2.0 &#x03BC;m Nd<sup>3+</sup>/Ho<sup>3+</sup>-doped tungsten tellurite fiber laser

L. X. Li; W. C. Wang; C. F. Zhang; J. Yuan; B. Zhou; Q. Y. Zhang

doi:10.1364/OME.6.002904

1. Introduction

In recent years, fiber lasers operating at the eye-safe spectral region of ~2.0 μm have been extensively investigated due to their numerous applications in coherent laser radar systems, laser imaging, remote chemical sensing, biomedical systems, pump sources as mid-infrared (MIR) lasers, optical parametric oscillators, and so on [1–3]. Tellurium oxide (TeO₂) based glasses have attracted a great deal of interest as they possess some important advantages over other commonly investigated fiber host glasses such as silicates, fluorides and germanates. Firstly, tellurite glass has a phonon energy of ~750 cm^–1, which is much lower than that of silicate (~1,100 cm^–1) and germanate (~900 cm^–1), extends the infrared transparency range to ~5 μm, resulting in high radiative rates and long lifetimes of the lasing levels of rare earth (RE) ions that are doped into the glass [4]. The lower phonon energy of tellurite glass also leads to a theoretically low background loss than silica at longer wavelengths, which helps to reduce the laser thresholds. Secondly, tellurite glass has much higher solubility of RE ion than silicate glass, enabling the development of ultra-compact fiber lasers by greatly increasing the RE ion concentration [5]. Thirdly, this material has a high refractive index (~2.05) and large absorption and emission cross sections [6]. Besides, tellurite glass is more chemically and environmentally stable than fluoride glass and has advantages in fabrication techniques as shown in oxide glass [1]. These merits make the tellurite glass to be an efficient laser medium for the mid-infrared fiber laser emission.

Among RE ions, Tm³⁺ and Ho³⁺ ions are capable of leading to the generation of ~2.0 μm laser because of Tm³⁺: ³F₄ → ³H₆ and Ho³⁺: ⁵I₇ → ⁵I₈ transitions. Considering the larger emission cross section (σ_e) and longer lifetime the lasing state, Ho³⁺ is made more suitable for the ~2.0 μm laser output, particularly for reducing the laser threshold [7,8]. However, Ho³⁺ can’t be pumped directly by a readily available 800 or 980 nm commercial laser diode (LD) due to the lack of appropriate ground state absorption bands. In order to achieve efficient excitation of Ho³⁺, RE ions with a strong absorption band at around 800 or 980 nm are considered necessary to be used as sensitizers, such as Yb³⁺, Tm³⁺ and Er³⁺ [9–12], and the lasing output at ~2.0 μm have been achieved in Ho³⁺-doped tellurite fibers by using these ions as sensitizers [13–16].

Besides the above mentioned sensitizer ions, Nd³⁺ has an intensive absorption band at 800 nm corresponding to the laser wavelength of high performance and low cost commercial LD. Recently, we have found two kinds of novel approaches for obtaining intense ~2.0 μm emission of Ho³⁺ by using Nd³⁺ as sensitizer in Nd³⁺/Ho³⁺ co-doped and Nd³⁺/Yb³⁺/Ho³⁺ triply doped tungsten tellurite glasses [17,18]. Figure 1 shows the simplified pump scheme and energy level diagram of the Nd³⁺-Ho³⁺ co-doped system. Under 795 nm excitation, Nd³⁺ ions are excited to the (⁴F_5/2, ²H_9/2) states from the ground state via the ground state absorption, leading to the population of ⁴F_3/2 followed by rapid nonradiative (NR) multi-phonon decay. This allows the energy transfer from Nd³⁺ to Ho³⁺ (ET: Nd³⁺: ⁴F_3/2 + Ho³⁺: ⁵I₈ → Nd³⁺: ⁴I_9/2 + Ho³⁺: ⁵I₅), and subsequently populates the lasing level of Ho³⁺: ⁵I₇ through nonradiative decay or cross relaxation (CR: Nd³⁺: ⁴I_9/2 + Ho³⁺: ⁵I₆ → Nd³⁺: ⁴I_13/2 + Ho³⁺: ⁵I₇) process [19], resulting in efficient ~2.0 μm emission. Under 795 nm excitation, three intense emission bands of Nd³⁺ peaking at around 905, 1064, and 1339 nm can be observed due to the Nd³⁺: ⁴F_3/2 → ⁴I_9/2, ⁴F_3/2 → ⁴I_11/2, and ⁴F_3/2 → ⁴I_13/2 transitions, respectively. Here it should be noted that no upconversion luminescence due to excited state absorption (ESA) is observed for Nd³⁺.

