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Abstract
We investigate the power scaling and thermal management of multi-point side-pumped 2.825 µm heavily-erbium-doped fluoride fiber lasers by numerical simulation. The 4-point (or 6-point) erbium-doped fluoride fiber laser with polished erbium-doped fluoride fiber-based side-pump couplers delivers an output laser power of over 100 W at each launched 981 nm pump power of 100 W (or 75 W). Meanwhile, the core temperature increases of the gain fiber tips are below 1 K, making it possible for a highly reflective fiber Bragg grating to work stably in high-power operation. Once the preparation processes of these erbium-doped fluoride fiber-based side-pump couplers and endcaps with effective coatings are mature, the proposed multi-point side-pumped erbium-doped fluoride fiber lasers with some feasibility may theoretically pave the way for the development of hundred-watt mid-infrared fiber lasers with effective thermal management.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Mid-infrared fiber lasers primarily operating at 2.8–5 µm have attracted considerable attention owing to their extensive potential applications in laser surgery, defense and security, bio-diagnostics, and gas sensing, to name a few [1–7]. They have been obtained using three approaches: Raman fiber lasers, fiber gas lasers, and rare-earth-ion-doped fiber lasers. However, Raman fiber lasers need low-loss soft-glass fibers such as chalcogenide fibers [6] and high-power mid-infrared pumps [8]. Fiber gas lasers need hollow-core fibers and involve complex and time-consuming preparation processes [9]. Rare-earth-ion-doped fiber lasers have drawn much attention in recent years. Dysprosium (Dy3+), holmium (Ho3+), erbium (Er3+), and terbium (Tb3+)-doped fibers have successfully been utilized to develop 2.7–3.9 µm and 5.1–5.4 µm fiber lasers [10–13]. Among these fiber lasers, Er3+-doped ones can easily generate high-power 2.8 µm laser through the 4I11∕2 → 4I13∕2 transition.
In the past three decades, several technical efforts including pumping at visible or near-infrared wavelengths [14–19], co-doping [20], cascaded lasing [21], and heavily-Er3+-doping [12], have been investigated to obtain 2.8 µm laser. Encouragingly, heavily-Er3+-doped fluoride fiber lasers end-pumped at 9xx nm (965–985 nm) can generate tens watts of laser [12,17,22–26]. High-power 976 nm end-pump schemes cause strong pump excited state absorption (ESA), negatively affecting on power scaling. Er3+-doped fluoride fiber tips suffer from severe heat load, which is mainly caused by the multiphonon relaxation (MPR) [27]. High temperatures cause changing of particles’ Boltzmann distribution at Stark sub-levels, thus decreasing laser powers and efficiencies. Therefore, on the one hand, double-end 98x nm pump schemes are proposed to limit pump ESA. On the other hand, several efforts including liquid coolant [22], blowing nitrogen [26], fusion splicing between silica fibers and fluoride fibers [12], fiber Bragg gratings (FBGs) [28], are utilized for heat dissipation and improving the system stability. In recent years, it has been found that fiber tip destruction occurs in high-power 2.8 µm Er3+-doped fluoride fiber lasers due to OH diffusion [29]. Endcaps [12] and coating film [30] are usually utilized to slow down OH diffusion. Combined with these technologies, Y. O. Aydin et al. [12] demonstrated a 980 nm bidirectional pumped continuous-wave (CW) 2.8 µm 7 mol. % Er3+-doped ZrF4-BaF2-LaF3-AlF3-NaF (ZBLAN) fiber laser with an output power of 41.6 W. However, the emission was still limited since that the thermal effect caused the instability of highly reflective FBG (HR-FBG). There are no other works in which laser powers are higher than 41.6 W in the past four years. This is primarily because high-power end-pump schemes lead to severe heat load near fiber ends, which further causes a shift of working wavelength of HR-FBG and a less cavity feedback. Effective thermal management technologies for high-power 2.8 µm fluoride fiber lasers are urgently needed.
