#
946/1030 nm Dual-Wavelength Laguerre-Gaussian (LG_{01}) Mode Vortex Laser Based on Intracavity Cascade Pumped Resonator

^{*}

## Abstract

**:**

_{01}mode vortex laser is obtained by applying the intracavity cascade pumped structure and annular-beam end-pumped method, an innovative and pioneering exploration of the transverse mode of the dual-wavelength laser. First, we demonstrate the oscillation characteristic theoretical model of the dual-wavelength LG

_{01}mode laser, considering the reabsorption effect. Then the length of the laser crystal and the transmittance of the output mirror are simulated and analyzed, respectively, related to the oscillation characteristics of the 946 and 1030 nm LG

_{01}mode vortex lasers. Finally, a 946/1030 nm LG

_{01}mode vortex laser with the same handedness is successfully achieved in our experiment. With 20 W of annular-beam pump power, the output power of 946 and 1030 nm LG

_{01}mode vortex lasers is 0.404 and 0.510 W, the slope efficiency is 3.6% and 6.2%, and the total optical-optical conversion efficiency is 4.6%. At the maximum output power, the fluctuations of output power within 1 h are 4.02% and 4.23%, and the beam quality factors M

^{2}are 2.32 and 2.27, respectively, for 946 and 1030 nm LG

_{01}mode vortex lasers. The wavefront phase $\mathrm{exp}(i\varphi )$ of the 946/1030 nm dual-wavelength is also proved by the self-interference method.

## 1. Introduction

_{01}mode vortex laser is first proposed by taking the intracavity cascade pumping structure and annular-beam end-pumped method. For the Section 2, the oscillation characteristic model of a 946/1030 nm intracavity cascade pumped dual-wavelength LG

_{01}mode laser is established. For the Section 3, the length of the laser crystal and the transmittance of the output mirror are under analysis, respectively, related to both the oscillation characteristics of the 946 nm (threshold pump power, output power, and intracavity power) and 1030 nm (threshold pump power and output power) LG

_{01}mode vortex laser. For the Section 4, the 946 and 1030 nm dual-wavelength LG

_{01}mode vortex laser with the same handedness is obtained, and the output power is 0.404 and 0.510 W at the 20 W annular-beam pump power, respectively. Details of the study of the 946/1030 nm dual-wavelength LG

_{01}mode vortex laser are given in the following sections.

## 2. Theoretical Analysis

_{00}mode, Hermite–Gaussian (HG) mode, and LG mode. The TEM

_{00}mode laser is obtained when the light source with point irradiance distribution pumps the gain medium along the direction of the optical axis, which is the pump source and pumping method used in the vast majority of lasers at present [32,33]. The HG mode laser can be excited by pumping off-axis with the help of a fiber-coupled laser diode, and the order of the HG laser will be increased as the transverse separation of the fiber from the optical axis increases [34,35]. In addition, the HG mode laser can be converted to an LG mode laser using a cylindrical lens set outside the resonant cavity, which is also an indirect method to obtain the LG mode laser [36]. However, a laser with annular-shaped irradiance distribution end-pumped gain media is currently more common for obtaining the LG laser [37,38]. Because the pump beam with an annular-shaped irradiance distribution and the LG laser has good mode-matching effects in the gain medium, the LG laser can be obtained directly in the cavity based on this method. In the previous work, we obtained a 946 nm LG

_{01}mode vortex laser by end-pumped Nd:YAG crystal with an 808 nm annular beam [39]. The 946 nm LG

_{01}mode vortex laser has a two-lobe transverse irradiance distribution at any position in the cavity. Meanwhile, the light irradiance of a 946 nm LG

_{01}mode vortex laser within a distance is superposed in the resonator to obtain an annular distribution, which can achieve a good mode-matching effect with a 1030 nm vortex laser equipped with Yb:YAG crystal.

_{01}mode, the oscillatory characteristic model of the 946/1030 nm intracavity cascade pumped dual-wavelength LG

_{01}mode laser considering the reabsorption effect is established. The rate equations describing the intracavity cascaded pumped dual-wavelength laser can be expressed as:

_{01}mode vortex laser as the intracavity pump source ${\xi}_{p}$ can be expressed as [40]:

_{01}mode vortex lasers is:

_{01}mode vortex laser are established:

_{01}mode laser is used as the pump power of the 1030 nm LG

_{01}mode laser. Further, the output power ${P}_{out\Pi}$ and threshold pump power ${P}_{th}{}_{\Pi}$ of the 1030 nm LG

_{01}mode vortex laser is expressed as:

## 3. Simulation Analysis

_{01}mode vortex laser and the threshold pump power and output power of the 1030 nm LG

_{01}mode vortex laser. The simulation results can provide a reference for subsequent experiments.