Fig. 1 Simplified energy level diagram and main energy transfer processes between Nd³⁺ and Ho³⁺ ions for achieving the ~2.0 μm emission in the Nd³⁺/Ho³⁺ co-doped tungsten tellurite glass under 795 nm excitation.

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Until now, there has no report about the ~2.0 μm laser in Nd³⁺/Ho³⁺ co-doped tungsten tellurite glass fibers. In this work, we report an efficient ~2.0 μm laser output in this material under the excitation of the 795 nm LD. The energy transfer, optical properties of the glass fiber and fiber laser are discussed.

2. Experimental

The molar composition of the core was 60TeO₂–30WO₃–3ZnO–6La₂O₃–0.5Ho₂O₃–0.5Nd₂O₃ (TWHN–0.5), which was demonstrated to be the best composition for the ~2.0 μm lasing output in our previous study [17]. A few content of Na₂O was added into the cladding composition in order to adjust and slightly reduce its refractive index, and the best cladding composition was designed to be 59TeO₂–30WO₃–3ZnO–7La₂O₃–1Na₂O. The fiber was fabricated by a convenient suction technique and the detailed fabricating process was described in our previous work [20]. The core and cladding diameters of the active fiber are 32 and 125 μm, respectively, with the numerical aperture (NA) of 0.28.

The absorption spectra of the glass samples were performed on a Perkin-Elmer Lambda 900 UV-VIS-NIR spectrophotometer (Waltham, MA) with a resolution of 1 nm. The fluorescence spectra were measured by a computer controlled Triax 320 spectrofluorimeter (Jobin-Yvon Corp., HORIBA, Ltd.,) with a SR510 lock-in amplifier (Stanford Research Systems, Sunnyvale, CA), a C-995 Optical chopper (Terahertz Technologies Inc., USA), and a LE-SP-DInAs-3.4A optical detector (LEO Photonics Co., Ltd., China) for measuring the mid-infrared emission. The propagation loss of the Nd³⁺/Ho³⁺ co-doped tungsten tellurite fiber was measured at 1310 nm using the cutback technique. The output power was tested by a Nova II Display ROHS optical power meter (Ophir Optronics Solutions Ltd., Israel). The wavelength of the pump LD (LE-LS-795-700TFCF, LEO Photonics Co., Ltd., China) was centered at 795 ± 5 nm with a maximum output power of 1500 mW, spot diameter of 30 μm, and NA of 0.154. The characteristic temperatures of glass transition, onset crystallization peak, and top crystallization were analyzed using a Netzsch STA 449 C Jupiter Different scanning calorimetery (DSC, GER) under Ar atmosphere at a heating rate of 10 °C/min from 25 °C to 700 °C. The lifetime of Ho³⁺: ⁵I₇ level was obtained from the first e-folding time of the emission intensity in the decay curve tested with a TDS3052B digital oscilloscope (Tektronix INC., USA). All the measurements were carried out at room temperature.