Side-pump devices enable pump light to be coupled into gain fibers by sides instead of fiber ends, thus few pump light transmits through fiber tips. The heat load in the fiber tips is accordingly low. Side-pump devices have been investigated to improve thermal management of ytterbium-doped silica fiber lasers [31,32]. Besides, side-pump schemes have the advantage of multi-point pumping, which can decrease the power of each pump and enable uniform pump absorption. Multi-point side-pump schemes have been successfully utilized used in near-infrared fiber lasers [33]. A side-pump fluoride fiber coupler/combiner can overcome the heat load problem of Er3+-doped fluoride fiber tips. C. A. Schäfer et al. [34] demonstrated two polished Er3+-doped fluoride-fiber-based side-pump couplers for a 2.8 µm fiber laser with a power of 20 W and a slope efficiency of 18.1%. The device had a coupling efficiency of 83% and was driven with an incident pump power of up to 83.5 W. These indicate that the side-pump scheme for high-power fiber lasers is highly of efficiency and feasibility. S. Magnan-Saucier et al. [35] demonstrated a fuseless side-pump combiner where a tapered pump fiber wrapped on a double-clad Er3+-doped fluoride fiber for efficient pumping. The side-pump combiner was successfully operated during several hours at an incident power of 44 W. All in all, side-pump schemes show the immense potential. However, there are no works on multi-point side-pump schemes for mid-infrared fiber lasers to date. Therefore, the potential of power scaling and thermal management of multi-point side-pumped 2.8 µm Er3+-doped fluoride fiber laser should be investigated.
In this work, we present numerical modeling of multi-point side-pumped heavily-Er3+-doped fluoride fiber lasers with polished Er3+-doped fluoride-fiber-based side-pump couplers. Comparisons between double-end pumped and multi-point side-pumped 6 mol. % Er3+-doped fluoride fiber lasers are presented. The effects of fiber length, pump power, spacing and number of side-pump points, pump leakage rate, Er3+ concentration, and Boltzmann distributions on power scaling and core temperature increases of multi-point side-pumped heavily-Er3+-doped fluoride fiber lasers are investigated.
2. Numerical modeling
Figure 1(a), (b), and (c) respectively depict the double-end pump scheme, 4-point bidirectional side-pump scheme, and 6-point bidirectional side-pump scheme for 2.825 µm Er3+:ZBLAN fiber lasers. Figure 1(d) depicts the double-clad Er3+-doped fluoride fiber-based side-pump coupler [34]. The FBG1 and FBG2 are a HR-FBG with the reflectivity of Rs0 and a low-reflectivity FBG (LR-FBG) with the reflectivity of RsL, respectively. All FBGs are located at the tips of gain fibers. The AlF3-based endcaps with Si3N4 coatings are used to slow down OH diffusion [12,30]. The endcaps are cleaved with a 8° angle to reduce broadband feedback. Si3N4 coatings may be a solution. But it requires intensive research since long-term performance of such coatings at high power level is unknown.
Fig. 1. (a) Double-end pump scheme, (b) bidirectional 4-point side-pump scheme, (c) bidirectional 6-point side-pump scheme for high-power Er3+:ZBLAN fiber lasers, (d) double-clad Er3+-doped fluoride fiber-based side-pump coupler, and (e) energy level system for 2.8 µm heavily-Er3+-doped fluoride fiber laser.
Figure 1(e) shows the energy level scheme for 2.825 µm heavily-Er3+-doped ZBLAN fiber lasers [27]. The pump ground state absorption (GSA) process at ∼ 976 nm (or 981 nm) excites Er3+ from the ground state level 4I15/2 to the excited state level 4I11/2. The pump ESA process at ∼ 976 nm (or 981 nm) excites Er3+ from the 4I11/2 level to the 4F7/2 level. The laser transition between the 4I11/2 and 4I13/2 levels is potentially self-terminated because the lifetime of the lower laser level 4I13/2 is longer than that of the upper laser level 4I11/2. The energy transfer upconversion process from the 4I11/2 level (ETU2, 4I11/2, 4I11/2 → 4F7/2, 4I15/2) depopulates the 4I11/2 level, which increases the threshold pump power. The energy transfer upconversion process from the 4I13/2 level (ETU1, 4I13/2, 4I13/2 → 4I9/2, 4I15/2) works well in heavily-Er3+-doped fluoride fibers. In principle, it can efficiently depopulate the 4I13/2 level, thereby mitigating the population bottleneck. Er3+ are recycled to the 4I11/2 level by the MPR processes from the levels 4F7/2 to 4S3/2, 4S3/2 to 4F9/2, 4F9/2 to 4I9/2, and 4I9/2 to 4I11/2, which increases the quantum efficiency. The cross relaxation (CR) process is generated from the levels 4S3/2 to 4I9/2 and 4I15/2 to 4I13/2. Note that the strong green fluorescence generates in a 9xx nm pump scheme, which is usually not depicted in the energy level diagram [19].
