Ex) Article Title, Author, Keywords
Current Optics
and Photonics
Ex) Article Title, Author, Keywords
Curr. Opt. Photon. 2022; 6(6): 627-633
Published online December 25, 2022 https://doi.org/10.3807/COPP.2022.6.6.627
Copyright © Optical Society of Korea.
Hongfei Qi^{1}, Lanling Lan^{1}, Yan Liu^{1} , Pengfei Xiang^{1}, Yulong Tang^{2}
Corresponding author: ^{*}liuyan703@163.com, ORCID 0000-0003-2806-9264
^{*}^{*}yulong@sjtu.edu.cn, ORCID 0000-0001-7388-2516
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
To realize uniform side pumping of solar lasers and improve their output power, a solar concentrating system based on off-axis parabolic mirrors is proposed. Four identical off-axis parabolic mirrors with focal length of 1,000 mm are toroidally arranged as the primary concentrator. Four two-dimensional compound parabolic concentrators (2D-CPCs) are designed as a secondary concentrator to further compress the focused spot induced by the parabolic mirrors, and the focused light is then homogenized by four rectangular diffusers and provides uniform pumping for a laser-crystal rod to achieve solar laser emission. Simulation results show that the solar power received by the laser rod, uniformity of the light spot, and output power of the solar laser are 7,872.7 W, 98%, and 351.8 W respectively. This uniform pumping configuration and concentrator design thus provide a new means for developing high-power side-pumped solid-state solar lasers.
Keywords: Compound parabolic concentrator, Off-axis parabolic mirror, Side pumping, Solar laser
OCIS codes: (140.3580) Lasers, solid-state; (140.5560) Pumping; (350.6050) Solar energy
A solar laser is a laser pumped by sunlight. Because sunlight is a renewable and clean energy source, solar lasers are also called “green” lasers. Solar lasers have great application prospects in various areas, including energy utilization, space debris removal, space communication, measurement, and magnesium resource recycling [1–4].
Research on solar pumped solid-state lasers began in the 1960s. In 1965, Yong
Collecting more sunlight is the key to high-power solar lasers, and achieving uniform side-pumping of the laser medium can improve laser-beam quality. Compared to end pumping, side pumping features a larger light-receiving surface, and thus can collect more sunlight. What’s more, side pumping has the advantage of providing highly uniform solar pumping for a solid-state laser. Here we propose a solar concentrating system composed of off-axis parabolic mirrors, 2D-CPCs, and rectangular diffusers, and use it to collect sunlight to side-pump a Nd:YAG solid-state laser. Simulation shows that this solar collection system provides not only high concentrating power, but also excellent pumping uniformity. Total concentration of solar power as high as 7,872.7 W and side-pumping uniformity of 98% can be realized, leading to output power that reaches 351.8 W.
The primary concentrator consists of several off-axis parabolic mirrors. A fan-circular parabolic mirror with an inner radius of 1,000 mm, an outer radius of 3,000 mm, and a height of 2,000 mm can be divided into
The three-dimensional structure of the entire solar concentrator, composed of four subsystems, is shown in Fig. 2. One end of the rectangular diffuser is connected to the outlet of the 2D-CPC, and the other end is put close to the cooling-water channel. The Nd:YAG laser rod has a size of Φ6 × 30 mm, and is cooled by a circulating-water channel with outer and inner diameters of 9 mm and 6 mm respectively.
The concentrating characteristics of the primary concentrator are simulated by ray tracing with TracePro, and a circular light spot is obtained at the focal plane of each off-axis parabolic mirror. The irradiance diagram is shown in Fig. 3. According to the typical reduction of sunlight power density to 1/
To maximize the solar power converging on the side of the laser rod and improve the uniformity of the light spot, it is necessary to optimize the design of the number of parts
where
Here
The fan-shaped parabolic mirror is divided into
The total collected power is the sum from the
When the fan-circular parabolic mirror is divided into 4 (
Here
The heat distribution in the laser rod can be expressed as [25]
where
The temperature distribution in the laser rod is analyzed using the Comsol multiphysics software. The average absorption coefficient of the Nd:YAG laser rod across the whole solar spectrum is taken to be 0.35 cm^{−1} [26]. The surface heat-transfer coefficient is 1 W/(cm^{2}·℃) and the temperature of the cooling water is 293 K.
