3.6 W compact all-fiber Pr 3+ -doped green laser at 521 nm

. Green semiconductor lasers are still undeveloped, so high-power green lasers have heavily relied on nonlinear frequency conversion of near-infrared lasers, precluding compact and low-cost green laser systems. Here, we report the first Watt-level all-fiber CW Pr 3 þ -doped laser operating directly in the green spectral region, addressing the aforementioned difficulties. The compact all-fiber laser consists of a double-clad Pr 3 þ -doped fluoride fiber, two homemade fiber dichroic mirrors at visible wavelengths, and a 443-nm fiber-pigtailed pump source. Benefitting from > 10 MW ∕ cm 2 high damage intensity of our designed fiber dielectric mirror, the green laser can stably deliver 3.62-W of continuous-wave power at ∼ 521 nm with a slope efficiency of 20.9%. To the best of our knowledge, this is the largest output power directly from green fiber lasers, which is one order higher than previously reported. Moreover, these green all-fiber laser designs are optimized by using experiments and numerical simulations. Numerical results are in excellent agreement with our experimental results and show that the optimal gain fiber length, output mirror reflectivity, and doping level should be considered to obtain higher power and efficiency. This work may pave a path toward compact high-power green all-fiber lasers for applications in biomedicine, laser display, underwater detection, and spectroscopy.


Introduction
Green lasers are of great interest in biomedicine, laser display, spectroscopy, underwater optical communications, and scientific research. 1 In contrast to the well-developed red or blue laser diodes (LDs), LDs emitting directly in the green region are still under development and hence the "green gap" exists. 2 Currently, the leading technology for producing high-power continuouswave (CW) green lasers is still the nonlinear frequency conversion (e.g., frequency doubling) of near-infrared solid-state or fiber laser systems, 3,4 and the compactness, stabilization, and expenditure are still challenges. As a result, researchers are always looking for an alternate green-light laser solution that has the benefits of great brightness, compactness, and costeffectiveness. Due to intrinsic advantages, such as good beam quality, small footprint, user-friendliness, and low-to no-maintenance, green fiber lasers doped with trivalent rare-earthions (e.g., Pr 3þ , 5 Ho 3þ , 6 Er 3þ7 ) can satisfy these demands and bridge the "green gap," so there is a huge drive to develop compact high-power rare-earth-doped fiber lasers in the green spectral region.
Given recent advances in both rare-earth-doped fluoride fibers and blue GaN LD, frequency down conversion fiber lasers using trivalent rare-earth-doped fluoride fibers have emerged as a promising approach to directly generate visible-light emission, and much related work has been carried out and reported. [8][9][10][11][12][13][14] Among them, Pr 3þ -doped fluoride fiber laser is particularly appealing for visible lasers because it has a reasonably simple 4f-energy level scheme and exhibits a variety of transitions in the blue, green, orange, and red spectral regions. 8 At present, based on double-clad (DC) Pr 3þ -doped fluoride fiber, the high-power red fiber laser operating at 635.5 nm with a maximum output power of 2.3 W has been achieved. 13 However, the green Pr 3þ -doped fiber laser remains rather challenging due to the relatively modest optical gain in the green region, and only a few instances of progress have been reported. [15][16][17] Okamoto et al. demonstrated in 2011 an all-fiber laser operating at 521 nm with a maximum power of 322 mW through the splicing of a Pr 3þdoped fluoride fiber to a silica fiber pigtail mirror. 15 Meanwhile, Nakanishi et al. announced a Pr 3þ -doped fluoroaluminate single-clad fiber laser delivering 598 mW at 522.2 nm pumped by two space-coupling GaN LDs. 16 In the latter scenario, further utilizing the pulsed pumping, a quasi-CW laser generated a pulse peak power of 1.53 W at 522.2 nm with a slope efficiency of 33.8%. 17 However, up to now, the reported green fiber lasers have not reached Watt-level power output in the CW regime. What is more, all of the high-power green fiber lasers reported previously had used some free-space bulk components in those cavities, which sacrifices the all-fiber structure and undermines the reliability and robustness of the fiber lasers. Therefore, the development of a compact all-fiber green laser with high output power is highly anticipated.