According to the energy levels shown in Fig. 1(e), the rate equations for population densities Ni(z,t) along the fiber length (the z direction) are as follows:
For the side-pumped Er3+-doped fluoride fiber lasers in Fig. 1(b) and (c), $P_{launched}^ + (0 )$ and $P_{launched}^ - (L )$ are both zero. At the m-th (m = 1,2,3) forward side-pump point (z = zm), $P_{p\textrm{m}}^ + ({{z_m}} )$ and $P_{p\textrm{m}}^ - ({{z_m}} )$ denote forward and backward pump powers, respectively. At the n-th (n = 1,2,3) backward side-pump point (z = zn), $P_{pn}^ + ({{z_n}} )$ and $P_{pn}^ - ({{z_n}} )$ denote forward and backward pump powers, respectively. $P_{pm\_launched}^ + ({{z_m}} )$ and $P_{pn\_launched}^ - ({{z_n}} )$ denote the launched side-pump powers at the m-th (m = 1,2,3) forward side-pump point and n-th (n = 1,2,3) backward side-pump point. They are calculated by:
The output laser powers (Pout) of the end-pumped and side-pumped Er3+-doped fluoride fiber lasers are calculated by:
Only the steady-state model of CW laser is simulated, therefore, the time differential terms above are eliminated. The fiber length is discretized into uniform length elements, and the length of each discrete element is 0.01 m. The population density rate equations are solved with a routine suited to solving Stiff rate equations. Then, according to the solution obtained from the population density rate equations, the power propagation of pump light and laser are computed. All powers along the fiber length are calculated by using the fourth-order Runge-Kutta algorithm and the shooting method. Convergent results are ultimately obtained until the results meet the error condition.
Temperature distributions of Er3+-doped fluoride fiber lasers are analyzed in this modeling. The heat generation is relevant to the CR, ETU, and MPR processes. The core temperature excursion caused by each process (on the optical axis) can be given by the modified equation in Ref. [37]:
3. Results
3.1. Validation of parameters in end-pump systems and side-pump systems
To estimate the versatility and accuracy of the models of end-pumped and side-pumped Er3+-doped fluoride fiber lasers, numerical simulations are compared with published experimental reports [23,34]. The simulation parameters from published works are divided into four types: fiber parameters, pump light and laser parameters, spectroscopic parameters, and interionic parameters. The consistent spectroscopic parameters are listed in Table 1. The variable spectroscopic parameters, fiber parameters, and interionic parameters are listed in Table 2.
Table 1. Consistent Spectroscopic Parameters
Table 2. Variable Spectroscopic Parameters, Fiber Parameters and Interionic Parameters
Figure 2 shows the simulated and experimental results of the end-pumped Er3+-doped fluoride fiber laser in Ref. [23] and the 2-point side-pumped Er3+-doped fluoride fiber laser in Ref. [34]. It is seen that all laser powers from the simulations are in good agreement with the experimental data, which indicates that the two kinds of models are highly of versatility and accuracy. Therefore, it is feasible for the numerical models to be used to simulate high-power end-pumped and side-pumped Er3+-doped fluoride fiber lasers.
Fig. 2. Simulated powers and experimental powers in the Er3+-doped fluoride fiber lasers with (a) an end-pump scheme [23] and (b) a bidirectional 2-point side-pump scheme [34].