Nd:YAG is a typical four-level laser medium. By solving the four-level rate equations, the laser output power can calculated with the equation [27]
where
Here ν is the pump frequency and
When the Nd:YAG rod is pumped by sunlight, the laser absorption and solar-spectrum overlap is 0.16 [28]. The transmission efficiency is 0.85 [28], and the absorption efficiency is 0.82 in this laser system. The average weighted wavelength of sunlight is 660 nm [11], the laser output wavelength is 1,064 nm, and the Stokes factor is 0.62 [11]. The beam overlap efficiency is the ratio of the cavity mode volume to the pump volume of the laser rod; its value is assumed to be 0.91. The quantum efficiency is 0.9 [28], the fluorescence lifetime is 230 μs [27], and the stimulated emission cross section is 6.5 × 10^{−19} cm^{2} [27]. The scattering coefficient of the laser material is 0.003 cm^{−1} [28]. Based on Eqs. (5)–(8), the output power of this solar laser with varying reflectivity of the output cavity mirror and varying solar pump power are calculated, and the results are shown in Fig. 10. The reflectivity of the other end of the crystal is assumed to be 100%. When the reflectivity of the output cavity mirror is 83%, a maximum laser output power of 351.8 W is obtained, and the threshold pump power, the slope efficiency, and solar-to-laser conversion efficiency are 616 W, 4.85%, and 4.5% respectively.
To achieve uniform side pumping of a high-power solar laser, a solar concentrating system is proposed. The concentrator system consists of four off-axis parabolic mirrors with a focal length of 1,000 mm, and four 2D-CPCs and rectangular diffusers. To collect more solar power, the number of off-axis parabolic mirrors, the acceptance half-angle of the 2D-CPCs, and the length of the diffusers are optimized. When four off-axis parabolic mirrors are adopted, the solar power received by the side of the laser rod is the highest, being up to 7,872.7 W; the corresponding optimal acceptance half-angle of the 2D-CPCs is 40°; and the optimal length of the rectangular diffusers is 92 mm. The irradiance uniformity on the side of the laser crystal rod reaches 98%. Then the transverse temperature distribution of the laser rod is analyzed, and the center temperature is found to be 359 K, while the surface temperature is 325 K. Finally, based on the four-level rate equations, the output characteristics of the solar laser are analyzed. When the reflectivity of the output cavity mirror is 83%, the maximum laser output power, the threshold pump power, the slope efficiency, and the solar-to-laser conversion efficiency are 351.8 W, 616 W, 4.85%, and 4.5% respectively.
The authors declare no conflicts of interest.
Data underlying the results presented in this paper are not publicly available at the time of publication, but may be obtained from the authors upon reasonable request.
National Natural Science Foundation of China (61675129); the Natural Science Foundation of Hubei Province (2014 CFB671); Natural Science Foundation of Shanghai (19ZR1427100); Research Fund for Excellent Dissertation of China Three Gorges University (2021SSPY149).
Curr. Opt. Photon. 2022; 6(6): 627-633
Published online December 25, 2022 https://doi.org/10.3807/COPP.2022.6.6.627
Copyright © Optical Society of Korea.
Hongfei Qi^{1}, Lanling Lan^{1}, Yan Liu^{1} , Pengfei Xiang^{1}, Yulong Tang^{2}
^{1}Center for Astronomy and Space Science, College of Science, China Three Gorges University, Yichang, Hubei 443002, China
^{2}Key Laboratory for Laser Plasmas (MOE), School of Physics and Astronomy, Collaborative Innovation Center of IFSA, Shanghai Jiao Tong University, Shanghai 200240, China
Correspondence to:^{*}liuyan703@163.com, ORCID 0000-0003-2806-9264
^{*}^{*}yulong@sjtu.edu.cn, ORCID 0000-0001-7388-2516
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
To realize uniform side pumping of solar lasers and improve their output power, a solar concentrating system based on off-axis parabolic mirrors is proposed. Four identical off-axis parabolic mirrors with focal length of 1,000 mm are toroidally arranged as the primary concentrator. Four two-dimensional compound parabolic concentrators (2D-CPCs) are designed as a secondary concentrator to further compress the focused spot induced by the parabolic mirrors, and the focused light is then homogenized by four rectangular diffusers and provides uniform pumping for a laser-crystal rod to achieve solar laser emission. Simulation results show that the solar power received by the laser rod, uniformity of the light spot, and output power of the solar laser are 7,872.7 W, 98%, and 351.8 W respectively. This uniform pumping configuration and concentrator design thus provide a new means for developing high-power side-pumped solid-state solar lasers.
Keywords: Compound parabolic concentrator, Off-axis parabolic mirror, Side pumping, Solar laser
A solar laser is a laser pumped by sunlight. Because sunlight is a renewable and clean energy source, solar lasers are also called “green” lasers. Solar lasers have great application prospects in various areas, including energy utilization, space debris removal, space communication, measurement, and magnesium resource recycling [1–4].
Research on solar pumped solid-state lasers began in the 1960s. In 1965, Yong
Collecting more sunlight is the key to high-power solar lasers, and achieving uniform side-pumping of the laser medium can improve laser-beam quality. Compared to end pumping, side pumping features a larger light-receiving surface, and thus can collect more sunlight. What’s more, side pumping has the advantage of providing highly uniform solar pumping for a solid-state laser. Here we propose a solar concentrating system composed of off-axis parabolic mirrors, 2D-CPCs, and rectangular diffusers, and use it to collect sunlight to side-pump a Nd:YAG solid-state laser. Simulation shows that this solar collection system provides not only high concentrating power, but also excellent pumping uniformity. Total concentration of solar power as high as 7,872.7 W and side-pumping uniformity of 98% can be realized, leading to output power that reaches 351.8 W.
