Diode-pumped wavelength-switchable visible Pr 3+ :YLF laser and vortex laser around 670 nm

Here we developed a novel wavelength-switchable visible continuous-wave (CW) Pr 3+ :YLF laser around 670 nm. In single-wavelength laser operations, the maximum output powers of 2.60 W, 1.26 W, and 0.21 W, the maximum slope efficiencies of 34.7%, 27.3%, and 12.3% were achieved with good beam qualities ( M 2 < 1.6) at 670.4 nm, 674.2 nm, and 678.9 nm, respectively. Record-high output power (2.6 W) and record-high slope efficiency (34.7%) were achieved for the Pr 3+ :YLF laser operation at 670.4 nm. This is also the first demonstration of longer-wavelength peaks beyond 670 nm in the 3 P 1 → 3 F 3 transition of Pr 3+ :YLF. In multi-wavelength laser operations, the dual-wavelength lasings, including 670.1/674.8 nm, 670.1/679.1 nm, and 675.0/679.4 nm, were obtained by fine adjustment of one/two etalons within the cavity. Furthermore, the triple-wavelength lasings, e.g. 672.2/674.2/678.6 nm and 670.4/674.8/679.4 nm, were successfully demonstrated. Moreover, both the first-order vortex lasers (LG 0 +1 and LG 0 -1 modes) at 670.4 nm were obtained by off-axis pumping.


Introduction
Visible laser sources around 670 nm are in great demand in biomedical fields, such as photocoagulation 1 , photothermolysis 2 , hemangioma treatment 3 , treatment of melasma 4 , treatment of acne scars 5 and phototherapies 6−8 . Optical vortex lasers are also of great value in a wide scope of applications, especially in nanosurgery and nanomanipulation 9−11 . Benefiting from low absorption coefficients of 670 nm wavelength in some types of skin, subcutaneous, and muscle tissues 12 , the 670-nm vortex laser may have the potential to manipulate particles (like erythrocytes) in these tissues.
In general, laser operations around 670 nm are gener-ated by the conventional frequency-doubled Nd:YVO 4 lasers 13 and the AlGaInP/AlGaAs diode lasers 14 . Compared with the frequency-converted lasers, the diodepumped solid-state lasers that can be directly generated are simple, robust, and cost-effective laser sources that can provide high laser efficiency. Owing to the inherent good beam quality, laser sources directly emitting around 670 nm also show obvious advantages over the currently available diode lasers. The Pr 3+ :YLF crystal is a highlighted active medium for the direct generation of diode-pumped visible lasers 15−18 . This is mainly due to the fact that Pr 3+ ions provide abundant emission lines between 500 nm and 750 nm with large peak emission cross-sections, which is typically in an order of LG +1

0
LG −1 0 10 -19 cm 2 19−20 . Nevertheless, laser operations around 670 nm based on a Pr 3+ :YLF crystal were rarely reported 21−22 , and the highest output power (0.96 W) and the highest slope efficiency (12.7%) achieved so far were relatively low. Therefore, we proposed a novel wavelength-switchable continuous-wave (CW) visible Pr 3+ :YLF lasers around 670 nm. Record-high output power (2.6 W) and record-high slope efficiency (34.7%) were achieved for the π-polarized laser operation at 670.4 nm, which were more than two times higher than the values reported before.

Experimental setup
As shown in Fig. 1, a commercial InGaN laser diode (LD) array emitting at ~444 nm with the maximum output power of 24 W was applied as the pump source. To reduce the spherical aberration and make the focusing spot of the pump beam smaller, an aspherical plane-convex lens with a focal length of 75 mm was used to focus the pump light. A simple end-pumped plane-concave laser cavity with the insertion of one/two etalons (i.e., Etalon-1 and/or Etalon-2) was constructed to obtain the wavelength-switchable laser operation. The input coupler (IM) was based on a coated plane mirror, which has a high reflectivity (>99.9%) at 665−700 nm and high transmissions at 600−639 nm. A piece of 100 mm radius-of-curvature plane-concave mirror with transmissivities of 0.3% at 670 nm, 0.5% at 675 nm, and 0.9% at 679 nm was applied as the output coupler (OC). It is worth pointing out that the transmission of the OC at 698 nm is over 60%, and can effectively prevent the available optical gain from lasing. The etalons are made of optical glass BK7. The thickness of Etalon-1 is 100 μm, and it was inserted at the Brewster angle to suppress the π-polarized emissions. Another three pieces of Etalon-2 with different thicknesses of 100 μm, 150 μm, and 200 μm were vertically inserted into the cavity and tilted to achieve wavelength-switchable laser oscillations.
A commercial fabricated a-cut Pr 3+ :YLF crystal employed for the following experiments has a low Pr 3+ doping ratio of 0.12 at. %, the length of 15 mm, and 3 mm × 3 mm polished facets without anti-reflection coating. To protect the crystal from thermally induced fragmentation, we wrapped the crystal with indium foil and placed it in a water-cooled copper crystal holder. The temperature of the cooling water was set to 13 °C. A wide ~2.2 nm of full width at half maximum (FWHM) of the pump laser spectrum leads to a relatively low absorption efficiency ~51% of the Pr 3+ :YLF crystal. Here ~10% loss of pump laser power was introduced by the plane-convex lens and the plane mirror (i.e., IM). The physical cavity length was optimized to be 53 mm. It should be noted that the performance of the single-wavelength 670.4 nm laser was optimized with a concave-plane cavity (to reduce thermal effects) with the same cavity parameters, rather than the above-described plane-concave cavity.