Herein, we designed and experimentally demonstrated a compact high-power all-fiber CW Pr 3þ -doped green laser for the first time to our knowledge. To begin, an efficient buttcoupled all-fiber structure capable of high-power operation was constructed using a DC Pr 3þ -doped fluoride fiber treated by the cutting process and fiber dichroic mirrors (FDMs) with a high damage intensity. Following that, to achieve highefficiency emission and high-power output, we explored the effects of gain fiber length and output mirror reflectivity on green laser power scaling via experiments and numerical simulations. Finally, according to the optimization results, we designed and further presented an experimental study on the compact high-power green all-fiber laser, which comprises a 2.1-m DC Pr 3þ -doped fluoride fiber, two FDMs at visible wavelengths, and a 443-nm fiber-pigtailed pump source. The laser can directly generate a 3616-mW green laser output with a central wavelength of ∼521 nm and a slope efficiency of 18.8%.

Spectroscopy of DC Pr 3þ -Doped Fluoride Fiber
First, we briefly discuss the spectroscopic properties of DC Pr 3þ -doped fluoride fiber. The fiber is manufactured by Le Verre Fluoré and has the following features: a Pr 3þ doping concentration of 8000 ppm, a 7.5-μm core diameter, a 0.08numerical aperture (NA) of fiber core, 115∕125-μm inner cladding (double D-shaped), and 180-μm outer cladding diameter, respectively. The core cutoff wavelength of this gain fiber is 780 nm, and its V-parameter (normalized frequency) at 521 nm is about 3.6. We first measured the fiber attenuation spectrum (including doping absorption in the core and propagation loss in the inner cladding) at room temperature by a tungsten halogen lamp and a 350-to 1750-nm optical spectrum analyzer (OSA, AQ6315B, Ando), as shown in the inset of Fig. 1(a). The propagation loss spectrum is then estimated by fitting the data at different wavelengths (i.e., 1.10 dB/m at 543 nm, 0.88 dB/m at 650 nm, and 0.74 dB/m at 793 nm) [see the blue curve in the inset of Fig. 1(a)]. Finally, the ground state absorption of DC Pr 3þ -doped fiber is obtained by deducting the propagation loss spectrum from the attenuation spectrum, as shown in Fig. 1 where αðλÞ and ΓðλÞ are the absorption coefficient and power filling factor of the gain fiber, respectively. N represents the doping concentration of rare-earth ions in the gain fiber. For 8000 ppm DC Pr 3þ -doped fluoride fiber, it has a value of 1.55 × 10 26 m −3 . In addition, a and ω 0 are the core radius and mode field radius of the gain fiber, respectively. According to Eqs. (1) and (2), the absorption cross sections of DC Pr 3þdoped fluoride fiber are calculated as shown in Fig. 1(b). Note that the absorption cross sections at 441 and 443 nm are 1.01 × 10 −24 m 2 and 0.84 × 10 −24 m 2 , respectively. The simplified energy level scheme of Pr 3þ for visible fluorescence emission is shown in Fig. 1(c). The frequency down conversion fluorescence emission in the green spectral region is known to emanate from the 3 P 1 þ 1 I 6 levels. The excitation process is as follows: (1) 3 P 2 level is excited by ground state absorption of the 3 H 4 level with the ∼443 nm pump, (2) nonradiative relaxation from 3 P 2 to 3 P 1 þ 1 I 6 , and (3) radiative transition from 3 P 1 þ 1 I 6 to 3 H 5 , which can generate fluorescence emission at ∼521 and ∼536 nm. 20 Figure 1(d) shows the fluorescence emission spectrum of the 0.6-m DC Pr 3þ -doped fluoride fiber excited by a 443-nm laser. The stimulated emission spectrum displays the emission lines in the deep red (∼717 nm), red (∼635 nm), orange (∼603 nm), green (∼521 nm), and blue (∼480 nm) spectral regions, implying the potential of these different visible-wavelength fiber lasers. In addition, the emission cross sections are computed using the Füchtbauer-Ladenburg (F-L) theory, which is expressed as 21,22 σ e ðλÞ ¼ 1 8π where λ, β, n, c, and τ are the center wavelength, fluorescence branching ratio from 3 P 1 to 3 H 5 transition, core refractive index of the gain fiber, light speed, and radiative lifetime of upper laser energy level, respectively. I(λ) denotes the intensity of the emission spectrum. The stimulated emission cross section for 521 nm ( 3 P 1 → 3 H 5 ) can be calculated as 0.32 × 10 −24 m 2 .

