obtained. The 1.2 μm emission intensity decreases with increasing Ce³⁺ concentration, while the emission intensity of 2.0 μm increases with incorporation of Ce³⁺, and reaches the maximum when mol percentage of Ce³⁺ reaches to 0.1% at which the emission intensity almost enhances twice compared with YHC0. The 2.0 μm emission intensity was restrained with further Ce³⁺ ions adding. Insets in Fig. 2 show the decay curves of the ⁵I₆ and ⁵I₇ levels monitoring at 1200 and 2055 nm respectively, which are measured in both YHC0 and YHC0.1. It is found that the lifetime of ⁵I₇ level in YHC0.1 is 727 μs, which shows a clear increase compared with YHC0 (565 μs).

Fig. 2 Fluorescence spectra of YHC (0, 0.1, 0.25, 0.5) glasses. Insets in Fig. 2 show the decay curves of the YHC0 and YHC0.1 at 1200 and 2055 nm.

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The UC emission spectra of the samples were measured to further understand the enhancement of Ho³⁺ 2.0 μm emission. As shown in Fig. 3, intensive red emission (662 nm) dominates the UC luminescence, corresponding to the Ho³⁺:⁵F₅→⁵I₈ transitions. Two weak emission peaks located at 552 and 755 nm originating from Ho³⁺:(⁵F₄ + ⁵S₂)→⁵I₈ and (⁵F₄ + ⁵S₂)→⁵I₇ are also observed. Different from the variation tendency of 662 nm emission, the intensities of 552 and 755 nm emissions decrease with increasing Ce³⁺ concentration.

Fig. 3 Upconversion spectra of YHC (0, 0.1, 0.25, 0.5) glasses.

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According to the absorption, upconversion, fluorescence spectra in YHC (0, 0.1, 0.25, 0.5) glasses, the involved energy transfer mechanisms are indicated in Fig. 4. Ions on the Yb³⁺:²F_7/2 level are excited to the ²F_5/2 state by ground state absorption (GSA) when sample is pumped by 980 nm LD. Then the energy is transferred to a nearby Ho³⁺ in the ground state resulting in a population of the Ho³⁺:⁵I₆ by energy transfer process (ET) under the assistance of host phonons. Some of the Ho³⁺:⁵I₆ level are excited to the (⁵F₄ + ⁵S₂) manifolds via an energy transfer upconversion (ETU1) and excited state absorption (ESA1), resulting the green emission when it radiatively decays to the ground state. Meanwhile, the red upconversion emission centered at 662 nm shown in Fig. 4 is originated from the ⁵F₅→⁵I₈ transition. Population of the ⁵F₅ level is derived from two different processes which are nonradiative relaxation process from Ho³⁺:⁵F₄ + ⁵S₂ level to ⁵F₅ level and ETU2 or ESA2 processes [8,21]. The rest of ions in Ho³⁺:⁵F₄ + ⁵S₂ radiatively decay to Ho³⁺:⁵I₇ state with 755 nm emission. The CR process (Ho³⁺:⁵I₆ + Ce³⁺:²F_5/2→Ho³⁺:⁵I₇ + Ce³⁺:²F_7/2) between Ho³⁺ and Ce³⁺, the Ho³⁺ in ⁵I₆ state decays non-radiatively to the next lower Ho³⁺ 2.0 μm emission level ⁵I₇ with the energy transferred to a nearby Ce³⁺ in the ground state. Thus, the emissions occurred in the Ho³⁺:⁵I₆ level were reduced, which is confirmed by the decreased intensity of 552, 662, 755 and 1200 nm emissions. It should be noticed that the red emission at 662 nm shows a slight increment after initial decrease and the peak dropped again with increasing Ce³⁺ concentration while the green emission (552 nm) intensity reduces continuously. It is caused by the energy transfer upconversion (ETU2) and excited state absorption (ESA2) that takes place in the Ho³⁺:⁵I₇ level, which can also explain the variation tendency of 2.0 μm emission. When Ce³⁺ equals to 0.1 mol%, the Ho³⁺:⁵I₇ level is populated by CR process and few ions are excited to the Ho³⁺:⁵F₅ state; when adding 0.25% Ce³⁺, a portion of Ho³⁺:⁵I₇ level are excited to the Ho³⁺:⁵F₅ state; when Ce³⁺ concentration reaches to 0.5%, a large part of Ho³⁺:⁵I₇ level is excited to the Ho³⁺:⁵F₅ state. The reason why the emission at 662 nm in YHC0.5 is weakest may because of the Ho³⁺:⁵F₅ level is almost only derived from Ho³⁺:⁵I₇ level by ETU2 and ESA2 process.