The primary concentrator consists of several off-axis parabolic mirrors. A fan-circular parabolic mirror with an inner radius of 1,000 mm, an outer radius of 3,000 mm, and a height of 2,000 mm can be divided into
The three-dimensional structure of the entire solar concentrator, composed of four subsystems, is shown in Fig. 2. One end of the rectangular diffuser is connected to the outlet of the 2D-CPC, and the other end is put close to the cooling-water channel. The Nd:YAG laser rod has a size of Φ6 × 30 mm, and is cooled by a circulating-water channel with outer and inner diameters of 9 mm and 6 mm respectively.
The concentrating characteristics of the primary concentrator are simulated by ray tracing with TracePro, and a circular light spot is obtained at the focal plane of each off-axis parabolic mirror. The irradiance diagram is shown in Fig. 3. According to the typical reduction of sunlight power density to 1/
To maximize the solar power converging on the side of the laser rod and improve the uniformity of the light spot, it is necessary to optimize the design of the number of parts
where
Here
The fan-shaped parabolic mirror is divided into
The total collected power is the sum from the
When the fan-circular parabolic mirror is divided into 4 (
Here
The heat distribution in the laser rod can be expressed as [25]
where
The temperature distribution in the laser rod is analyzed using the Comsol multiphysics software. The average absorption coefficient of the Nd:YAG laser rod across the whole solar spectrum is taken to be 0.35 cm^{−1} [26]. The surface heat-transfer coefficient is 1 W/(cm^{2}·℃) and the temperature of the cooling water is 293 K.
Nd:YAG is a typical four-level laser medium. By solving the four-level rate equations, the laser output power can calculated with the equation [27]
where
Here ν is the pump frequency and
When the Nd:YAG rod is pumped by sunlight, the laser absorption and solar-spectrum overlap is 0.16 [28]. The transmission efficiency is 0.85 [28], and the absorption efficiency is 0.82 in this laser system. The average weighted wavelength of sunlight is 660 nm [11], the laser output wavelength is 1,064 nm, and the Stokes factor is 0.62 [11]. The beam overlap efficiency is the ratio of the cavity mode volume to the pump volume of the laser rod; its value is assumed to be 0.91. The quantum efficiency is 0.9 [28], the fluorescence lifetime is 230 μs [27], and the stimulated emission cross section is 6.5 × 10^{−19} cm^{2} [27]. The scattering coefficient of the laser material is 0.003 cm^{−1} [28]. Based on Eqs. (5)–(8), the output power of this solar laser with varying reflectivity of the output cavity mirror and varying solar pump power are calculated, and the results are shown in Fig. 10. The reflectivity of the other end of the crystal is assumed to be 100%. When the reflectivity of the output cavity mirror is 83%, a maximum laser output power of 351.8 W is obtained, and the threshold pump power, the slope efficiency, and solar-to-laser conversion efficiency are 616 W, 4.85%, and 4.5% respectively.
To achieve uniform side pumping of a high-power solar laser, a solar concentrating system is proposed. The concentrator system consists of four off-axis parabolic mirrors with a focal length of 1,000 mm, and four 2D-CPCs and rectangular diffusers. To collect more solar power, the number of off-axis parabolic mirrors, the acceptance half-angle of the 2D-CPCs, and the length of the diffusers are optimized. When four off-axis parabolic mirrors are adopted, the solar power received by the side of the laser rod is the highest, being up to 7,872.7 W; the corresponding optimal acceptance half-angle of the 2D-CPCs is 40°; and the optimal length of the rectangular diffusers is 92 mm. The irradiance uniformity on the side of the laser crystal rod reaches 98%. Then the transverse temperature distribution of the laser rod is analyzed, and the center temperature is found to be 359 K, while the surface temperature is 325 K. Finally, based on the four-level rate equations, the output characteristics of the solar laser are analyzed. When the reflectivity of the output cavity mirror is 83%, the maximum laser output power, the threshold pump power, the slope efficiency, and the solar-to-laser conversion efficiency are 351.8 W, 616 W, 4.85%, and 4.5% respectively.
The authors declare no conflicts of interest.
Data underlying the results presented in this paper are not publicly available at the time of publication, but may be obtained from the authors upon reasonable request.
National Natural Science Foundation of China (61675129); the Natural Science Foundation of Hubei Province (2014 CFB671); Natural Science Foundation of Shanghai (19ZR1427100); Research Fund for Excellent Dissertation of China Three Gorges University (2021SSPY149).