_{01}mode vortex lasers are shown in Table 1. Referring to the previous literature, the doping concentration of the Nd:YAG crystal is set at 1%, and the particle number density of the corresponding ground state energy level is 1.38 × 10

^{17}/mm

^{3}. The transmittance of the 1030 nm resonator’s total reflection mirror to the 946 nm laser is 99%, so the insertion loss is ${R}_{\mathit{loss}}\text{\hspace{1em}}=\text{\hspace{1em}}1-T\text{\hspace{1em}}=\text{\hspace{1em}}0.01$. The absorption coefficient ${\alpha}_{\Pi}$ of the Yb:YAG crystal to 946 nm laser is set as 0.5 cm

^{−1}, and the length of the Yb:YAG crystal is set as 2 mm, so the absorption loss is ${\gamma}_{\alpha}{}_{I}=1-\mathrm{exp}\left(-{\alpha}_{\Pi}{d}_{\Pi}\right)=0.095$. When the transmittance of the output mirror is 1%, 3%, 5%, and 10%, the relationship between the threshold pump power, output power, and intracavity power of the 946 nm LG

_{01}mode vortex laser and the length of the Nd:YAG crystal are shown in Figure 3a–c, respectively. When the length of the Nd:YAG crystal is 0–10 mm, the threshold pump power initially decreases rapidly, and then the trend of threshold pump power becomes flat after the crystal length is 2 mm; the output power increases rapidly before the crystal length is 3 mm, after which the growth rate slows down and gradually declines. The variation of intracavity power with the increase of crystal length is consistent with that of output power with the increase of crystal length. Combining the threshold pump power and output power, we set the length of the Nd:YAG crystal as 3 mm. When the pump power is 20 W and the length of the Nd:YAG crystal is 3 mm, the relationship between the threshold pump power, output power, and intracavity power of the 946 nm LG

_{01}mode vortex laser and the output mirror transmittance are shown in Figure 3d–f. The threshold pump power increases with the increase of the output mirror transmittance, and the intracavity power has the opposite variation. The output power first increases and then decreases with the increase of the output mirror transmittance. The transmittance is 2.5–25%, and the output power exceeds 1 W. On this basis, we set the output mirror transmittance at 946 nm as 2.5%.

^{3+}is set at 0.5%, and the particle number density of the corresponding ground state energy level is 6.9 × 10

^{16}/mm

^{3}. When the transmittance of the output mirror is 1%, 3%, 5%, and 10%, the relationship between the threshold pump power and output power of the 1030 nm LG

_{01}mode vortex laser and the length of the Yb:YAG crystal are shown in Figure 4a,b, respectively. When the length of the Yb:YAG crystal is 0–10 mm, the threshold pump power originally decreases rapidly, and then the trend of threshold pump power becomes flat after the crystal length is 2 mm; the output power gradually increases as the length of the crystal increases. In addition, considering the intracavity loss of the Yb:YAG crystal to 946 nm laser, the crystal length should not be too long. Therefore, we set the Yb:YAG crystal length as 2 mm. When the pump power is 20 W and the length of Yb:YAG crystal is 2 mm, the relationship between the threshold pump power and output power of the 1030 nm LG

_{01}mode vortex laser and the output mirror transmittance are shown in Figure 4c,d. The threshold pump power increases with the increase of the output mirror transmittance. As the output mirror transmittance increases, the output power first increases rapidly, then decreases slowly. The lower operating threshold is preferred, so we set the output mirror transmittance at 1030 nm as 4%.

## 4. Experiment Setup

_{01}mode laser is shown in Figure 5. The pump source is an 808 nm laser diode connected and output by a fiber pigtail with a core diameter of 200 μm and a numerical aperture of 0.22. First, the pump beam passes through the lens L

_{1}(f = 43 mm) and is collimated into a parallel beam. Then, it is shaped into an annular beam by a reflector M placed at 45°, where the center of the reflector M is an elliptical etched area (the long axis: 5$\sqrt{2}$ mm, the short axis: 5 mm). Then, the beam diameter is adjusted by aperture D, and finally, it is converged into the laser crystal through lens L