Fig. 4 Energy level diagrams and energy transfer mechanism among Yb³⁺, Ho³⁺ and Ce³⁺ ions.

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3.3 Cross sections and emission parameters

Emission cross section is an important parameter to estimate the possibility for achieving laser action. Higher emission cross section means that better laser gain can be achieved in prepared glass [45]. The emission cross section (σ_em) can be calculated according to Fuchtbauer–Ladenburg (FL) equation [46]

σ_{e m} (λ) = \frac{λ^{4} A_{r a d}}{8 π c n^{2}} \times \frac{λ I (λ)}{\int λ I (λ) d λ}

where λ is the emission wavelength, A_rad is the spontaneous radiative transition probability of Ho³⁺:⁵I₇→⁵I₈ transition, I(λ) is the 2.0 μm fluorescence intensity, c is the velocity of light in vacuum, n is the refractive index of glass host.

The absorption cross section (σ_abs) can be derived from the calculated σ_em using the McCumber (MC) formula [47]

σ_{e m} (λ) = σ_{a b s} (λ) \times \frac{Z_{l}}{Z_{u}} \times \exp [\frac{h c}{k t} \times (\frac{1}{λ_{Z L}} - \frac{1}{λ})]

where Z_l and Z_u are the partition functions for the lower and the upper levels, respectively. Parameter h, k, T are the Planck constant (6.63 × 10⁻³⁴ J·S), Boltzmann constant (1.38 × 10⁻²³ J/K) and the temperature (here it is the room temperature), respectively, and λ_ZL is the wavelength for the transition between the lower Stark sublevels of the emitting multiplets and the lower Stark sublevels of the receiving multiplets.

The absorption and emission cross sections of Ho³⁺ in YHC0.1 are shown in Fig. 5(a). The maximal value of the calculated emission cross section spectrum centers at 2055 nm and reaches as high as 4.43 × 10⁻²¹ cm². This value is higher than the reported ones of germanate (4.0 × 10⁻²¹ cm²) [48], silicate (3.07 × 10⁻²¹ cm²) [12] and fluoride (4.3 × 10⁻²¹ cm²) glasses [5]. The Yb³⁺/Ho³⁺/Ce³⁺ tri-doped silica-germanate glasses possessing large emission cross section can be an excellent candidate in achieving intense 2.0 μm laser.

Fig. 5 (a) The calculated absorption and emission cross sections (b) Gain coefficient for prepared glass (YHC0.1).

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Gain coefficient is another characteristic parameter to evaluate 2.0 μm emission properties quantitatively. The wavelength dependent gain coefficient is calculated in detail as a function of population inversion for the upper laser level on the basis of the σ_abs and σ_em. The gain cross-section spectrum G(λ), can be calculated by

G (λ) = N [P σ_{e m} (λ) - (1 - P) σ_{a b s} (λ)]

where P is the population inversion given by the ratio between the population of Ho³⁺:⁵I₇ level and the total Ho³⁺ concentration and N is the total concentration of Ho³⁺. Figure 5(b) presents the calculated gain coefficient versus wavelength for different population inversion parameter P. Obviously, the positive gain is obtained when P > 0.4, which is similar to the case in other glasses with Ho³⁺ doped [10,14]. Meanwhile, the maximum gain coefficient is up to 1.9 cm⁻¹ around 2055 nm, which is higher than those in fluoride (0.58 cm⁻¹) [5], silicate (1.75 cm⁻¹) [49] and germanate-tellurite glasses (0.53 cm⁻¹) [14]. These results indicate that Yb³⁺/Ho³⁺/Ce³⁺ tri-doped silica-germanate glass can be used as a suitable optical material to obtain 2.0 μm infrared emission.