3.2. Results of the double-end pumped and the multi-point side-pumped fiber lasers
Considering the damage threshold (25 MW/cm2@2.8 µm) of fluoride fibers reported in Ref. [17], the core diameters of the gain fibers in the modeling should not be less than 23 µm for hundred-watt-level 2.825 µm laser. In this section, the specifications of the gain fibers used in the simulations are as follows: a core with a diameter of 25 µm, an NA of 0.12, and an ErF3 concentration of 6 mol. % (FiberLabs Inc., Japan) [22]. The D-shaped inner clad has a diameter of 350 µm and an NA of 0.51, while the outer polymer cladding diameter is 450 µm. The gain fibers have a damage threshold laser power of ∼ 122.72 W. The gain fibers are conductively cooled by placing them between aluminum plates that are maintained at a constant temperature of 20 °C by water cooling. Note that V is 3.36, which indicates that LP01 and LP11 modes can exist in the fiber. For simplicity, only the LP01 mode is considered in the simulations; the LP11 mode can be suppressed by bend-induced loss [27,41]. The consistent spectroscopic parameters are listed in Table 1. The variable spectroscopic parameters, fiber parameters, and interionic parameters are listed in Table 3.
Table 3. Variable spectroscopic, fiber, and interionic parameters used in the following simulations
3.2.1. Results of the double-end pumped fiber laser
Splicing fluoride fibers and silica fibers is critical for manufacturing high-power mid-infrared all-fiber laser modules. S. Cozic et al. [43] demonstrated splices between silica fibers and undoped fluoride fibers that withstand 220 W power at 976 nm without any damage and drastic temperature increase. However, researchers are unclear about the upper limit of the pump power that splices between silica fibers and Er3+-doped fluoride fibers can withstand. To limit the thermal load and prevent possible heat damage at the tip of the Er3+-doped fluoride fiber, the maximum launched pump power at each fiber end is limited to 200 W. For simplicity, the two pumps are simultaneously adjusted at the same rate to the same value.
A comparison between the laser powers of the double-end 981-nm-pumped 2.825 µm Er3+-doped fluoride fiber laser and 976-nm-pumped one as a function of the gain fiber length is presented in Fig. 3(a). The each launched pump power is 200 W. In the 976 nm pump scheme, the laser power is less than 100 W regardless of the fiber length. The maximum laser power is 78.66 W, and the corresponding optimum length is 13 m. It indicates that a 976 nm end-pump scheme is unsuitable for hundred-watt laser generation. In the 981 nm pump scheme, the output laser power is much higher than that in the 976 nm pump scheme under the same launched pump power. When the gain fiber length exceeds 11 m, the output laser power exceeds 100 W. The maximum laser power is 114.83 W, corresponding to an optimum fiber length of 15 m. Therefore, the 981 nm pump scheme is worth proposing. Hundred-watt 981 nm pumps are now commercially available. Figure 3(b) shows the output laser power as a function of the total launched pump power under the condition of the fiber length of 15 m. The laser slope efficiency (η) decreases from 32.8% to 23.2% with the increase of the total launched pump power. At the total launched pump power of 400 W, a maximum output laser power of 114.83 W is obtained.
Fig. 3. (a) Laser power of the 25-µm-core 6 mol. % Er3+-doped fluoride fiber laser with double-end 976 nm and 981 nm pump schemes as a function of the gain fiber length; (b) laser power of the double-end 981-nm-pumped 15 m-long Er3+-doped fluoride fiber laser as a function of total launched pump power; (c) distributions of the fiber core temperature increases of the double-end 981-nm-pumped Er3+-doped fluoride fiber laser along the fiber length.
The distributions of the fiber core temperature increases compared to the ambient temperature in the double-end 981 nm pump scheme, are showed in Fig. 3(c). The fiber length is 15 m. The core temperature increases in the fiber tips are always higher than those of the other parts of gain fiber, and the core temperature increases along the fiber length are highly symmetric. As each launched pump power is increased from 25 W to 200 W, the core temperature increase at the center of the gain fiber increases from 0.2 K to ∼ 43 K, and the core temperature increase in the left fiber end increases from ∼ 31 K to ∼ 123 K. In our calculation, the core temperature increase is ∼ 87 K at each launched pump power of 110 W, and the corresponding core temperature is ∼ 107 °C. It can be comparable to that in Ref. [12]. The authors claimed that the temperature of the gain fiber’s polymer surface reached a maximum value of about 80 °C at the maximum heat load (i.e., at 110 W of forward launched pump power) between the fusion splice and the HR-FBG. The corresponding core temperature of the gain fiber was estimated to be ∼ 110 °C. In the simulation, the core temperatures in the fiber ends are as high as 143 °C (the corresponding core temperature increase is 123 K) at each launched pump power of 200 W. It will cause fiber expansion and shift of working wavelength of the HR-FBG located at the fiber tip, and further result in laser operation failure.