Results and discussion
Visible single-wavelength laser operation Figure 2 presented the experimental results of the singlewavelength laser operation around 670 nm. The maximum output powers of 2. above-mentioned without etalons. To obtain singlewavelength operations at two σ-polarized wavelengths, Etalon-1 was inserted into the cavity at the Brewster angle to suppress emission at π-polarized 670.4 nm. Meanwhile, two pieces of Etalon-2 with thicknesses of 100 μm and 150 μm were vertically inserted into the cavity to obtain lasing at 674.2 and 678.9 nm, respectively. The laser spectra were measured by a spectrometer (Ocean Optics, HR4000+). Due to the relatively low resolution (0.3 nm), the linewidths appeared to be a bit large. Since the YLF crystal generally exhibits negative thermal lensing effects 23 , the mode volume of the laser in the gain medium will be enlarged in a plane-concave or a concave-plane cavity as the thermal lensing effects become strong. Thus, the laser slope efficiency can increase under high-power pumping due to the increment of overlap efficiency, as detailedly shown in Fig. 2(a). Three single-wavelength lasing spectra were given in . Correspondingly, the beam qualities of the single-wavelength lasers were also characterized in Fig. 2(c), including 670.4 nm laser with 1.2 and 1.4 in the x and y directions, respectively; 674.2-nm laser with 1.5 and 1.4 in the x and y directions, respectively; 678.9-nm laser with 1.4 and 1.4 in the x and y directions, respectively. The M 2 factor was calculated through (ISO 11146), where is the divergence half-angle, is the beam waist radius, and is the laser wavelength. Power stabilities of these single-wavelength lasers are presented in Fig. 2(d). Due to the relatively low absolute output power as well as the noises from the environment and the thermal power meter (Thorlabs S425C-L, detection sensitivity > 2 mW), the power stability of the 678.9-nm laser appeared to be little higher. Wavelength drift was not observed during the power stability measuring. Here the polarization directions of these single-wavelength lasers, i.e., 670.4 nm in π-polarization,  and both 674.2 nm and 678.9 nm in σ-polarization, were confirmed by a Glan-Taylor prism. The polarization results we obtained were coincident with the spectroscopy characteristics around 670 nm (see Fig. 3).
z To further understand the high-power and high-efficiency performance under high-power pumping conditions, simulations of the 670-nm laser with different beam radius (affected by the thermal lensing effects) were carried out. The input-output power characteristics can be expressed by 24 (the spatial distribution is expressed under a normal cartesian coordinate system; is the direction perpendicular to the facets of the crystal) where is the output power; is the input power; is the effective mode area; is the total logarithmic single-pass loss; is the saturation intensity; can be treated as the Stokes efficiency (because we used the absorbed power in the simulation and we assumed that the optical transfer efficiency is one); is the normalized pump distribution inside the crystal; is the dimensional mode distribution factor of the laser (the specific definition of the and the can be found in ref. 24 ); is the power transmissivity at the wavelength of the laser; the integral symbol and the means the integration of the whole space. For a circular Gaussian beam, the can be written as w l where is the radius of the laser beam. Since the Rayleigh distance is much longer than the length of the crystal in this cavity scheme, the variation of the beam z g(x, y, z) radius along the direction can be reasonably neglected. Due to the different pump beam sizes and M 2 factors in the x and y directions, the pump beam can be approximately described as an elliptical Gaussian beam. Thus, the can be written as where is the absorption efficiency; is the ratio of minor to major beam size; is the average beam radius in the minor direction; is the length of the active medium. Then the input-output power characteristics with different laser beam sizes can be calculated. The results were presented in Fig. 4 and the parameters for the simulation were listed in Table 1. As can be seen from Fig. 4, the slope efficiency became higher while the laser beam size became larger. The simulation results obtained can clearly explain the rising trend of the slope efficiency of the experimental results. Compared with that of the previous works on 670-nm lasers 21−22 , the high-power and high-efficiency results were achieved because, except for the advantages brought by the thermal lensing effects mentioned above, we did not use the etalon to obtain the lasers at 670 nm. Since the power transmissivity of the OC at 670 nm is quite low, the total single-pass loss ( ) is very sensitive to the intracavity losses. As can be seen from Eq. (1), the is very sensitive to the when the other parameters remain unchanged. Thus, the elimination of the intracavity losses introduced by the etalon is also very critical to achieve high output power and high slope efficiency (at 670 nm).   The intensities of these pairwise lasers in the dualwavelength operations were comparable, which implied the potential of obtaining a higher power laser at ~679 nm with suitable etalons to match the emission peak. Then, as seen in Fig. 5(c), two types of triple-wavelength laser operations were also achieved. The triplewavelength laser at 670.4/674.8/679.4 nm with output power of 1.78 W was obtained by tilting the crystal, and it only appeared at the available highest pumping. The triple-wavelength laser at 672.2/674.2/678.6 nm with the maximum output power of 0.84 W also only appeared under the available highest pumping, but it was achieved by inserting both Etalon-1 with 100-μm thickness and Etalon-2 with 150-μm thickness. Power stabilities of these multi-wavelength lasers are presented in Figs. 5(d) and 5(e). Due to the mode competition, the stabilities of the multi-wavelength lasers are generally worse than the single-wavelength lasers. Wavelength drift was not observed during the output power stability measuring.
The power transmission of the etalon can be expressed by 25 where is the power transmissivities; is the reflectivity of the surface (~0.04 in our schemes); is the refractive index of the glass (~1.51 at 675 nm); is the thickness of the etalon; is the angle between the rays and the normal to the reflective faces. According to Eq. (4), the tilting angle of the etalons can be estimated (the main deviation was introduced by the resolution of the spectrometer we used). For example, for the dual-wavelength laser at 670.1/679.1 nm, when the angle of the etalon with a 200-μm thickness was tilted to 1.68°, the power transmissivities were over 99.8% at 670.1 and 679.1 nm as well as only 85.2% at 674.2 nm. Similar analyses can also be applied to other tuning results, including the single-wavelength results in the above section.