3. Results and discussions

3.1 Spectroscopic characterization

Figure 2 shows the absorption spectra of Nd³⁺, Ho³⁺, and Nd³⁺/Ho³⁺ co-doped tellurite glasses from 770 to 2200 nm. The characteristic absorption bands corresponding to transitions from the ground state to the excited states are labeled in the spectra. An intense absorption band near 800 nm was observed in Nd³⁺ and Nd³⁺/Ho³⁺ co-doped glasses due to the Nd³⁺: ⁴I_9/2 → ⁴F_5/2, ²H_9/2 transition, but it could not be observed in the Ho³⁺-doped glass. In addition, the absorption band of Ho³⁺ nearby 900 nm (inset of Fig. 2) is very close to the emission band of Nd³⁺ at around 905 nm result from the Nd³⁺: ⁴F_3/2 → ⁴I_11/2 transition (as shown in Fig. 1), indicating that Ho³⁺ can absorb the energy from Nd³⁺ efficiently (e.g., Nd³⁺: ⁴F_3/2 → Ho³⁺: ⁵I₅).

Fig. 2 The absorption spectra of Nd³⁺, Ho³⁺, and Nd³⁺/Ho³⁺ co-doped glasses. Inset: magnified absorption spectra of Ho³⁺ nearby 900 nm.

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The emission spectra of Ho³⁺ and Nd³⁺/Ho³⁺ co-doped tellurite glasses under the excitation using a 795 nm LD is presented in Fig. 3. In the spectra, no fluorescence emission was observed when only Ho³⁺ was doped into the glass because there was no ground absorption band at 795 nm. However, an intense broadband fluorescence emission at ~2.0 μm was obtained in the Nd³⁺/Ho³⁺ co-doped glass, further confirming that Nd³⁺ can act as an efficient sensitizer of Ho³⁺.

Fig. 3 Emission spectra of Ho³⁺ and Nd³⁺/Ho³⁺ co-doped tungsten tellurite glasses. Inset: gain coefficient of the Ho³⁺: ⁵I₇ → ⁵I₈ transition in the current host glass.

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The gain coefficient of Ho³⁺ can be calculated by the following Eq. [21]:

G (λ) = N_{0} [p σ_{e} (λ) - (1 - p) σ_{a}^{} (λ)]

where N₀ is the Ho³⁺ concentration, p is the inversion factor given by the ratio of upper and lower energy levels. The absorption cross section σ_a(λ) and emission cross section σ_e(λ) will be calculated by the following Eqs. (2) and (3). The calculated gain coefficients as a function of wavelength with different p values are shown in the inset of Fig. 3. When the population inversion levels equal to 0.4, the gain coefficient becomes positive, which demonstrate that a low pump threshold can be achieved. Additionally, the maximum gain coefficient at ~2.0 μm reaches 1.2 cm^–1, which is higher than that of germanate glass (0.47 cm^–1) [22] and fluorophosphate glass (0.66 cm^–1) [23], indicating excellent gain performance of the present host glass.

3.2 Basic parameters

Based on the measured absorption spectra shown in Fig. 2, the absorption cross section σ_a(λ) can be determined by the Beer-Lamber law [15]:

σ {}_{a}{(λ)} = \frac{2.303 \log \frac{I_{0} (λ)}{I (λ)}}{N l}

where

\log I_{0}^{} (λ) / I (λ)

is the absorptivity [3], N is the concentration of the corresponding RE ions, and l is the sample thickness. The σ_a of Nd³⁺ at 795 nm is calculated to be 2.64 × 10⁻²⁰ cm², which is larger than that of Tm³⁺ (0.98 × 10⁻²⁰ cm² nearby 808 nm) [24] and Yb³⁺ (1.89 × 10⁻²⁰ cm² nearby 976 nm) [25]. Large σ_a of Nd³⁺ at 795 nm is benefit for increasing the absorptivity of Nd³⁺, absorbing more pump power and improving the pump efficiency [17,18], which is in favor of indirect energy transfer from Nd³⁺ to Ho³⁺. And the σ_a of Ho³⁺ at 900 nm is calculated to be 0.573 × 10⁻²⁰ cm².