3.4 Energy transfer microscopic parameters between Yb³⁺, Ho³⁺ and Ce³⁺

In order to further investigate energy transfer processes between Yb³⁺, Ho³⁺ and Ce³⁺ ions quantitatively, energy transfer microscopic parameters were calculated by the determination of their absorption and emission cross sections and the extended integral method is used to analyze energy transfer microscopic parameters.

The probability rate of energy transfer between Yb³⁺ and Ho³⁺ can be estimated as [50,51]

W_{D - A} = (\frac{2 π}{ℏ}) {| H_{D A} |}^{2} S_{D A}^{N}

where \H_DA\ is the matrix element of the perturbation Hamiltonian between initial and final states in energy transfer process, S

N DA

is the integral overlap between the m-phonon emission sideband of donor ions (D, here D stands for Yb³⁺) and k-phonon absorption line shapes of acceptor ions (A, here A stands for Ho³⁺) and N is the total phonons in the transfer process (m + k = N). In the case of weak electron-phonon coupling which is suitable for rare earth ions, S

N DA

can be approximated by

S_{D A}^{N} \approx \sum e^{- (S_{0}^{D} + S_{0}^{A})} \times [\frac{{(S_{0}^{D} + S_{0}^{A})}^{N}}{N!}] S_{D A} (0, 0, E) δ (N, Δ E / ℏ w_{0})

where S

D 0

and S

A 0

are the Huang-Rhys factors of the Yb³⁺ and Ho³⁺ in silica-germanate glass, S_DA(0,0,E) is the overlap between the zero phonon lines shape of Yb³⁺ emission and Ho³⁺ absorption. Then the integral overlap in the case of m-phonon emission by the donor and no phonon involvement by the acceptor can be expressed as

S_{D A} (m, 0, E) = \int [\frac{S_{0}^{m}}{m!} e^{- S_{0}} \int g_{e m i s}^{D} (E - Δ E)] g_{a b s}^{A} (E) d E

where ΔE = mħw₀. Since the measurements are carried out at some finite temperature T, the multi-phonon probability must be included, the emission cross section (σ_emis) of Yb³⁺ with m phonon emission and absorption cross section (σ_abs) of Ho³⁺ with k phonon absorption can be proposed as

σ_{e m i s (m - p h o n o n)}^{D} = σ_{e m i s}^{D} (λ_{m}^{+}) \approx \frac{S_{0}^{m} e^{- S_{0}}}{m!} {(\bar{n} + 1)}^{m} σ_{e m i s}^{D} (E - E_{1})

σ_{a b s (k - p h o n o n)}^{A} = σ_{a b s}^{A} (λ_{k}^{-}) \approx \frac{S_{0}^{k} e^{- S_{0}}}{k!} {(\bar{n})}^{k} σ_{a b s}^{A} (E + E_{2})

where E1 = mħw₀, E2 = kħw₀. λ

+ m

denotes the translation of Yb³⁺ emission cross section wavelength by m-phonon emission, and λ

- k

represents the translation of Ho³⁺ absorption cross section spectra wavelength due to k-phonon absorption

λ_{m}^{+} = 1 / (1 / λ - m ℏ w_{0})

λ_{k}^{-} = 1 / (1 / λ + k ℏ w_{0})

If we ignore the k phonon annihilation process and just focus on the m phonon creation process, the probability rate of energy transfer can be obtained using the following direct transfer equation

