Stable Emissions from a Four-Rod Nd:YAG Solar Laser with ±0.5° Tracking Error Compensation Capacity

: Conventional solar-pumped lasers rely on expensive and highly accurate solar tracking systems, which present a significant economic barrier to both solar laser research and practical applications. To address this challenge, an end-side-pumped four-rod solar laser head was designed and built for testing at PROMES-CNRS. Solar radiation was collected and concentrated using a he-liostat–parabolic mirror system. A fused silica aspheric lens further concentrated the solar rays into a flux homogenizer within which four Nd:YAG rods were symmetrically positioned around a reflective cone and cooled by water. Four partially reflective mirrors were precisely aligned to extract continuous-wave 1064 nm solar laser power from each laser rod. The prototype demonstrated stable multibeam solar laser operation with the solar tracking system turned on. Even when the tracking system was turned off, the total output power extracted from the solar-pumped laser remained stable for 1 min, representing, to the best of our knowledge, the first successful demonstration of a stable multibeam solar laser operation without solar tracking. For typical solar tracking errors up to ±0.5°, the loss in the total solar laser power produced was only about 1%, representing an 8.0-fold improvement over the previous solar laser experiments under tracking error conditions.


Introduction
Laser technology is widely used in modern society, playing a crucial role in various applications, such as manufacturing, material processing, telecommunications, defense, and healthcare [1].However, the intensive electricity consumption associated with laser technology raises concerns regarding its costs and environmental impacts.For instance, laser additive manufacturing offers potential environmental benefits, such as reduced material use and the elimination of molds, dies, cutting tools, and cutting fluids.Nevertheless, it can consume up to 100 times more energy when compared to conventional manufacturing methods [2].To address these challenges, there is growing interest in the development of solar-pumped lasers [3].These systems use natural sunlight to directly pump solid-state lasers, representing a sustainable and cost-effective alternative for laser material processing, particularly in off-grid locations with abundant sunlight [4].Solarpumped laser systems are particularly well suited for space-based applications, including long-range optical communication and networking [5], atmospheric remote sensing and pollution control [6], laser-induced asteroid trajectory deviation [7], probe photonic acceleration [8], and wireless energy transmission [9].Furthermore, by completely avoiding semiconductor laser arrays and their inherent limitations, such as limited lifetime and performance degradation over time, reliable spaceborne laser operations could be achieved for extended durations.
Solar energy has been used to pump solid-state lasers since the 1960s [10,11].Over the last two decades, significant advancements have been made in optical pumping designs and gain media [12][13][14][15][16][17][18].A few research teams have played a crucial role in this field, primarily utilizing Cr:Nd:YAG and Nd:YAG crystals as laser media [12][13][14] and, more recently, exploring the potential of the Ce:Nd:YAG laser crystal [15,16].Solar-pumped laser performance can be evaluated by the system's collection efficiency, which measures the laser power emitted per unit area of the primary concentrator, usually parabolic mirrors or Fresnel lenses.Still, the solar-to-laser conversion efficiency is considered a more reliable metric for comparing the efficiency of different solar laser systems.By considering solar irradiance, which varies with geographic location, the solar-to-laser conversion efficiency evaluates the percentage of laser power produced from the total available input of solar power.A state-of-the-art solar-to-laser conversion efficiency of 4.6% was achieved by Liang et al. in 2022 [15].In the experiment, a heliostat-parabolic mirror system was used to end-side pump three 2.5 mm diameter, 25 mm length Ce:Nd:YAG rods within a single conical pump cavity.Considering an effective collection area of 0.4 m 2 , a record collection efficiency of 41.3 W/m 2 was also experimentally attained [15].