The stimulated emission cross section σ_e(λ) is obtained from the fluorescence spectra using the Fuchtbauer-Ladenburg theory [26]:

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

where n is the refractive index, c is the speed of light, A_r is the spontaneous emission probability of the transition, and I(λ) is the fluorescence spectra intensity. The σ_e of Nd³⁺ at 905 nm in the present glass is 1.323 × 10⁻²⁰ cm². It is worth mentioning that the σ_e of Nd³⁺: ⁴F_3/2→⁴I_9/2 and the σ_a of Ho³⁺: ⁵I₈ →⁵I₅ at around 905 nm overlapped completely, indicating that the energy transfer process is resonant with large possibility [17]. And the σ_e of Ho³⁺ at 2052 nm is 5.66 × 10⁻²¹ cm², which is larger than that in fluoride glass (5.3 × 10⁻²¹ cm²) and germanate glass (4.0 × 10⁻²¹ cm²) [27]. All these advantages are benefit for the ~2.0 μm laser output.

Energy transfer coefficient (C_D-A) from Nd³⁺ to Ho³⁺ was achieved from the overlapped absorption and emission cross section by the following Eq. [20,25]:

C_{D - A} = \frac{3 c}{8 π^{4} n^{2}} \cdot \frac{g_{l o w}^{D}}{g_{u p}^{D}} \cdot \int σ_{e}^{D} (λ) σ_{a}^{A} (λ) d λ

Where

g_{l o w}^{D}

and

g_{u p}^{D}

are the degeneracy of the lower and upper (

{}^{4}I_{9 / 2}

and

{}^{4}F_{3 / 2}

) levels of the donor (D: Nd³⁺), and the values are 10 and 4, respectively,

σ_{e}^{D} (λ)

and

σ_{a}^{A} (λ)

are the emission cross section of the donor and the absorption cross section of the acceptor (A: Ho³⁺) nearby 900 nm, respectively. Combining with Eqs. (2) and (3), the C_D-A was calculated to be 3.8 × 10⁻⁴⁰ cm⁶·s^–1. Meanwhile, the energy transfer efficiency

η

from Nd³⁺ to Ho³⁺ can be determined from the lifetime value by using the following formula [28]:

η = 1 - \frac{τ}{τ_{0}}

where τ₀ and τ are the lifetimes of Nd³⁺: ⁴F_3/2 level in Nd³⁺ singly doped and Nd³⁺/Ho³⁺ co-doped samples, respectively. The value of energy transfer efficiency is 36.4%.

The Judd-Oflet (J-O) intensity parameters Ω_i (i = 2, 4, 6) of the Ho³⁺ doped tungsten tellurite glass are presented in Table 1. Generally, the spectroscopic quality factor χ (Ω₄/Ω₆) is an important parameter to predict the stimulated emission in a laser-active host and a large χ is beneficial to obtain intense laser output [29]. The χ of the Ho³⁺ doped tungsten tellurite glass is the highest when compared with other glass hosts such as fluoride, fluorophosphate, phosphate glasses etc [17].

Table 1. The J-O intensity parameters of Ho³⁺ doped tungsten tellurite glass.

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Table 2 lists the basic parameters of the Nd³⁺/Ho³⁺ co-doped tellurite glass. The value of transition temperature T_g (453 °C) is much higher than the classical TeO₂–ZnO–Na₂O (TZN) glass (299 °C) [4], so it can effectively increase the damage threshold of the glass fiber. The ΔT of this glass is as high as 122 °C, suggesting a wide range of operating temperature and outstanding glass stability against crystal nucleation or growth during the fiber drawing process. The measured lifetime of Ho³⁺ at ⁵I₇ level (τ_m) is about 2.99 ms, extremely longer than that of fluorophosphate glass (0.95 ms), germanate glass (0.36 ms) [30], and silicate glass (0.32 ms) [27]. In short, higher values of ΔT, σ_a, σ_e, and τ_m demonstrate that the present TWHN–0.5 glass is a promising host material to obtain efficient 2.0 μm laser.

Table 2. Basic physical parameters of the Nd³⁺/Ho³⁺ co-doped tungsten tellurite glass.