3.2.2. Results of the multi-point side-pumped fiber laser
Considering that the upper limit of withstanding 981 nm pump power of the Er3+-doped fluoride fiber side-pump couplers is unknown, the withstanding pump power is set to be 100 W in view of feasibility. The pump leakage rates at the side-pump points are all set to be 17% [34]. For simplicity, all side pumps are simultaneously adjusted at the same rate to the same value.
Firstly, the Er3+-doped fluoride fiber laser with a 4-point side-pump scheme is investigated. Two forward and two backward pumps are distributed on the left and right parts of the gain fiber, respectively. For simplicity, this pump scheme is called the “2:2” type, as shown in Fig. 1(b). The spacing of the co-directional side-pump points is 3 m, and the first and fourth coupling points are both 0.1 m away from the left end and right end (i. e. the output end) of the gain fiber, respectively. The output laser power as a function of the gain fiber length is showed in Fig. 4(a). Each launched pump power is 100 W. It is seen that the output laser power exceeds 100 W as the length is as long as 12 m. The maximum laser power is 115.86 W, corresponding to an optimum fiber length of 17 m. Note that the “2:2”-type 981 nm side-pump scheme can deliver a higher laser power than the double-end one.
Fig. 4. (a) Laser power of the 25-µm-core 6 mol. % Er3+-doped fluoride fiber laser with a “2:2”-type 981 nm side pump scheme as a function of the gain fiber length; (b) power distribution of the forward and backward pumps and laser in the condition of each launched pump power of 100 W; (c) laser power as a function of total launched pump power; (d) distributions of the fiber core temperature increases along the gain fiber length.
Figure 4(b) shows the power distributions of the forward & backward pump light and laser along the fiber length. In the conditions of a fiber length of 17 m and each launched pump power of 100 W, almost all pump light is absorbed and the stimulated radiation light is sufficiently amplified. Note that the pump powers in both fiber tips are very low. Figure 4(c) shows the output laser power as a function of the total launched pump power. The laser slope efficiency decreases from 32.5% to 24.5% with the increase of the total launched pump power. At the total launched pump power of 400 W, a maximum output laser power of 115.87 W is obtained.
Figure 4(d) shows the distributions of the fiber core temperature increases along the fiber length. The trend of the temperature increase distribution with a high degree of symmetry, is similar to that of the total launched pump power distribution showed in Fig. 4(b). The core temperature increase at the x-th (x = 1,2) side-pump point in the right hand of the gain fiber is almost the same as that at the y-th (y = 2,1) side-pump point in the left hand of the gain fiber. It is caused by the highly symmetrical distribution of Er3+ in the energy levels involving in ETU, CR, and MPR processes along the fiber length. It is worth noting that the core temperature increases at both fiber ends are below 1 K due to the fact that the pump power is very low in the fiber tips. This is of great benefit to the stability of the HR-FBG and the operation of the fiber laser under high-power pump conditions, which is a huge advantage of multi-point side-pump schemes. Thus, this kind of side-pump scheme is strongly proposed. As the each launched pump power is increased from 12.5 W to 100 W, the core temperature increase at the first (or second) side-pump point in the left hand of the gain fiber increases from 17 K (or 19 K) to 84 K (or 99 K). Note that the maximum core temperature increase is significantly lower than that (123 K) in a double-end 981 nm pump scheme. It indicates that the multi-point side-pump scheme has an advantage of lower temperatures, compared with the double-end pump scheme.
4. Discussion
In the following section, the effects of various parameters, including spacing of co-directional side-pump points, pump leakage rate, withstanding pump power, number of side pumps, Er3+ concentration, and variable Boltzmann factors on power scaling and core temperature increases are investigated. In addition, the proposed multi-point side-pumped Er3+-doped fluoride fiber lasers are compared with reported Er3+-doped fluoride fiber master oscillator power amplifiers (MOPA) and amplifiers.