_{2}(f = 80 mm). The efficiency of the coupling system is 58.5%. The gain medium of the 946 nm laser is a Φ4 mm × 3 mm 1%-doped Nd:YAG crystal, which is coated with 808 and 946 nm antireflection film on the S

_{1}side and 946 nm antireflection film on the S

_{2}side. The gain medium of the 1030 nm laser is a Φ4 mm × 2 mm 0.5%-doped Yb:YAG crystal and its S

_{1}and S

_{2}sides are coated with 946 and 1030 nm antireflection coatings. The two crystals are wrapped with indium foil and installed in water-cooled fixtures made of red copper, and the temperature is controlled at 15 °C. The resonator of this laser includes 946 and 1030 nm resonators. The 946 nm resonator is composed of M

_{1}, Nd:YAG crystal and M

_{2}, and its cavity length is 75 mm. The 1030 nm resonator is composed of the M

_{3}, Yb:YAG crystal, and M

_{2}, and its cavity length is 35 mm. M

_{1}is a plane-concave mirror (curvature radius: 300 mm). Its S

_{1}and S

_{2}sides are coated with 808 and 1064 nm antireflection films, and the S

_{2}side is also coated with 946 nm high-reflection film. M

_{3}is also a plane-concave mirror (curvature radius: 300 mm). Its S

_{1}side is coated with a 946 nm antireflection film, and its S

_{2}side is coated with a 946 nm antireflection film and 1030 nm high-reflection film. M

_{2}is a plane-plane mirror, and its S

_{1}and S

_{2}sides are coated according to the simulation results. The final transmittance of M

_{2}to 946 and 1030 nm is 2.5% and 3.9%, respectively. The output laser is divided into 946 and 1030 nm LG

_{01}mode vortex lasers by dichroic mirror M

_{4}, which is convenient for measuring the parameters of different wavelength lasers separately.

## 5. Results and Discussion

_{01}mode vortex laser has been achieved by adjusting the transverse position of the Nd:YAG crystal [39]. A mode converter composed of cylindrical lenses converts the generated vortex laser into a Hermite–Gaussian (HG) laser. The vortex laser’s topological charge and handedness change are determined by the number of node lines and the direction of the long axis of the HG laser. The 946 nm vortex laser is adjusted to a direction parallel to the optical axis by a reflector to facilitate the measurement. The measurement diagram and results are shown in Figure 7. By carefully adjusting the lateral position or pitch angle of the laser crystals, the long-axis of the 946 and 1030 nm HG

_{01}mode lasers have the same handedness over the whole pump range. The results show that the 946 and 1030 nm lasers are LG

_{01}mode and have the same handedness.

_{01}mode vortex lasers and the pump power of the annular beam, respectively, and the results are shown in Figure 8. When the pump power of the annular beam is 9.7 W, the 946 nm LG

_{01}mode vortex laser comes to the start of the output; When the pump power of the annular beam is increased to 11.9 W, the 946 and 1030 nm LG

_{01}mode vortex laser start to output simultaneously. When the pump power of the annular beam is increased to 16.1 W, the output power of the 946 and 1030 nm LG

_{01}mode vortex laser is consistent, and their size is 0.277 W; When the pump power of the annular beam is 20 W, the output power of 946 and 1030 nm LG

_{01}mode vortex lasers is 0.404 and 0.510 W, while the corresponding slope efficiency is 3.6% and 6.2% respectively. The total optical-optical conversion efficiency is 4.6%. Since the full mirror M

_{3}and Yb:YAG crystal will bring losses to the 946 nm laser oscillation, this is one of the reasons for the lower output power and slope efficiency of the 946 nm LG

_{01}mode laser. Another reason is that the dual-wavelength vortex laser is output only in a single handedness, and the laser with opposite handedness is suppressed.

_{01}mode vortex laser and 808 nm LD varies steadily over time, shown in Figure 9. The output power of the 946 and 1030 nm vortex lasers was recorded every 2 min for a total test time of 1 h. The output power of the 946 and 1030 nm LG

_{01}mode lasers fluctuates by 4.02% and 4.23% with the time, respectively. However, the total output power fluctuation is 0.91%, which is smaller than the fluctuation of the 946 and 1030 nm LG

_{01}mode vortex lasers, respectively. This phenomenon indicates weak competition between the output power of the dual-wavelength vortex laser. In addition, the pump power of 808 nm LD fluctuates by 0.37% over time.