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3.3 Fiber performance

The background loss ( $α$ ) of the Nd³⁺/Ho³⁺ co-doped tungsten tellurite fiber is one of the important parameters to evaluate the fiber properties, and it is closely related with the pump threshold and output power. The fiber background loss can be determined by Eq. (6):

α = - \frac{10 \log (\frac{P_{o u t}}{P_{i n}})}{L}

where P_out and P_in are the valid output and input power of the fiber, L is the fiber length. The propagation data of the Nd³⁺/Ho³⁺ co-doped tungsten tellurite fiber at 1310 nm was measured by using the cutback method, as presented in Fig. 4. By linear fitting to specific output power values of different points, the background loss was calculated to be 4.44 dB/m. The value is higher than the results reported by Richards et al. (1.0 dB/m at 1400 nm) [11] and Li et al. (2.86 dB/m at 1310 nm) [2]. The high background loss is mainly due to the chemical impurities and tiny defects introduced during the fiber preform fabrication process, and there was no atmosphere protection in the fiber drawing process, which results in secondary pollution of the fiber preform in the heating process. In order to reduce the fiber background loss, the purity of the raw material, the technology of fabricating the fiber preform and the drawing process need to be optimized in our future research. The inset in Fig. 4 shows the photomicrograph of the Nd³⁺/Ho³⁺ co-doped multimode fiber cross section.

Fig. 4 The measured fiber background loss of Nd³⁺/Ho³⁺ co-doped tungsten tellurite fiber. Inset: photomicrograph of the fiber cross section.

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3.4 Fiber laser

The one-end pumped experimental configuration is shown in Fig. 5. The output power from the 795 ± 5 nm LD with spot diameter of 30 μm was collimated and focused into the tellurite fiber. The optical cavity was made up of a pair of dichroic mirrors and a 5 cm-long Nd³⁺/Ho³⁺ co-doped tungsten tellurite fiber. The dichroic mirror near the pump end is highly reflective (HR: 99.7%) at ~2.0 μm and highly transparent (HT: 91.2%) at the pump wavelength, which is to ensure vast majority of the ~2.0 μm laser being reflected back to the cavity and most of the pump power being launched into the active fiber. The other dichroic mirror near the output end is partially reflective (PR: 86.8%) at ~2.0 μm and highly reflective (HR: 89.7%) at the pump wavelength in order to reflect most of the unabsorbed pump light back into the fiber. Meanwhile, it was demonstrated that highly reflective is benefit for decreasing the threshold pump power by using the theoretical modeling method with Matlab software [31]. An optical power meter was used to measure the output power of the 2052 nm laser after processed by a band-pass filter.

Fig. 5 Schematic of Nd³⁺/Ho³⁺ co-doped tungsten tellurite fiber laser experiment configuration.

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Figure 6 shows the laser output power with respect to the absorbed pump power, and the inset presents the laser spectrum of the present fiber laser. The absorbed pump power in the Fig. 6 was estimated by the differences between the power of the front-end and the back-end surface of the active fiber, both values were measured by the optical power meter, while measuring the back-end power, a low pass filter (λ<1200 nm) was placed in front of the power meter to prevent the influence of the laser output power. According to Fig. 6, the output laser power rises linearly versus the absorbed pump power, yielding a maximum value of 12 mW with a slope efficiency of 11.2%, the output power shows no signs of saturation. The laser wavelength is centered at 2052 nm, which is 32 nm longer than the emission peak in the bulk glass.

Fig. 6 Laser output power as a function of the absorbed pump power. Inset: laser spectrum of a 5-cm-long Nd³⁺/Ho³⁺ co-doped tungsten tellurite fiber under excitation of the 795 nm LD.

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Table 3 summarizes the active fiber length, pump and laser wavelengths, laser threshold, maximum laser output power, and slope efficiency of various RE ions doped tellurite fiber lasers. Compared with other RE ions doped tellurite glass fibers, laser output can be obtained from the 5 cm ultra-short Nd³⁺/Ho³⁺ co-doped fiber which confirms its high gain per unit length. Meanwhile, the laser threshold pump power is as low as 38 mW, which is around one order of magnitude lower than that of the Tm³⁺/Yb³⁺ doped tellurite fiber laser with similar pump scheme and fiber geometry [11]. The shortest fiber length and lower threshold pump power make this material a promising candidate for developing the ultra compact MIR laser sources.