Despite solar laser emissions having been already achieved without the use of concentration optics [17], in order to reach and maintain a competitive solar-to-laser conversion efficiency, the incorporation of not only concentrators but also a highly accurate solar tracking system (STS) is required [18].Nevertheless, doubling the accuracy could lead to a 10-fold increase in cost [19].Additionally, highly accurate STSs require continuous operation, constantly rotating their motors to precisely follow the Sun's trajectory.This continuous motion leads to increased energy consumption and reduced system lifetime.Hence, there is an economic advantage in developing solar laser systems capable of sustaining performance for short durations using low-cost STSs, like those commonly employed in photovoltaic energy systems [19].
The ability of solar laser systems to compensate for solar tracking errors has been evaluated based on the solar tracking error width at 10% laser power loss (TEW10%).In 2022, a dual-rod side-pumping prototype was experimentally studied, achieving up to 1.40° TEW10% in the vertical configuration; however, the solar laser's efficiency was seriously limited by its side-pumping configuration [18].End-side-pumping schemes lead to higher efficiencies; however, focusing the concentrated solar radiation onto the end face of a single laser rod requires a highly accurate STS [15].Therefore, multi-rod end-sidepumping solar laser designs were numerically studied, demonstrating the higher efficiency of end-side-pumping configurations as compared to that of side-pumping, while attaining high solar tracking error compensation capacity [20,21].Furthermore, multibeam laser systems hold tremendous potential for significantly reducing processing time in industry [22].By using beam overlapping techniques to increase intensity or optimizing each beam for specific tasks within the overall procedure, these systems can rapidly execute tasks that would take days or even weeks to perform using a single beam [23,24].
In this work, an end-side-pumped four-rod solar laser head was designed and built for testing at PROMES-CNRS solar facility in Odeillo, France.A heliostat-parabolic mirror system collected and concentrated the solar radiation towards the solar laser head composed of a fused silica aspheric lens, a flux homogenizer, a reflective cone, and four Nd:YAG rods, actively cooled by water.Each Nd:YAG rod had its top end face coated with a high-reflection 1064 nm coating (HR 1064 nm).A mini output mirror with a partial reflection 1064 nm coating (PR 1064 nm) was precisely aligned with each laser rod, forming four identical optical resonators.Stable multibeam solar laser operation was demonstrated with the STS turned on.Even when the STS was turned off, the total output power extracted from the solar-pumped laser remained stable for 1 min, representing, to the best of our knowledge, the first successful demonstration of a stable multibeam solar laser operation without solar tracking.For typical solar tracking errors of up to ±0.5°, the four-rod solar laser head achieved a loss in the total solar laser power produced of about 1%, representing an 8.0-fold improvement over that demonstrated by the dual-rod side-pumping prototype that was previously studied [18].The reduction in the sensitivity of the solar laser head to variations in the solar angles can significantly alleviate the necessity of expensive, high-precision solar trackers.