Experimental Setup
To construct an effective butt-coupled all-fiber structure capable of high-power operation in our experiment, we must first prepare the high-performance FC/PC fiber connectors at both ends of DC Pr 3þ -doped fluoride fiber. At present, due to fragile mechanical properties of fluoride fiber, it is inevitable that the fiber end-facet will be damaged to some extent by the traditional polishing processing [see Fig. 2(a)], which leads to the lower damage intensity of the fiber end-facet and blocks high-power operation. Therefore, to enable visible high-power laser operation, a new reliable processing technology for fluoride fiber end-facet nondestructive processing must be developed. Continuous experiments have revealed that fluoride fiber cutting technology based on a commercial fiber cleaver (CT104+, Fujikura) combined with the fabrication technology of a standard FC/PC fiber connector can effectively solve the aforementioned issues. First, the fiber cleaver is used to cleave the fluoride fiber to obtain the fiber end-facet with high smoothness. The fiber is then inserted into the ceramic core with an inner diameter of 180 μm until it is parallel to the end-facet of the ceramic core. Finally, a small amount of UV-curing adhesive is added to the end of the ceramic core for curing, and the DC Pr 3þ -doped fluoride fiber connector with high smoothness is successfully prepared, as shown in Fig. 2(b). The above process skillfully applies the fiber cutting technology to fabricate the high-quality fluoride fiber connector and ensures the construction of an effective all-fiber structure capable of high-power operation. Furthermore, to obtain high-performance FDMs at visible wavelengths, heat-resistant epoxy resin combined with grinding and polishing technology is first utilized to produce fiber end-facets with high stability and smoothness. The main processes are as follows: (1) producing the silica fiber connector by using the ceramic core and heat-resistant epoxy resin; (2) solidifying the fiber connector at high temperature; and (3) grinding and polishing the end-facet of the solidified fiber connector by a commercial polishing machine. The FDMs at visible wavelengths with high laser damage intensity (> 10 MW∕cm 2 ) are then successfully prepared using an ion beam-assisted deposition system and a specific electric field manipulation of film layers, which is also one of the key factors for achieving high-power green all-fiber lasers.
After finishing the processing of the fluoride fiber connector and the preparation of FDMs with high damage intensity, we designed the all-fiber Pr 3þ -doped green laser. The schematic of green laser is shown in Fig. 3(a), and Fig. 3(b) shows the corresponding photograph. This laser consists of a DC Pr 3þdoped fluoride fiber, two FDMs, and a 443-nm pump source. The pump can deliver 20-W pump power at 443 nm through a standard multimode 105∕125-μm (0.22 NA) silica fiber pigtail. Two ceramic sleeves with a 2.5-mm inner diameter are used to realize the low-loss all-fiber coupling between the DC Pr 3þdoped fluoride fiber and the visible FDMs. The compact fiber linear cavity for green-light oscillation is constructed by two homemade FDMs (M 1 , M 2 ). The FDM was fabricated by directly coating the dielectric films onto the end-facet of standard multimode silica fiber. The reflectivity of M 1 is as high as 99.7% at 521 nm, and it has a high transmittance of 95.4% at 443 nm [see Fig. 3(c)]. The reflectivity of M 2−1 and M 2−2 is 74.9% and 87.2% at 521 nm, respectively, and both have a high reflectivity of >95% at 443 nm [see Fig. 3(c)], which ensures the sufficient utilization of the residual pump laser. All FDMs are designed to have a >90% high transmittance at 635 nm to suppress red laser emission. The propagation loss of the pump laser through the DC Pr 3þ -doped fluoride fiber is measured to be 1.45 dB/m [see the inset of Fig. 1(a)], whereas the loss of the core is estimated to be ∼0.4 dB∕m at 521 nm. 10 In addition, the green laser was measured by the OSA (AQ-6315E, Ando), and the output power was recorded by a 350-to 1100-nm optical power meter (S425C-L, Thorlabs, Inc.).