^{2}of the 946/1030 nm LG

_{01}mode vortex laser with incident pump power as well as time is given in (a) and (b) in Figure 10, respectively. The theoretical value of the beam quality factor M

^{2}for the LG

_{01}mode vortex laser is 2. When the pump power is 13 W to 20 W, the beam quality factor M

^{2}for the 946 nm LG

_{01}mode vortex beam is in the range of 2.20 to 2.32, and the beam quality factor M

^{2}for the 1030 nm LG

_{01}mode vortex beam is in the range of 2.14 to 2.27. The beam quality factors M

^{2}of both 946 and 1030 nm LG

_{01}mode vortex lasers increase slightly with increasing pump power. The inset in Figure 10a shows the beam factor test results for the 946 nm and 1030 nm LG

_{01}mode vortex lasers at a pump power of 20 W, and the results are 2.32 and 2.27, respectively. In addition, we measured the beam quality factor over time for the 946 and 1030 nm LG

_{01}mode vortex lasers at a pump power of 20 W. In the early stage, the beam quality factors of the 946 and 1030 nm vortex lasers are relatively stable, and with the increase of time, the beam quality factors of the 946 and 1030 nm vortex lasers show a slowly rising trend due to the accumulation of thermal effects.

_{01}mode laser with a plane wave or spherical wave was carried out, and the interference pattern with Y-shaped stripes or single-arm spiral stripes proved that the output laser has a wavefront phase $\mathrm{exp}(i\varphi )$ [48,49]. In addition, based on the Michelson interferometer, the self-interference of the 4th-order vortex laser was also carried out, and the interference pattern containing a pair of fork-shaped stripes (four forks separated from one singularity) demonstrated that the output laser has the spiral phase $\mathrm{exp}(i4\varphi )$ [50]. We also used the self-interference method to measure the wavefront phase of the 946 and 1030 nm LG

_{01}mode vortex lasers. The optical path diagram of the measuring device and the results are shown in Figure 11a,b. The output laser is at first divided into two beams of transmitted laser and reflected laser with equal irradiance through the spectroscope G

_{1}, in which the reflected laser passes through the mirror M

_{1}and then passes through the spectroscope G

_{1}again. The transmitted laser passes through the compensation plate G

_{2}, the mirror M

_{2}, the compensation plate G

_{2}and then passes through the spectroscope G

_{1}again. Finally, the two lasers come to the CCD element and have an interference there. We adjust the front and rear positions of mirror M

_{1}to make the optical paths of the two paths equal. The self-interference patterns of the 946 and 1030 nm lasers both contain a pair of opposite Y-shaped fringes, which are marked with dashed red lines. Separating a fork from a singularity indicates that the 946/1030 nm LG

_{01}mode vortex laser contains the wavefront phase $\mathrm{exp}(i\varphi )$.

## 6. Conclusions

_{01}mode vortex laser is designed and experimentally studied in this paper. Firstly, the theoretical model of oscillation characteristics of intracavity cascade pumped dual-wavelength LG

_{01}mode vortex laser considering the reabsorption effect is established, and the length of the laser crystal and the transmittance of the output mirror are simulated and analyzed related to the oscillation characteristics of the 946 and 1030 nm LG01 mode vortex lasers. Finally, the experimental setup is built, and the parameters of the 946 nm and 1030 nm LG

_{01}mode lasers are presented, respectively. With the annular-beam pump power of 20 W, the output power is 0.404 and 0.510 W, and the slope efficiency is 3.6% and 6.2% for the 946 and 1030 nm LG

_{01}mode vortex lasers. The total optical-optical conversion efficiency is 4.6%. For the maximum output power, the power fluctuates by 4.02% and 4.23% within 1 h. The beam quality factors M

^{2}are 2.32 and 2.27 for the 946 and 1030 nm LG

_{01}mode vortex lasers, respectively. The interference patterns of the 946 and 1030 nm lasers measured by the self-interference method contain a pair of opposite Y-shaped fringes, indicating that the generated dual-wavelength vortex laser has the wavefront phase $\mathrm{exp}(i\varphi )$. The 946/1030 nm dual-wavelength LG

_{01}mode vortex laser is developed for the first time, and the feasibility of intracavity pumping for dual-wavelength LG