Solar Energy Collection and Concentration System
In order to harvest the necessary input power to stimulate laser emission, a heliostatparabolic mirror system at PROMES-CNRS was considered, as shown in Figure 1a.The Sun's annual path in Odeillo, France (latitude 42°29'36"N, longitude 2°01'44"E) is also represented.Figure 1b presents an illustration of the medium-sized solar furnace (MSSF) used in the experiments.The heliostat was capable of rotation in two axes, enabling it to compensate for solar tracking errors in both azimuth and altitude directions.The 36 flat, square-shaped mirrors mounted on the heliostat, each one with a 0.25 m 2 collection area, and the 2 m diameter parabolic mirror installed inside the laboratory were back-surface silver-coated, presenting a measured total combined reflectance of only 59%.A shutter controlled the solar power that entered the laboratory.

End-Side-Pumped Four-Rod Solar Laser Head
Figure 2a,b present the front view of the solar laser head composed of the fused silica aspheric lens of 99.995% optical purity, the rectangular-shaped flux homogenizer within which the four Nd:YAG rods were water-cooled, and the reflective cone positioned at the center of a rod holder.Figure 2c shows the four small PR 1064 nm output mirrors used to extract continuous-wave 1064 nm solar laser power from the four 4.5 mm diameter, 15 mm length Nd:YAG rods.Four positioners were mechanically fixed into the laser head in order to individually place and align each one of the four PR 1064 nm output mirrors.The solar laser head was mounted on top of an X-Y-Z positioner, allowing precise adjustments in all the three directions.As shown in Figure 3a, the aspheric lens further concentrated the solar radiation towards the entrance of the homogenizer.The front surface of the lens (z) followed the sag equation (Equation ( 1)), with an aspheric coefficient α2 of −0.0005, a radial distance r from the optical axis of 43.5 mm, an input face with a radius of curvature c of 60 mm, and a conic constant k of 0. The 33 mm thick (LL), 87 mm diameter (DL) aspheric lens had a plane output surface.
Fused silica was the material chosen for the aspheric lens due to its resistance to thermal shock, low coefficient of thermal expansion, and transparency over the Nd:YAG absorption spectrum.In addition, since its index (nsilica = 1.46) was relatively higher than that of water (nwater = 1.33), the contact of the output surface of the aspheric lens with water ensured efficient optical coupling.Due to its low viscosity, easy availability, high specific heat, and thermal conductivity, water was primarily used to remove the heat in the laser rods associated with the intense optical pumping.Cooling water provided by the local plumbing system with 4.5 bar at room temperature was used.A 6 mm gap between the lens's flat surface and the input aperture of the homogenizer provided more than enough spacing for the passage of the cooling water.
The concentrated solar radiation was then transmitted through the rectangularshaped homogenizer with an input aperture width Win of 21 mm, an output aperture width Wout of 16 mm, and a constant height of 15 mm along its length LH of 22 mm.A silver-coated aluminum foil of 94% reflectivity was applied to each one of the four inner walls of the homogenizer.As illustrated in Figure 3b, for side-pumping (blue line), the solar rays zigzagged on the homogenizer wall and the reflective cone, entering the active media through the lateral surface of each rod.For end-pumping (green line), the solar rays were focused onto the active media through the top end face of each Nd:YAG rod, where the HR 1064 nm (99.95% @ 1064 nm) coating is deposited.These HR coatings played a crucial role in the laser emission process, allowing the passage of solar radiation while selectively reflecting photons at a wavelength of 1064 nm.Each one of the four 4.5 mm diameter, 15 mm length Nd:YAG rods also had an anti-reflection (AR) coating (<0.2% @ 1064 nm) on the back-end face.The laser crystals were acquired from Beijing Jiepu Trend Technology Co., Ltd.(Beijing, China).The four optical resonators were composed of the HR 1064 nm on top of each laser rod and the four mini PR 1064 nm output mirrors, positioned at a distance L from the AR 1064 nm coating on the back-end face of each Nd:YAG rod.A laser resonator with L = 70 mm was adopted to provide sufficient spacing for fixing and calibrating the complex opto-mechanical assembly required for the simultaneous extraction of four laser beams.The solar laser parameters mentioned above are illustrated in Figure 3c.By using Zemax® 13 non-sequential ray-tracing software, the key dimensions of the solar laser head were optimized to ensure uniform pump absorption across the four Nd:YAG laser rods.The source data were defined based on the 22 absorption peak wavelengths and the 16% absorption efficiency of the 1.0 at.%Nd:YAG laser medium, as well as the terrestrial direct solar irradiance of 800 W/m 2 .The spectral irradiance at each wavelength was consulted from the direct standard solar spectrum for one-and-a-half air mass [25].The transmission and reflectance data were programmed for the heliostat-parabolic mirror system, the flux homogenizer, the reflective cone, and the rod holder.Figure 4 presents the absorbed pump distribution on five transversal cross-sections for each of the four laser rods.The flux homogenizer and the reflective cone were crucial to ensure uniform pump power distribution among the four Nd:YAG rods, considering shadowing effects and solar tracking error conditions.The absorbed pump power data from the Zemax ® analysis was then imported into the LASCAD TM 3.3 software to optimize the PR output mirror parameters.A mean absorbed and intensity-weighted solar pump wavelength of 660 nm was considered [26].For 1.0 at.%Nd:YAG media, a fluorescence lifetime of 230 μs, a stimulated emission cross section of 2.8 × 10 −19 cm 2 [27], and an absorption/scattering loss of 0.002 cm −1 were defined [15].Through finite element analysis, an optimized reflectivity of 98% and a radius of curvature of -10 m were determined for the four mini PR 1064 nm output mirrors.