Table 3. Summary of the active fiber length, pump and laser wavelengths, laser threshold, maximum laser output power, and slope efficiency of various RE ions doped tellurite fiber lasers.

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The output power and slope efficiency are limited by several factors. As shown in Fig. 1, three intense fluorescence peaks around 905 nm, 1064 nm, and 1339 nm were observed due to Nd³⁺: ⁴F_3/2 → ⁴I_9/2, ⁴F_3/2 → ⁴I_11/2, and ⁴F_3/2 → ⁴I_13/2 transitions, respectively, and the near infrared (NIR) fluorescence spectra have been measured in our previous report [17]. However, among the three fluorescence peaks, the branching ratio for the 1064 nm transition is the largest [34], which restricts the energy transfer efficiency from Nd³⁺ to Ho³⁺ because the absorption peek of Ho³⁺ is nearby 900 nm. On the other hand, from Eq. (4), the energy transfer coefficient (C_D-A) from Nd³⁺ to Ho³⁺ is proportional to the emission cross section of the donor $σ_{e}^{D} (λ)$ and the absorption cross section of the acceptor $σ_{a}^{A} (λ)$ , but the absorption cross section of Ho³⁺ at 900 nm (in Fig. 2) is relatively low, which result in lower energy transfer coefficient. Meanwhile, the mismatch of NA between the pump LD and the as-drawn tellurite glass fiber, Fresnel reflection loss from the fiber end surface, and tiny placement skewing would result in pump power wastage and reducing the coupling efficiency when collimating and focusing the experiment system. Other possible reasons responsible for the limited output power and slope efficiency include the high absorption coefficient of OH^- and high fiber background loss in the present fiber etc.

To improve the energy transfer efficiency and laser output, RE ions, such as Yb³⁺, can be added into the present glass fiber through acting as an energy bridge ion for promoting the energy transfer efficiency from Nd³⁺ to Ho³⁺. Meanwhile, the coupling efficiency has to be improved by optimizing the match ratio of NA between the as-drawn tellurite glass fiber and the pump LD, improving the collimation and focus degree of the experiment system. More efforts are needed to further reduce the fiber background loss. Additionally, different fiber length and reflectivities of the dichroic mirrors will be chosen in the laser experiment, a pair of fiber Bragg gratings instead of the dichroic mirrors will be adopted to form the optical cavity. We believe significant improvements can be achieved by optimizing these factors in our further research.

4. Conclusion

In summary, we have demonstrated the laser emission at ~2.0 μm from a new-type of 5-cm-long Nd³⁺/Ho³⁺ co-doped multimode tungsten tellurite glass fiber by one-end pumped with a 795 nm LD. The laser wavelength is centered at 2052 nm with a maximum output power of 12 mW and a slope efficiency of 11.2%. The laser threshold (38 mW) is around one order of magnitude lower than that of a Tm³⁺/Yb³⁺ co-doped tellurite fiber lasers with similar pump scheme and fiber geometry. The shortest fiber length and the lower threshold pump power allow simple pumping with a single laser diode. Our results give a deeper understanding of the interactions involving RE ions, and more importantly, offer a promising candidate material and scheme design for the development of ultra-compact and efficient MIR ~2.0 μm fiber laser which has shown extensive applications in remote sensing, medicine, and lidar, etc.

Acknowledgments

This work is financially supported by the National Natural Science Foundation of China (NSFC) (Grant Nos. 51125005, 51472088 and 51302086), and the Fundamental Research Funds for the Central Universities, SCUT.