W_{D A} (R) = \frac{6 c g_{l o w}^{D}}{{(2 π)}^{4} n^{2} R^{6} g_{u p}^{D}} \sum_{m = 0}^{\infty} e^{- (2 \bar{n} + 1) S_{0}} \frac{S_{0}^{m}}{m!} \times {(\bar{n} + 1)}^{m} \int σ_{e m i s}^{D} (λ_{m}^{+}) σ_{a b s}^{A} (λ) d λ = \frac{C_{D A}}{R^{6}}

where R is the distance of separation between donor and acceptor, C_D-A is the energy transfer coefficient (cm⁶/s), = (1/e^ħw0/Kt-1) is the average occupancy of phonon mode at temperature T. The energy transfer coefficient is then expressed by

C_{D A} = \frac{6 c g_{l o w}^{D}}{{(2 π)}^{4} n^{2} g_{u p}^{D}} \sum_{m = 0}^{\infty} e^{- (2 \bar{n} + 1) S_{0}} \frac{S_{0}^{m}}{m!} \times {(\bar{n} + 1)}^{m} \int σ_{e m i s}^{D} (λ_{m}^{+}) σ_{a b s}^{A} (λ) d λ

The energy transfer properties of Yb³⁺→Ho³⁺ in YHC0 and YHC0.1 are calculated using the Eqs. (4)–(12) and listed in Table 4. The result shows the direct transfer microscopic parameter of Yb³⁺→Ho³⁺ in YHC0 is found to be 5.50 × 10⁻⁴⁰ cm⁶/s in a quasi resonant process with non-phonon (8.82%), having a participation of 1 (89.06%) and 2 (2.12%) phonons. The transfer microscopic parameter of Yb³⁺→Ho³⁺ in YHC0.1 is as high as 7.54 × 10⁻⁴⁰ cm⁶/s, which is larger than that in YHC0 without Ce³⁺, the result indicates the high energy transfer efficiency from Yb³⁺ to Ho³⁺ after the introduction of Ce³⁺.

Table 4. Calculated microscopic parameters C_D-A ( × 10⁻⁴⁰ cm⁶/s) for Yb³⁺→Ho³⁺ energy transfer in YHC0 and YHC0.1 glasses. The number # of phonons necessary to assist the energy transfer process is also revealed with their percent contributions.

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4. Conclusions

By incorporating Ce³⁺, the upconversion occurred in Ho³⁺:⁵I₆ state is remarkably reduced through the cross relaxation process (Ho³⁺:⁵I₆ + Ce³⁺:²F_5/2→Ho³⁺:⁵I₇ + Ce³⁺:²F_7/2), the luminescence intensity of Ho³⁺ 2.0 μm emission is nearly two times enhanced in YHC0.1 compared with YHC0. The emission cross section and the maximum gain coefficient in YHC0.1 is calculated to be 4.43 × 10⁻²¹ cm² and 1.9 cm⁻¹ around 2055 nm. Meanwhile, the measurements of decay lifetimes in several levels were carried out to further examine energy transfer mechanism and enhanced mid-infrared emissions. In addition, the energy transfer coefficient from Yb³⁺→Ho³⁺ in YHC0.1 is 7.54 × 10⁻⁴⁰ cm⁶/s, which is larger than that in YHC0 (5.50 × 10⁻⁴⁰ cm⁶/s) and almost has 1.5 fold increased. All results suggest that the Yb³⁺/Ho³⁺/Ce³⁺ tri-doped silica-germanate glass is promising for the improvement of Ho³⁺ 2.0 μm fiber laser performance.

Funding

National Natural Science Foundation of China (NSFC) (No. 61605192, 51472225, 51401197, and 51502022); Open Fund of the Guangdong Engineering Technology Research and Development Center of Special Optical Fiber Materials and Devices (South China University of Technology).