Visible vortex laser operation
LG +1

0
LG −1 0 A visible vortex laser at 670.4 nm was obtained by using an off-axis pumping technique. The laser cavity was designed as the concave-plane one above-mentioned. By carefully rotating the plane mirror in x and y directions, two diagonal Hermite-Gaussian (HG) 01 modes could be obtained because the threshold of the fundamental mode could exceed the HG 01 mode under off-axis conditions. Then, two diagonal HG 01 modes at 3π/4 and π/4 angles (relative to the horizontal direction) could form the Laguerre-Gaussian (LG) mode with an introduced Gouy phase of π/2 26 . As known, such a hollow beam could be coherently or incoherently superposed by two diagonal beams 27 . Thus, it's necessary to verify the phase of the wavefront (helical or not) and rotate the plane mirror repeatedly. This step is the main challenge to obtain vortex laser. As seen in Fig. 6(a), the maximum output power of 0.23 W with a slope efficiency of 10.8% was obtained. By slightly moving the crystal perpendicularly to the propagation direction of the laser, both the first-order vortex lasers ( and modes) were realized. The output power characteristics of both modes are almost the same. The beam patterns of the vortex lasers were measured by a charge-coupled device (CCD) placed after the OC (the distance between the OC and the CCD is ~30 mm). When the absorbed pump power was over 2.9 W, the lasers did not sustain vortical forms because the increased thermal lensing effects might break the mode-matching conditions of the first order LG modes. Under high-power pumping, it is challenging to meet the mode-matching conditions of the vortex laser in the π direction due to the larger thermo-optic coefficient (compared with the σ direction) and the complex spatial distribution of the pump beam. To verify the vortex operations, a plane-concave mirror with a high reflective dielectric coating at ~670 nm on the concave surface was applied as an improved Fizeau interferometer 28 to get the interference patterns. Figure 6(   LG 0

+1
LG 0  details in the future to propose more rational schemes to obtain higher output power.