High-Power All-Fiber Green Laser
According to the optimization results, a ∼2.1-m DC Pr 3þ -doped fluoride fiber and M 2−2 were employed for the high-power allfiber green laser experiment. Figure 4 exemplifies the output characteristics of the green laser. The threshold of the CW green laser is about 1030 mW. Figure 4(a) shows the green output power at different pump powers. With the increase of pump power, the output power increases linearly without saturation, and the slope efficiency is 18.8%. Accordingly, a maximum output power of 3616 mW was attained pumped at 20.01 W. The wide range of the output spectrum at 5.71 W pump power is shown in Fig. 4(b). Note that the central wavelength of the spectrum is 521.2 nm, and the intensity of the green laser is >24 dB higher than that of the residual pump laser, indicating that > 99% of the output laser is green laser. The spectra of the green laser under different pump powers are given in Fig. 4(c). With the increase of pump power, the center wavelength of the green laser shows a slight redshift, and the 3-dB spectral bandwidth also expands. Under strong pumping, the green laser oscillates at multiple wavelengths and has a wide spectral bandwidth due to the design of a high Q cavity in a wide reflective waveband [see Fig. 4(c)]. As shown in Fig. 4(d), to evaluate the operation stability of the all-fiber green laser, we monitored the power curve of the green laser operating at 3.0 W for over 60 min. The intensity fluctuation is <1.0%, showing the excellent long-term stability of the laser operation. In addition, the laser intensity distribution and M 2 factors of the generated green fiber laser beam were measured by a beam quality analyzer (WinCamD-UCD12, DataRay), and the measurement results are shown in the inset of Fig. 4(d). The measured M 2 parameters are 4.99 and 4.25, respectively, indicating that the green fiber laser is multitransverse mode operation.

Output Characteristics of All-Fiber Green Lasers with Different Designs
The output characteristics of the all-fiber green lasers with different designs were investigated experimentally, as shown in Fig. 5. Figure 5(a) shows the green laser power versus the pump power with the different gain fiber lengths (L) and the laser reflectivity (R 2 ) of M 2 . For the R 2 reflectivity of 74.9%, varying the gain fiber from 4 to 1.9 m, both the green output power and slope efficiency increase from 536 to 830 mW pumped at 5.07 W and from 13.0% to 20.9%, respectively. When L ¼ 1.9 m, with R 2 decreasing from 87.2% to 74.9%, both the green output power and slope efficiency increase from 801 to 1344 mW pumped at 7.63 W and from 11.9% to 20.9%, respectively.  designs, the output performance of the all-fiber green laser with ∼2.0-m DC Pr 3þ -doped fiber and ∼25% output coupling is superior.

Numerical Analysis
To better understand and further optimize the performance of the all-fiber Pr 3þ -doped green laser, numerical simulations of this laser were carried out. The laser transition process of ∼521 nm in Pr 3þ is a typical four-level system, which can be simulated using the numerical model of the strongly pumped quasi-four-level laser system, as shown in Fig. 6. This model focuses on the correlation transitions among the four energy levels of Pr 3þ [i.e., 3 H 4 (N 0 ), 3 P 0 (N 3 ), 3 P 1 (N 2 ), and 3 H 5 (N 1 )]. In this case, the steady-state rate equations and power transmission equations can be expressed as follows: 23-25 where P þ p ðzÞ [P − p ðzÞ] and P þ s ðzÞ [P − s ðzÞ] are the pump and signal laser powers propagating along the positive (negative) z directions, respectively. v p and v s are the pump and signal frequency. σ ap (σ as ) and σ ep (σ es ) represent the absorption and emission cross sections of the pump (signal) laser, respectively. α p and α s are the loss coefficients of the pump and signal laser. Γ p and Γ s are the power filling factors of the pump and signal laser. A c is the cross sectional area of the fiber core. The boundary conditions of the end-pumped fiber laser can be written as follows: where P l p and P r p are the pump power injected into the gain fiber from the positive (negative) z directions. R 1p (R 1 ) and R 2p (R 2 ) represent the pump (signal) laser reflectivity of the front and back cavity mirrors, respectively. Some of the parameters used in our simulation are calculated based on the measurements of the DC Pr 3þ -doped fluoride fiber (see Fig. 1), and some are obtained from the literature. 10,20 The specific parameters are summarized in Table 1. After obtaining the simulation parameters, the shooting method and bvp4c function are used to solve Eqs. (4)-(10). The numerical results are shown in Figs. 7 and 8.