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Physical meaning	Symbol	Value	Unit
J-O intensity parameters	Ω₂	6.02	10⁻²⁰ cm²
	Ω₄	3.77	10⁻²⁰ cm²
	Ω₆	1.24	10⁻²⁰ cm²
Quality factor	χ	3.04	–

Physical meaning	Symbol	Value	Unit
Nd³⁺ concentration	N_Nd³⁺	1.91	10²⁰ ions/cm³
Ho³⁺ concentration	N_Ho³⁺	1.91	10²⁰ ions/cm³
Refractive index	n	2.13	–
Transition temperature	T_g	453	°C
Initial crystallization temperature	T_x	575
Hurber parameter	ΔT	122
OH^- absorption coefficient	α_OH^-	0.73	cm^–1
Energy transfer coefficient	C_D-A	3.8	10⁻⁴⁰ cm⁶·s^–1
Energy transfer efficiency from Nd³⁺ to Ho³⁺	η	36.4	%
Absorption cross-section at 795 nm of Nd³⁺	σ_a(λ_p)	2.64	10⁻²⁰ cm²
Absorption cross-section at 2052 nm of Ho³⁺	σ_a(λ_s)	2.17	10⁻²¹ cm²
Emission cross-section at 2052 nm of Ho³⁺	σ_e(λ_s)	5.66	10⁻²¹ cm²
Radiative lifetimes of Ho³⁺	τ_r	5.49	ms
Measured lifetimes of Ho³⁺	τ_m	2.99	ms
Figure of merit	σ_e × τ_m	4.08	10⁻²¹ cm²·ms

Tellurite fiber	Fiber length (cm)	Pump wavelength (nm)	Laser wavelength (nm)	Laser threshold (mW)	Maximum output power(mW)	Slope Efficiency	Reference
Nd³⁺ doped	60	818	1061	27	5	23%	[32]
Tm³⁺ doped	32	1570–1610	1880–1990	153	280	20%	[33]
Tm³⁺/Ho³⁺ co-doped	76	1600	2100	100	26	62%	[16]
Tm³⁺ /Yb³⁺ co-doped	9	1088	1910–1994	394	67	8%	[9]
Yb³⁺/Tm³⁺/Ho³⁺ triply-doped	17	1100	2100	15	60	25%	[13]
Nd³⁺/Ho³⁺ co-doped	5	795	2052	38	12	11.2%	This work

Physical meaning	Symbol	Value	Unit
J-O intensity parameters	Ω₂	6.02	10⁻²⁰ cm²
	Ω₄	3.77	10⁻²⁰ cm²
	Ω₆	1.24	10⁻²⁰ cm²
Quality factor	χ	3.04	–

Physical meaning	Symbol	Value	Unit
Nd³⁺ concentration	N_Nd³⁺	1.91	10²⁰ ions/cm³
Ho³⁺ concentration	N_Ho³⁺	1.91	10²⁰ ions/cm³
Refractive index	n	2.13	–
Transition temperature	T_g	453	°C
Initial crystallization temperature	T_x	575
Hurber parameter	ΔT	122
OH^- absorption coefficient	α_OH^-	0.73	cm^–1
Energy transfer coefficient	C_D-A	3.8	10⁻⁴⁰ cm⁶·s^–1
Energy transfer efficiency from Nd³⁺ to Ho³⁺	η	36.4	%
Absorption cross-section at 795 nm of Nd³⁺	σ_a(λ_p)	2.64	10⁻²⁰ cm²
Absorption cross-section at 2052 nm of Ho³⁺	σ_a(λ_s)	2.17	10⁻²¹ cm²
Emission cross-section at 2052 nm of Ho³⁺	σ_e(λ_s)	5.66	10⁻²¹ cm²
Radiative lifetimes of Ho³⁺	τ_r	5.49	ms
Measured lifetimes of Ho³⁺	τ_m	2.99	ms
Figure of merit	σ_e × τ_m	4.08	10⁻²¹ cm²·ms

2.0 μm Nd³⁺/Ho³⁺-doped tungsten tellurite fiber laser

Abstract

1. Introduction

2. Experimental

3. Results and discussions

3.1 Spectroscopic characterization

3.2 Basic parameters

3.3 Fiber performance

3.4 Fiber laser

4. Conclusion

Acknowledgments

References and links

Cited By

Figures (6)

Tables (3)

Equations (6)

Optical Materials Express