_{01}mode vortex laser is verified, which is of great significance for research on dual-wavelength intracavity sum-frequency.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- He, W.; Li, D.; Zhu, L.Q.; Dong, M.L.; Luo, F. Tunable multiwavelength erbium-doped fiber laser employing PM-FBG and Mach–Zehnder interferometer with optical fiber delay line. IEEE Photon. J.
**2017**, 9, 2695671. [Google Scholar] [CrossRef] - He, W.; Yuan, H.W.; Lou, X.P.; Zhu, L.Q.; Dong, M.L. Multi-wavelength switchable erbium-doped fiber laser based on a hybrid filter incorporating a bi-tapered mach-zehnder interferometer and sagnac loop. Phys. Scr.
**2019**, 94, 125502. [Google Scholar] [CrossRef] - Chen, J.J.; Wei, W.Q.; Qin, J.L.; Yang, B.; Huang, J.Z.; Wang, Z.H.; Wang, T.; Yu, C.Y.; Zhang, J.J. Multi-wavelength injection locked semiconductor comb laser. Photonics Res.
**2022**, 10, 1840–1847. [Google Scholar] [CrossRef] - Liu, L.; Dai, C.; Wang, X.-Z. A continuous 1052 nm and 1061 nm dual-wavelength Nd:YAG laser. Optoelectron. Lett.
**2020**, 16, 181–184. [Google Scholar] [CrossRef] - Jaffres, L.; Labruyère, A.; Couderc, V.; Carreaud, J.; Maître, A.; Boulesteix, R.; Brenier, A.; Boulon, G.; Guyot, Y.; Rabinovitch, Y.; et al. Gain structuration in dual-wavelength Nd: YSAG ceramic lasers. Opt. Express
**2012**, 20, 25596–25602. [Google Scholar] [CrossRef] [PubMed] - Akbari, R.; Zhao, H.; Major, A. High-power continuous-wave dual-wavelength operation of a diode-pumped Yb: KGW laser. Opt. Lett.
**2016**, 41, 1601–1604. [Google Scholar] [CrossRef] - Wang, B.B.; Gao, C.C.; Dou, R.Q.; Nie, H.K.; Sun, G.H.; Liu, W.P.; Yu, H.J.; Wang, G.J.; Zhang, Q.L.; Lin, X.C.; et al. Dual-wavelength mid-infrared CW and Q-switched laser in diode end-pumped Tm,Ho:GdYTaO
_{4}crystal. Laser Phys. Lett.**2018**, 15, 025801. [Google Scholar] [CrossRef] - Shang, L.H.; Wen, Y.; Li, T.Y.; Guo, Y.Y.; Wang, Y.H.; Wu, C.T.; Wang, C.; Jin, G.Y. Pulse peaks synchronize dual-wavelength laser based on Q-switch delay trigger. Infrared Phys. Technol.
**2021**, 116, 103751. [Google Scholar] [CrossRef] - Lin, H.F.; Zhu, W.Z.; Xiong, F.B.; Ruan, J.J. Simultaneous dual-wavelength Q-switched Nd: YAG laser at 1052 and 1073 nm. Appl. Opt.
**2017**, 56, 948–951. [Google Scholar] [CrossRef] - Scheller, M.; Baker, C.W.; Koch, S.W.; Moloney, J.V. Dual-Wavelength Passively Mode-Locked Semiconductor Disk Laser. IEEE Photonics Technol. Lett.
**2016**, 28, 1325–1327. [Google Scholar] [CrossRef][Green Version] - Waritanant, T.; Major, A. Dual-wavelength operation of a diode-pumped Nd:YVO
_{4}laser at the 1064.1 & 1073.1 nm and 1064.1 & 1085.3 nm wavelength pairs. Appl. Phys. B**2018**, 124, 87. [Google Scholar] - Qi, Y.Y.; Yu, H.J.; Zhang, J.Y.; Zhang, L.; He, C.J.; Lin, X.C. A compact dual-wavelength Nd:LuVO
_{4}laser with adjustable power-ratio between 1064 nm and 1342 nm lines by controlling polarization dependent loss. Opt. Commun.**2017**, 382, 302–306. [Google Scholar] [CrossRef] - Chen, H.B.; Huang, Y.S.; Li, B.X.; Liao, W.B.; Zhang, G.; Lin, Z.B. Efficient orthogonally polarized dual-wavelength Nd:LaMgB
_{5}O_{10}laser. Opt. Lett.**2015**, 40, 4659–4662. [Google Scholar] [CrossRef] - Cheng, H.P.; Liu, Y.C.; Huang, T.L.; Liang, H.C.; Chen, Y.F. Orthogonally polarized single-longitudinal-mode operation in a dual-wavelength monolithic Nd:YAG laser at 1319 nm and 1338 nm. Photonics Res.
**2018**, 6, 815–820. [Google Scholar] [CrossRef] - White, A.; Elder, I.; Hall, G. Single longitudinal mode and dual wavelength CW VBG lasers at 1342 nm and 1064 nm. In Technologies for Optical Countermeasures IX; SPIE: Bellingham, WA, USA, 2012; Volume 8543, pp. 68–75. [Google Scholar]
- Men, S.J.; Liu, Z.J.; Cong, Z.H.; Li, Y.F.; Zhang, X.Y. Electro-optically Q-switched dual-wavelength Nd:YLF laser emitting at 1047 nm and 1053 nm. Opt. Laser Technol.