Methods and Measurements
The solar laser prototype was first designed and built in Lisbon in 2023 and then tested at the PROMES-CNRS solar facility.The experiments were conducted on 20 July 2023 with high diffusivity and an average direct solar irradiance of 800 W/m 2 , measured locally by a Kipp and Zonen CH1 pyrheliometer on a Kipp and Zonen 2AP solar tracker from Kipp and Zonen, Delft, The Netherlands.The external annular area of the MSSF parabolic mirror was masked so that only a 1.48 m diameter central circular area was used.Note that the MSSF parabolic mirror had a central circular opening with a diameter of 0.30 m, as previously illustrated in Figure 1b.An effective collection area of 1.12 m 2 was considered by discounting the shadow area caused by the solar laser head, the X-Y-Z positioner, the blades of the shutter, and the gap between the heliostat mirrors.The input solar radiation was controlled by the rotation angle of the shutter.A Thorlabs PM100D (Newton, NJ, USA) power meter measured the total output power extracted from the solar-pumped laser.
Initially (12:30 CEST, 20 July 2023), the total output power was registered with the STS turned on and accurately following the apparent motion of the Sun. Figure 5a presents the total output power as a function of the solar power at focus with a direct solar irradiance of 790 W/m 2 .The four-rod solar laser head started laser emission with the shutter open to 73% of its maximum capacity, corresponding to an input solar power at the focus of 365 W. Upon fully opening the shutter, a 3.40 W total output power was measured.Then, the STS was turned off and the total output power extracted from the solar-pumped laser was registered after 60 s of solar laser operation without STS assistance, as shown in Figure 5b.For 800 W/m 2 direct solar irradiance, the solar laser head started laser emission with the shutter open to 72% of its maximum capacity, corresponding to an input solar power at the focus of 370 W. Upon fully opening the shutter, a 3.52 W total output power was measured.As demonstrated, the performance of the solar laser system remained unaffected, even with the STS turned off for 60 s.Considering the time and date of the experiment (12:50 CEST, 20 July 2023) and its geographical position (latitude 42°29'36"N, longitude 2°01'44"E), it is possible to determine the variation in both the azimuth (Δα) and altitude (Δh) solar angles during the time that the STS was turned off [18].For 60 s, that corresponded to Δα = 0.5° and Δh = 0.1°.In order to study the performance of the four-rod solar laser prototype in terms of power stability, the normalized total output power extracted from the solar-pumped laser was continuously measured for a time t = 60 s with the STS turned on, as presented in Figure 6a.Upon fully opening the shutter, the solar laser emission was immediately detected.The total output power peaked in the initial seconds and stabilized after 15 s, maintaining the same laser output power values throughout the recorded 60 s.This initial variation was attributed to the water temperature reaching thermal equilibrium, affecting the emission cross-section of the Nd 3+ dopant due to its strong dependence on temperature.In Figure 6b, the STS was turned off while the shutter was fully opened, yet the total output power remained consistent, demonstrating stability even without the STS working.It is worth noting that after 60 s, the STS computer displayed a complete misalignment of the Sun's position.As the Sun apparently moves in the sky along the day, the variations in both azimuth and altitude angles can be considered as azimuth and altitude solar tracking errors, respectively, when the STS is deactivated.For a couple of hours around the solar noon, the variations in the solar angles are relatively more significant in the azimuthal direction [18].Figure 7 presents the normalized total solar laser power produced from the four-rod solar laser prototype as a function of the azimuth solar tracking error, since these results were obtained around the local solar noon at 13:00 CEST.First, the shutter was fully opened, and the four-rod solar laser prototype worked with the STS turned on until the water inside the laser head reached thermal equilibrium.Then, the STS was stopped (t = 0 s), and the total output power extracted from the solar-pumped laser was measured without Sun tracking for 2 min.The Sun apparently kept moving and, consequently, the focal spot changed its position (1-3) as shown in Figure 7.During the first minute without solar tracking, the total output power remained stable.The experiment continued for another minute, with the total output power decreasing by approximately 8%.Considering the time and date of the experiment (13:00 CEST, 20 July 2023) and its geographical position (latitude 42°29'36"N, longitude 2°01'44"E), it is possible to determine the variation in both the azimuth and altitude solar angles during the time that the STS was turned off [18].For 2 min, that corresponded to Δα = 1.0° and Δh = 0.2°.