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Absorption	λ (nm)	Oscillator Strength		Silicate [36]	Germanate [34]
		f_mea( × 10⁻⁶)	f_cal( × 10⁻⁶)	f_mea( × 10⁻⁶)	f_mea( × 10⁻⁶)
⁵I₈→⁵I₆	1152	0.688	0.736	0.455	0.605
⁵I₈→⁵F₅	642	2.674	2.912	1.810	2.380
⁵I₈→⁵F₄ + ⁵S₂	538	3.477	2.687	2.577	3.017
⁵I₈→⁵F₁ + ⁵G₆	453	16.637	16.628	14.358	14.504
δ_rms		0.82 × 10⁻⁶

Samples	Ω₂	Ω₄	Ω₆	Ω₄/Ω₆	Reference
H	3.29	3.14	1.05	2.99	This work
Fluoride	1.86	1.90	1.26	1.51	38
Fluorophosphate	2.54	3.19	1.27	2.51	39
Silicate	5.52	2.43	1.15	2.11	40
Germanate	6.59	2.77	1.90	1.46	41

Transition	λ	A_rad(s⁻¹)	β(%)	τ(ms)
⁵I₇→⁵I₈	1948	85.89	100	11.64
⁵I₆→⁵I₈	1152	132.94	80.78	6.08
⁵I₆→⁵I₇	2828	31.63	19.22
⁵I₅→⁵I₈	887	50.83	39.52	7.77
⁵I₅→⁵I₇	1631	64.27	49.97
⁵I₅→⁵I₆	3856	13.53	10.52
⁵I₄→⁵I₈	757	6.33	9.31	14.72
⁵I₄→⁵I₇	1240	30.86	45.42
⁵I₄→⁵I₆	2208	24.71	36.36
⁵I₄→⁵I₅	5165	6.05	8.91

Energy Transfer	Sample	N(#phonons-assist) (%contribution)			C_D-A
Yb³⁺→Ho³⁺	YHC0	0(8.82)	1(89.06)	2(2.12)	5.50
	YHC0.1	0(10.78)	1(87.48)	2(1.74)	7.54

Absorption	λ (nm)	Oscillator Strength		Silicate [36]	Germanate [34]
		f_mea( × 10⁻⁶)	f_cal( × 10⁻⁶)	f_mea( × 10⁻⁶)	f_mea( × 10⁻⁶)
⁵I₈→⁵I₆	1152	0.688	0.736	0.455	0.605
⁵I₈→⁵F₅	642	2.674	2.912	1.810	2.380
⁵I₈→⁵F₄ + ⁵S₂	538	3.477	2.687	2.577	3.017
⁵I₈→⁵F₁ + ⁵G₆	453	16.637	16.628	14.358	14.504
δ_rms		0.82 × 10⁻⁶

Positive influence of Ce³⁺ on effective transfer Yb³⁺:²F_5/2 → Ho³⁺:⁵I₆ in silica-germanate glass for mid-infrared applications

Abstract

Corrections

1. Introduction

2. Experimental

3. Results and discussion

3.1 Absorption spectra and Judd-Ofelt analysis

3.2 Fluorescence spectra and energy transfer mechanism

3.3 Cross sections and emission parameters

3.4 Energy transfer microscopic parameters between Yb³⁺, Ho³⁺ and Ce³⁺

4. Conclusions

Funding

Reference and links

Cited By

Figures (5)

Tables (4)

Equations (12)

Optical Materials Express

Abstract

Corrections

1. Introduction

2. Experimental

3. Results and discussion

3.1 Absorption spectra and Judd-Ofelt analysis

3.2 Fluorescence spectra and energy transfer mechanism

3.3 Cross sections and emission parameters

3.4 Energy transfer microscopic parameters between Yb3+, Ho3+ and Ce3+

4. Conclusions

Funding

Reference and links

Cited By

Figures (5)

Tables (4)

Equations (12)

Optical Materials Express

3.4 Energy transfer microscopic parameters between Yb³⁺, Ho³⁺ and Ce³⁺