**2015**, 68, 48–51. [Google Scholar] [CrossRef] - Liu, Y.; Dong, Y.; Yu, Y.J.; Wang, C.; Zhang, X.H. Output characteristics of no gain competition 912 nm and 1064 nm dual-wavelength lasers. Opt. Laser Technol.
**2019**, 115, 125–128. [Google Scholar] [CrossRef] - Hu, W.W.; Li, Y.L.; Hu, C.W.; Gu, X.K.; Liu, H.X.; Zhang, Y.P.; Zhang, Y.M. Intra-cavity cascaded pumped 912 nm/1030 nm dual-wavelength laser output. Opt. Commun.
**2019**, 452, 440–444. [Google Scholar] [CrossRef] - Čižmár, T.; Brzobohatý, O.; Dholakia, K.; Zemánek, P. The holographic optical micro-manipulation system based on counter-propagating beams. Laser Phys. Lett.
**2011**, 8, 50–56. [Google Scholar] [CrossRef] - Padgett, M.; Bowman, R. Tweezers with a twist. Nat. Photonics
**2011**, 5, 343–348. [Google Scholar] [CrossRef] - Vicidomini, G.; Bianchini, P.; Diaspro, A. STED super-resolved microscopy. Nat. Methods
**2018**, 15, 173–182. [Google Scholar] [CrossRef] - Perez-Garcia, B.; Francis, J.; McLaren, M.; Hernandez-Aranda, R.I.; Forbes, A.; Konrad, T. Quantum computation with classical light: The Deutsch Algorithm. Phys. Lett. A
**2015**, 379, 1675–1680. [Google Scholar] [CrossRef][Green Version] - Willner, A.E.; Huang, H.; Yan, Y.; Ren, Y.; Ahmed, N.; Xie, G.; Bao, C.; Li, L.; Cao, Y.; Zhao, Z.; et al. Optical communications using orbital angular momentum beams. Adv. Opt. Photonics
**2015**, 7, 66–106. [Google Scholar] [CrossRef][Green Version] - Wang, B.; Tanksalvala, M.; Zhang, Z.; Esashi, Y.; Jenkins, N.W.; Murnane, M.M.; Kapteyn, H.C.; Liao, C.T. Coherent Fourier scatterometry using orbital angular momentum beams for defect detection. Opt. Express
**2021**, 29, 3342–3358. [Google Scholar] [CrossRef] - McCarter, M.R.; Saleheen, A.I.; Singh, A.; Tumbleson, R.; Woods, J.S.; Tremsin, A.S.; Scholl, A.; De Lon, L.E.; Hastings, J.T.; Morley, S.A.; et al. Antiferromagnetic real-space configuration probed by dichroism in scattered x-ray beams with orbital angular momentum. Phys. Rev. B
**2023**, 107, L060407. [Google Scholar] [CrossRef] - Li, Z.; Liu, T.; Ren, Y.; Qiu, S.; Wang, C.; Wang, H. Direction-sensitive detection of a spinning object using dual-frequency vortex light. Opt. Express
**2021**, 29, 7453–7463. [Google Scholar] [CrossRef] - Wang, B.; Brooks, N.J.; Johnsen, P.C.; Jenkins, N.W.; Esashi, Y.; Binnie, I.; Tanksalvala, M.; Kapteyn, H.C.; Murnane, M.M. High-fidelity ptychographic imaging of highly periodic structures enabled by vortex high harmonic beams. arXiv
**2023**, arXiv:2301.05563. [Google Scholar] - Gold, M.H. Dual wavelength treatment protocol with a picosecond laser for the reduction of facial wrinkles. J. Cosmet. Laser Ther.
**2018**, 21, 147–151. [Google Scholar] [CrossRef] - Mark Danson, F.; Sasse, F.; Schofield, L.A. Spectral and spatial information from a novel dual-wavelength full-waveform terrestrial laser scanner for forest ecology. Interface Focus
**2018**, 8, 20170049. [Google Scholar] [CrossRef] - Liu, X.Y.; Li, X.W.; Zhao, S.Z.; Yang, K.J.; Guo, L.; Li, T.; Qiao, W.C.; Li, M.; Zhang, B.T.; He, J.L.; et al. Dual-wavelength synchronously mode-locked Tm-doped bulk laser with terahertz frequency beating. Chin. Opt. Lett.
**2019**, 17, 091401. [Google Scholar] [CrossRef] - Kerdoncuff, H.; Christensen, J.B.; Brasil, T.B.; Novikov, V.A.; Polzik, E.S.; Hald, J.; Lassen, M. Cavity-enhanced sum-frequency generation of blue light with near-unity conversion efficiency. Opt. Express
**2020**, 28, 3975–3984. [Google Scholar] [CrossRef][Green Version] - Hall, D.G.; Smith, R.J.; Rice, R.R. Pump-size effects in Nd: YAG lasers. Appl. Opt.