Discussion
The end-side-pumped four-rod solar laser head was able to produce a maximum multimode solar laser power of 3.52 W using a 1.12 m 2 collection area, resulting in a collection efficiency of 3.14 W/m 2 .Considering a direct solar irradiance of 800 W/m 2 , the solar-to-laser conversion efficiency was only 0.4%.The performance in terms of efficiency fell significantly below the state-of-the-art solar laser efficiency due to a combination of the following issues: 1.The collection and concentration system: The end-side-pumped four-rod solar laser head was tested at the PROMES-CNRS MSSF facility, which presents a combined reflectance of only 59%.Still, the accurate dual-axis STS was crucial to demonstrate the stability of the total output power extracted from the solar laser prototype; 2. Active media: Recent progress in solar-pumped laser efficiency has been possible by exploiting the superior absorption efficiency of the Ce:Nd:YAG laser medium [28].However, thermal issues also increased, leading to the fracture of the active medium when subjected to intense solar pumping levels [15].In contrast, the Nd:YAG crystal, while exhibiting a relatively lower absorption efficiency, stands as a well-established laser medium characterized by robust mechanical strength and good thermal conductivity.This makes it a prominent choice within the solid-state laser industry and solar laser research; 3. Resonator length: The output mirrors are usually mounted relatively close (10-20 mm) from the AR 1064 nm coating to ensure that the energy of the higher-order modes is not wasted by diffraction losses [15].In this experiment, the primary focus was not on achieving the highest efficiency, so each mini output mirror was positioned 70 mm away from the AR 1064 nm coating on the back-end face of each Nd:YAG rod.This spacing allowed for the proper installation and alignment of the complex opto-mechanics required to fix and calibrate the four separate mini output mirrors.
To the best of our knowledge, this end-side-pumped four-rod solar laser head achieved the first successful demonstration of a stable multibeam solar laser operation without solar tracking.In previous solar tracking error experiments conducted by Tibúrcio et al., the side-pumped dual-rod solar laser head lost over 10% of the initial total output power extracted from the solar-pumped laser after 1 min of operation without solar tracking [18].In this experiment, the total output power extracted from the solar-pumped laser remained stable for 1 min with the STS turned off.After 2 min, the total output power only dropped by approximately 8%.
In Figure 8, the normalized total output power is presented as a function of the azimuth solar tracking error, ranging from the optimal alignment (0.0°) to ±1.0°, in order to compare this study with that of Tibúrcio et al. [18].The variation in output power (∆P) is also represented as a percentage for the azimuth solar tracking errors of 0.5° and 1.0°.Table 1 summarizes the progress achieved by this study in solar laser operation under solar tracking error conditions.Figure 8. Normalized total output power as a function of the azimuth solar tracking error, ranging from the optimal alignment (0.0°) to ±1.0° for this study and for the work of Tibúrcio et al. [18].The variation in solar laser output power is also represented as a percentage for azimuth solar tracking errors of 0.5° and 1.0° (∆P0.5° and ∆P1.0°, respectively).Table 1.Progress on solar laser power stability under solar tracking error conditions.