As visualized in Fig. 7(a), for a fixed input pump power, the laser output power first increases and then falls as the gain fiber length increases. The figure also reveals that with the decrease of R 2 , the L of gain fiber realizing the maximum output power becomes longer. Figure 7(b) shows the laser threshold and slope efficiency of the green fiber laser versus the L under R 2 ¼ 75%, R 2p ¼ 95%. A maximum slope efficiency is 23.3% at L ¼ 1 m, yielding a laser threshold of 0.84 W. For the designed laser (R 2 ¼ 75%, R 2p ¼ 95%), although there exists an optimum fiber length (∼1 m), sufficient pump absorption should be considered to ensure that the remaining reverse pump laser does not affect the pump source, and the ∼2-m gain fiber is thus  show the laser output power, slope efficiency, and threshold versus the R 2 under L ¼ 2 m, R 2p ¼ 95%. It can be seen the output power first increases and then decreases with the reducing of R 2 under a fixed pump power. As the pump increases, the laser reflectivity R 2 for maximum power output decreases [see the dotted arrow in Fig. 7(c)]. As shown in Fig. 7(d), with the increase of R 2 , the laser threshold and slope efficiency decrease. It is worth mentioning, however, that in DC Pr 3þ -doped fluoride fiber, the emission cross section of red light is substantially bigger than that of green light (i.e., the red gain is much stronger than that of green light). Even with only ∼4% feedback at both ends of the resonant cavity, red laser oscillation is easily formed under vigorous pumping. In practice, with the decrease of R 2 (i.e., the threshold of green laser increases), red laser oscillation may be established first in the Pr 3þ -doped fiber laser, resulting in the failure of green laser emission. Therefore, in designing the output mirror reflectivity of an all-fiber Pr 3þ -doped green laser, various factors (e.g., gain fiber length, output mirror transmittance in the red region) should be considered comprehensively to ensure the successful establishment of green laser oscillation. For example, in experiment, a ∼2-m DC Pr 3þ -doped fluoride fiber was used, and the threshold of the red laser is about 1.6 W without the FDMs. According to the green laser threshold  in Fig. 7(d), it can be inferred that R 2 should be designed to be ∼50% at this time to obtain higher efficiency and output power on the premise of the smooth establishment of the green laser. We also carried out relevant simulations of the high-power all-fiber green laser with different optimization designs, and the results are shown in Fig. 8(a). For the R 2 ¼ 75%, varying the gain fiber from 2.1 to 1.5 m, both the green output power and slope efficiency increase from 3.63 to 4.23 W pumped at 20 W and from 19.0% to 22.1%, respectively. When the L ¼ 2.1 m, with the R 2 decreasing from 75% to 50%, both the green output power and slope efficiency increase from 3.63 to 5.41 W pumped at 20 W and from 20.5% to 30.0%, respectively. Therefore, the output power and efficiency can be further improved by reasonably reducing the length of the gain fiber and increasing the green laser output coupling. Furthermore, as shown in Fig. 8(b), neglecting the loss caused by a higher doping level, it can be found that the green laser output power increases with the increase of the Pr 3þ doping concentration, indicating that the output green laser power can also be further increased by increasing the Pr 3þ doping concentration. In short, the numerical model well explains the experimental results of the all-fiber green laser [see the black sphere in Figs. 7(b), 7(d), and 8(a)], and predicts the potential of the visible DC Pr 3þ -doped all-fiber laser pumped by a standard multimode fiber-pigtailed blue LD.

Conclusions
A compact high-efficiency Watt-level CW all-fiber Pr 3þ -doped green laser pumped by a 443-nm fiber-pigtailed pump source was demonstrated. To achieve high-efficiency and high-power operation, the DC Pr 3þ -doped fluoride fiber connector was processed based on the cutting technology, and then the all-fiber green laser design was optimized using experiments and numerical simulations. According to the optimization results, we designed and demonstrated a compact high-power green all-fiber laser, which consists of a 2.1-m DC Pr 3þ -doped fiber, two homemade FDMs at visible wavelengths with a high damage intensity, and a 443-nm fiber-pigtailed pump source. The maximum output green laser power is up to 3.62 W at 521 nm, and the maximum slope efficiency is as high as 20.9%. To the best of our knowledge, this is the largest output power from the visible fiber lasers so far. Simulation performance of all-fiber green laser also shows that it is necessary to consider the optimum gain fiber length, output mirror reflectivity, and doping level. We believe the laser power scaling and slope efficiency could be further improved via (1) reducing the reflectivity of the output mirror at the laser wavelength, (2) uprating the power of 443 nm fiber-pigtailed pump laser, and (3) reducing the propagation loss and enhancing the doping level of DC Pr 3þdoped fiber.