**1980**, 19, 3041–3043. [Google Scholar] [CrossRef] [PubMed] - Hall, D.G. Optimum mode size criterion for low-gain lasers. Appl. Opt.
**1981**, 20, 1579–1583. [Google Scholar] [CrossRef] [PubMed] - Laabs, H.; Ozygus, B. Excitation of Hermite Gaussian modes in end-pumped solid-state lasers via off-axis pumping. Opt. Laser Technol.
**1996**, 28, 213–214. [Google Scholar] [CrossRef] - Chu, S.C.; Chen, Y.T.; Tsai, K.F.; Otsuka, K. Generation of high-order Hermite-Gaussian modes in end-pumped solid-state lasers for square vortex array laser beam generation. Opt. Express
**2012**, 20, 7128–7141. [Google Scholar] [CrossRef] [PubMed] - Koshel, R.J. Novel methods of intracavity beam shaping. In Laser Beam Shaping II; SPIE: Bellingham, WA, USA, 2001; Volume 4443, pp. 47–57. [Google Scholar]
- Zhao, Y.G.; Liu, Q.Y.; Zhou, W.; Shen, D.Y. ~1 mJ pulsed vortex laser at 1645 nm with well-defined helicity. Opt. Express
**2016**, 24, 15596–15602. [Google Scholar] [CrossRef] [PubMed] - Liu, Q.Y.; Zhao, Y.G.; Ding, M.M.; Yao, W.C.; Fan, X.L.; Shen, D.Y. Wavelength-and OAM-tunable vortex laser with a reflective volume Bragg grating. Opt. Express
**2017**, 25, 23312–23319. [Google Scholar] [CrossRef] - Yang, Y.S.; Li, Y.L.; Wang, C.; Yang, C. Research on 946 nm LG
_{01}mode laser considering thermal effect. Laser Phys.**2022**, 32, 095801. [Google Scholar] [CrossRef] - Kim, J.W.; Clarkson, W.A. Selective generation of Laguerre–Gaussian (LG
_{0n}) mode output in a diode-laser pumped Nd:YAG laser. Opt. Commun.**2013**, 296, 109–112. [Google Scholar] [CrossRef] - Hanson, F. Efficient operation of a room-temperature Nd:YAG 946-nm laser pumped with multiple diode arrays. Opt. Lett.
**1995**, 20, 148–150. [Google Scholar] [CrossRef] - Clarkson, W.; Koch, R.; Hanna, D. Room-temperature diode-bar-pumped Nd:YAG laser at 946 nm. Opt. Lett.
**1996**, 21, 737–739. [Google Scholar] [CrossRef] - Lindsay, I.D.; Ebrahimzadeh, M. Efficient continuous-wave and Q-switched operation of a 946-nm Nd:YAG laser pumped by an injection-locked broad-area diode laser. Appl. Opt.
**1998**, 37, 3961–3970. [Google Scholar] [CrossRef] - Fan, T.; Byer, R. Modeling and CW operation of a quasi-three-level 946 nm Nd:YAG laser. IEEE J. Quantum Electron.
**1987**, 23, 605–612. [Google Scholar] - Wang, X.D.; Zhao, Z.W.; Zeng, X.H.; Mao, H.M.; Liang, X.Y. Study on Spectra and Laser Properties of 0.5at% Yb:YAG Crystal. J. Synth. Cryst.
**2014**, 43, 758–764. [Google Scholar] - Saito, T.; Takeo, Y.; Mimura, H. Precise characterization of focused vortex beams. Jpn. J. Appl. Phys.
**2017**, 56, 092501. [Google Scholar] [CrossRef] - Esashi, Y.; Liao, C.-T.; Wang, B.; Brooks, N.; Dorney, K.M.; Hernández-García, C.; Kapteyn, H.; Adams, D.; Murnane, M. Ptychographic amplitude and phase reconstruction of bichromatic vortex beams. Opt. Express
**2018**, 26, 34007–34015. [Google Scholar] [CrossRef] - Liu, Q.Y.; Zhao, Y.G.; Zhou, W.; Shen, D.Y. Vortex operation in Er:LuYAG crystal laser at 1.6 μm. Opt. Mater.
**2017**, 71, 31–34. [Google Scholar] [CrossRef] - He, H.S.; Chen, Z.; Dong, J. Direct generation of vector vortex beams with switchable radial and azimuthal polarizations in a monolithic Nd:YAG microchip laser. Appl. Phys. Express
**2017**, 10, 052701. [Google Scholar] [CrossRef] - Qiao, Z.; Xie, G.Q.; Wu, Y.H.; Yuan, P.; Ma, J.G.; Qian, L.J.; Fan, D.Y. Generating High-Charge Optical Vortices Directly from Laser Up to 288th Order. Laser Photonics Rev.
**2018**, 12, 1800019. [Google Scholar] [CrossRef][Green Version]