Tibúrcio et al. (2022) [18]
This study Improvement ∆P±0.5°8% 1% 8.0 times ∆P±1.0°-8% -TEW8% 1.0° 2.0° 2.0 times For typical solar tracking errors of up to ±0.5°, the four-rod solar laser head achieved a variation in the total solar laser power produced ∆P±0.5° of about 1%, representing an 8.0fold improvement over Tibúrcio et al.'s study [18].It was not possible to calculate the TEW10% for this study, as the total output power only dropped 8% during the recorded 2 min.Instead, the TEW8% was considered.This study attained a TEW8% of 2.0°, which is 2.0 times higher than that verified by Tibúrcio et al. [18].

Conclusions
Solar-pumped laser technology typically requires costly and highly accurate solar tracking systems, imposing a substantial financial barrier on solar laser research and applications.To address this challenge, an end-side-pumped four-rod solar laser head was designed using Zemax ® and LASCAD TM software and built for testing at the PROMES-CNRS solar facility in Odeillo, France.The MSSF heliostat-parabolic mirror system collected and concentrated the solar radiation into the solar laser head composed of the aspheric lens and the flux homogenizer, within which four Nd:YAG rods were symmetrically positioned around a reflective cone and cooled by water.The four PR 1064 nm output mirrors were accurately aligned with their corresponding laser rod to extract a continuous-wave 1064 nm solar laser.In the experiment, the four-rod solar laser prototype demonstrated a stable multibeam solar laser operation with the STS turned on.Even when the STS was turned off, the total output power extracted from the solar-pumped laser remained stable for 1 min.After 2 min, the total output power only dropped by approximately 8%.For typical solar tracking errors of up to ±0.5°, the four-rod solar laser head achieved a variation in the total solar laser power produced of about 1%, representing an 8.0-fold improvement over the state-of-the-art solar laser operation under tracking error conditions [18].
By significantly reducing the solar laser head's sensitivity to variations in solar angles, the STS's stepper motor does not need to be continuously running, thus reducing the power consumption and extending the lifetime of the system.Moreover, the end-sidepumped four-rod solar laser approach offers a cost-effective solution to build a stable solar laser system with a cheap, low-accuracy STS.

Figure 1 .
Figure 1.PROMES-CNRS MSSF heliostat-parabolic mirror system.(a) Photograph of the system operating on 20 July 2023 at 16:06 CEST.(b) Illustration of the system redirecting and concentrating the solar radiation towards a solar laser head mounted on top of a positioning system.A shutter controlled the solar radiation that entered the laboratory.

Figure 2 .
Figure 2. Photograph of the solar laser head and the four laser resonators.(a) Front view showing the aspheric lens and the flux homogenizer within which (b) four Nd:YAG rods were water-cooled.The reflective cone positioned at the center of the rod holder is also shown.(c) Back view of the solar laser head with four small output couplers accurately aligned to their respective rods.

Figure 3 .
Figure 3. Design of the solar laser head.(a) 3D view of the solar laser system composed of the fused silica aspheric lens, the flux homogenizer, the reflective cone, and the four Nd:YAG rods.The solar laser resonant cavities are also represented.(b) The interior of the flux homogenizer, where the laser rods were end-side-pumped and water-cooled.(c) Top view of the solar laser system and its key dimensions.

Figure 5 .
Figure 5.Total output power as a function of the solar power at the focus of the MSSF parabolic mirror.The measurements were taken (a) with the STS turned on and (b) after 60 s of solar laser operation without STS assistance.

Figure 6 .
Figure 6.Normalized total output power during 60 s (a) with the STS turned on and (b) with the STS turned off at t = 0 s.In the latter, the STS computer window displayed a complete misalignment with the Sun's position at t = 60 s.

Figure 7 .
Figure 7. Normalized total output power as a function of the azimuth solar tracking error (Δα), ranging from Δα = 0.0° (position 2) to Δα = ±1.0°(position 1 and 3).These results were obtained around local solar noon at 13:00 CEST and the variation in altitude solar tracking error (Δh) was relatively smaller.