4.1. Effects of the spacing of co-directional side-pump points, pump leakage rate, and withstanding pump power
Figure 5(a) shows the output laser power of the 25-µm-core 6 mol. % Er3+-doped fluoride fiber laser with the “2:2”-type 981 nm side-pump scheme as a function of the spacing of co-directional side-pump points. Each launched pump power is 100 W. The fiber length is 17 m and the pump leakage rate is 17%. As the spacing of the co-directional side-pump points is increased from 2 m to 4 m, the laser power increases from 113.75 W to 116.23 W. Further increasing the spacing to 5 m, the laser power decreases to 114.85 W. The system structure exhibits high flexibility. Figure 5(b) shows the output laser power as a function of the pump leakage rate. The fiber length is 17 m and the spacing of the co-directional side-pump points is 3 m. As the pump leakage rate is decreased from 17% to 5%, the output laser power increases from 115.86 W to 117.41 W at each launched side-pump power of 100 W. In the future, output laser powers will further be improved by improving the preparation process of Er3+-doped fluoride fiber side-pump couplers. In addition, the launched side-pump power can be further increased. The output laser powers are 123.09 W, 124.28 W, and 125.13 W, when each launched side-pump power is 110 W and the pump leakage rates are 17%, 10%, and 5%, respectively, as shown in Fig. 5(b).
Fig. 5. Laser power of the 17-m-long 25-µm-core 6 mol. % Er3+-doped fluoride fiber laser with the “2:2”-type 981 nm side-pump scheme as a function of (a) the spacing of co-directional side-pump points and (b) the pump leakage rate at each launched pump power of 100 W or 110 W.
4.2. Effect of number of side pumps
To further increase the output laser power, more side-pump couplers are considered. A 6-point 981 nm side-pump scheme where three forward and three backward pumps are respectively distributed on the left and right parts of the gain fiber is proposed. For simplicity, this 6-point side-pump scheme is called the “3:3” type, as shown in Fig. 1(c). The length of the 25-µm-core 6 mol. % gain fiber is 19 m. The spacing of the co-directional side-pump points is 3 m, and the first and sixth coupling points are both 0.1 m away from the left end and right end (i. e. the output end) of the gain fiber, respectively. The pump leakage rates are all set to be 17%. Figure 6(a) shows the output laser power as a function of the total launched pump power. The laser slope efficiency decreases from 31.7% to 22.2% with the increase of the total launched pump power. At the total launched pump power of 450 W, a maximum output laser power of 124.57 W is obtained. Figure 6(b) shows the distribution of the fiber core temperature increases along the fiber length in the “3:3”-type 981 nm side-pump scheme at the total launched pump power of 450 W (each launched side pump power is 75 W). It is worth noting that the core temperature increases at both fiber ends are below 1 K. The core temperature increases are 70 K and 82 K at the first and second side-pump points in the left hand of gain fiber, respectively. The core temperature increase at the third side-pump point in the left hand of the gain fiber is the highest, and the value is as high as 91 K, corresponding to the maximum pump power in the fiber. They are significantly lower than that (123 K) in a double-end 981 nm pump scheme, indicating that the “3:3”-type 981 nm side-pump scheme also has the advantage of lower temperatures. The core temperature increase at the x-th (x = 1,2,3) side-pump point in the right hand of gain fiber is almost the same as that at the y-th (y = 3,2,1) side-pump point in the left hand of gain fiber.
Fig. 6. (a) Laser power of the 19-m-long 25-µm-core 6 mol. % Er3+-doped fluoride fiber laser with the “3:3”-type 981 nm side-pump scheme as a function of the total launched pump power; (b) distribution of the fiber core temperature increase along the fiber length at each launched 981 nm pump power of 75 W.
The fiber laser with such a “3:3”-type side-pump scheme can deliver a higher laser power than that with the “2:2”-type side-pump scheme, whereas the former needs more side-pump couplers, which causes higher costs and make the system more complex. The “2:2”-type and “3:3”-type 981 nm side-pump schemes can both deliver hundred-watt-level laser, showing high flexibility of system structure.