**Figure 3.**The relationship between (

**a**) the threshold pump power, (

**b**) output power, and (

**c**) intracavity power of the 946 nm LG

_{01}mode vortex laser and the length of the Nd:YAG crystal at a pump power of 20 W; the relationship between (

**d**) the threshold pump power, (

**e**) output power and (

**f**) intracavity power of the 946 nm LG

_{01}mode vortex laser and the output mirror transmittance at a pump power of 20 W and Nd:YAG crystal length of 3 mm.

**Figure 4.**The relationship between (

**a**) the threshold pump power and (

**b**) the output power of the 1030 nm LG

_{01}mode vortex laser and the length of the Yb:YAG crystal at a pump power of 20 W; the relationship between (

**c**) the threshold pump power and (

**d**) output power of the 1030 nm LG

_{01}mode vortex laser and the output mirror transmittance at a pump power of 20 W and Yb:YAG crystal length of 2 mm.

**Figure 8.**The relationship between the power of the 946/1030 nm LG

_{01}mode vortex laser and the pump power of the annular beam.

**Figure 10.**The relationships between the beam quality factors M

^{2}of the 946/1030 nm LG

_{01}mode vortex laser and (

**a**) pump power and (

**b**) time.

**Figure 11.**(

**a**) The optical path diagram of the wavefront phase detection device, and (

**b**) the measurement results.

Parameter | Nd:YAG | Yb:YAG |
---|---|---|

${\lambda}_{p}$ [nm] | 808 | 946 |

${L}_{0I}$ | 0.05 | 0.05 |

$\sigma $ [cm^{2}] | 4 × 10^{−20} | 1.8 × 10^{−20} |

$\tau $ [μs] | 230 | 950 |

$\alpha $ [cm^{−1}] | 8 (808 nm) | 0.56 (946 nm) |

${f}_{1}$ | 0.0074 | 0.046 |

${f}_{2}$ | 0.6 | 0.7 |

${\omega}_{0}$ [μm] | 200 | 180 |

$a$ and $b$ [μm] | 200 and 100 | - |

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## Share and Cite

**MDPI and ACS Style**

Yang, Y.; Li, Y.; Wang, C.; Yang, C.
946/1030 nm Dual-Wavelength Laguerre-Gaussian (LG_{01}) Mode Vortex Laser Based on Intracavity Cascade Pumped Resonator. *Photonics* **2023**, *10*, 441.
https://doi.org/10.3390/photonics10040441

**AMA Style**

Yang Y, Li Y, Wang C, Yang C.
946/1030 nm Dual-Wavelength Laguerre-Gaussian (LG_{01}) Mode Vortex Laser Based on Intracavity Cascade Pumped Resonator. *Photonics*. 2023; 10(4):441.
https://doi.org/10.3390/photonics10040441

**Chicago/Turabian Style**

Yang, Yashuai, Yongliang Li, Chi Wang, and Chao Yang.
2023. "946/1030 nm Dual-Wavelength Laguerre-Gaussian (LG_{01}) Mode Vortex Laser Based on Intracavity Cascade Pumped Resonator" *Photonics* 10, no. 4: 441.
https://doi.org/10.3390/photonics10040441