4.3. Effect of Er3+ concentration
Given the cost and complexity of the system, it is necessary to reduce the number of side pump couplers and the length of the gain fiber. Therefore, the “2:2”-type 981 nm side-pump scheme is maintained. Additionally, increasing the Er3+ concentration and controlling the fiber core diameter are considered to achieve hundred-watt laser while reducing the required gain fiber length. The specifications of the gain fiber is set to be as follows: a core with a diameter of 23 µm, an NA of 0.12, and an ErF3 concentration of 7 mol. %. The length is optimized to 12 m. The circular, double truncated inner-cladding and coating layer diameters are 240 × 260 µm and 450 µm, respectively. Such an Er3+-doped fluoride fiber can be customized from FiberLabs or Le Verre Fluore. The fiber has a damage threshold laser power of ∼ 102.72 W. V is 3.0, which indicates that LP01 and LP11 modes can exist in the fiber. For simplicity, only the LP01 mode is considered; the LP11 mode can be suppressed by bend-induced loss. Other parameters are the same as the parameters showed in Table 1 and Table 2.
Figure 7(a) shows the output laser power as a function of the total launched pump power. As the total launched pump power is increased from 40 W to 150 W, the output laser power increases from 13.43 W to 55.24 W. The slope efficiency is 37.6%, higher than the Stokes efficiency limit (ηS=λp/λl = 34.7%), which is due to energy recycling [44]. The first experimental confirmation of energy recycling was presented in Ref. [23] where the slope efficiency decreased from 35.4% to 28.5% with the increase of the pump power. As the total launched pump power is increased to 320 W, the output laser power increases to 112.20 W with the slope efficiency of 32.4%. Such a high slope efficiency shows that a high Er3+ concentration exhibits a huge advantage in power scaling of multi-point side-pumped Er3+-doped fluoride fiber lasers. Figure 7(b) shows the distribution of the core temperature increases along the fiber length at each launched pump power of 80 W. It is worth noting that the core temperature increases at both fiber ends are below 1 K. The maximum core temperature increase at the second side-pump point is as high as 136 K, which is higher than that in the 6 mol. % Er3+-doped fluoride fiber laser with a double-end pump scheme or multi-point side-pump scheme. However, the advantage of low temperatures in the fiber tips still exists.
Fig. 7. (a) Laser power of the 12-m-long 23-µm-core 7 mol. % Er3+-doped fluoride fiber laser with the “2:2”-type 981 nm side-pump scheme as a function of the total launched pump power; (b) distribution of the fiber core temperature increase along the fiber length at each launched 981 nm pump power of 80 W.
4.4. Effect of variable Boltzmann factors
Considering the McCumber theory [45], the core temperature increase actually influences the cross-sections and Boltzmann distributions of the upper and lower energy levels of Er3+ [37]. Indeed, the temperature field and excited particles have different distribution along the fiber length and the core region, respectively. They are highly of complexity. b2 and b1 should be variable. Accurate, complex temperature and power feedback modeling are needed to make the temperature model and power model to be self-consistent. Therefore, no temperature feedback is conducted in the sections above.
Hereby, b2 and b1 from formula (25) are calculated and modified for the previous modeling. The laser powers of Er3+-doped fluoride fiber lasers with variable b2 and b1 are compared with those with constant b2 and b1 (b2 = 0.211, b1= 0.1148). For simplicity, variable b2 and b1 are considered to be same along the fiber length. Figure 8(a), (b), and (c) respectively show the output laser powers of the previous double-end 981-nm pumped, 4-point 981-nm side-pumped, and 6-point 981-nm side-pumped 6 mol. % Er3+-doped fluoride fiber lasers with the constant or variable b2 and b1 as a function of the total launched pump powers. Figure 8(d) shows the output laser power of the previous 4-point 981-nm side-pumped 7 mol. % Er3+-doped fluoride fiber laser with the constant or variable b2 and b1 as a function of the total launched pump power. It is seen that the output laser powers and corresponding slope efficiencies with variable b2 and b1 are all lower than those with constant b2 and b1, respectively. Increasing temperatures definitely reduces output laser powers, resulting in several watts of power difference. However, these do not affect our judgment of laser power trends. At the corresponding maximum launched pump powers of 400 W, 400 W, 450 W, and 320 W, the output laser powers of four fiber lasers with variable b2 and b1 are 102.32 W, 105.73 W, 114.15 W, and 101.64 W. Hundred-watt-level of laser can still be obtained. Note that the slope efficiency in Fig. 8(d) decreases from 34.8% to 27.7%, in good agreement with that in Ref. [23], as each launched pump power is increased from 10 W to 80 W. The fiber core temperature increases along the fiber length in the revised models all increase slightly. However, the results of the double-end pumped fiber laser are still out of practical significance because of the high core temperatures in the fiber tips. The impact of Boltzmann distributions on high-power Er3+-doped fluoride fiber lasers will further be explicitly addressed in the future.
Fig. 8. Laser powers of (a) the 15-m-long 25-µm-core 6 mol. % Er3+-doped fluoride fiber laser with the double-end 981 nm pump scheme, (b) the 17-m-long 25-µm-core 6 mol. % Er3+-doped fluoride fiber laser with the “2:2”-type 981 nm side-pump scheme, (c) the 19-m-long 25-µm-core 6 mol. % Er3+-doped fluoride fiber laser with the “3:3”-type 981 nm side-pump scheme, and (d) the 12-m-long 23-µm-core 7 mol. % Er3+-doped fluoride fiber laser with the “2:2”-type 981 nm side-pump scheme, and the constant or variable b2 and b1, as a function of the total launched pump powers.
4.5. Comparisons between multi-point side-pumped Er3+-doped fluoride fiber lasers and fiber amplifiers
H. Uehara et al. [46] demonstrated a 33-W Er3+-doped fluoride fiber MOPA using two Er3+-doped fluoride fiber side-pump couplers. A 100-W-level output is expected from a 9-m-long 6 mol. % Er3+-doped fluoride fiber amplifier with six combiners (550–600 W 976 nm pumping) in theory. By Comparison, the proposed “2:2”-type and “3:3”-type 981 nm side-pumped Er3+-doped fluoride fiber lasers have the advantage of delivering a higher output laser power at a lower total pump power. In our previous work [47], a 2.8 µm and 1.6 µm cascaded heavily-Er3+-doped fluoride fiber amplifier theoretically achieves a 2.8 µm laser power of ∼ 100 W when the powers of the 2.8 µm, 1.61 µm seed lasers and the total pump light are 5 W, 20 W, and 300 W, respectively. However, there are some drawbacks. The core temperatures of the fluoride fiber ends are as high as 373 K (100 °C). Besides, the 1.61 µm laser source is expensive and such a fiber amplifier with dual-seed lasers results in a more complex system. In addition, the fiber amplifier is spatially structured for lack of a mid-infrared fiber-based isolator. By comparison, the proposed multi-point side-pumped Er3+-doped all-fiber lasers exhibit much lower temperatures in fiber tips and higher compactness. However, the system complexity of the multi-point side-pumped fluoride fiber laser should be considered. The fragility of these fluoride fibers makes it challenging to fabricate multiple side-pump coupler/combiners along a long fiber segment without causing damage.
5. Conclusion
Numerical models and comparisons of double-end pumped and multi-point side-pumped 2.8 µm heavily-Er3+-doped fluoride fiber lasers are presented. At each launched pump power of 200 W, the double-end 981-nm-pumped 6 mol. % Er3+-doped fluoride fiber laser delivers an output laser power of over 100 W, while the core temperature increases in the fiber tips are as high as 123 K, easily resulting in the laser failure. By comparison, the 4-point (or 6-point) bidirectional side-pumped 6 mol. % Er3+-doped fluoride fiber laser delivers a higher output laser power with a slope efficiency of over 20% (or 18%) when each launched 981 nm pump power is 100 W (or 75 W). More importantly, the core temperature increases of the fiber tips are below 1 K, making it possible for a high highly reflective fiber Bragg grating to work stably. When each launched 981 nm pump power is 80 W, the 7 mol. % Er3+-doped fluoride fiber laser with the 4-point side-pump scheme also delivers an output laser power of over 100 W with a slope efficiency of over 27%. These results indicate that the multi-point side-pump schemes with high feasibility have the advantages of high flexibility of system structure, improving the laser power, and decreasing the temperatures of Er3+-doped fluoride fiber tips. This investigation gives a preliminary insight into power scaling and thermal management of multi-point side-pumped 2.8 µm Er3+-doped fluoride fiber lasers.
Funding
National Natural Science Foundation of China (61935006, 62005312, 62090065); Natural Science Foundation of Shaanxi Province (2023-JC-JQ-31); China Postdoctoral Science Foundation (2021M700994); the Open Research Fund for development of high-end scientific instruments and core components of the Center for Shared Technologies and Facilities,Xi'an Institute of Optics and Precision Machinery, Chinese Academy of Sciences.
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Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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