To significantly improve the solar-pumped laser beam brightness, a multi-Fresnel lens scheme is proposed for side-pumping either a single-crystal Nd:YAG or a core-doped ceramic Nd:YAG disk. Optimum laser system parameters are found through ZEMAX and LASCAD numerical analysis. An ultrahigh laser beam figure of merit of 53 W is numerically calculated, corresponding to a significant enhancement of more than 180 times over the previous record. collection efficiency is also numerically attained. The strong thermal effects that have hampered present-day rod-type solar-pumped lasers can also be largely alleviated.
© 2012 Optical Society of America
Solar-pumped lasers have gained an ever-increasing importance in recent years . Compared to electrically powered lasers, solar laser is much simpler and more reliable due to the complete elimination of the electrical power generation and conditioning equipment. This technology has a large potential for many applications, e.g., high-temperature materials processing, renewable magnesium-hydrogen energy cycle, free space laser communications, space to earth power transmission, and so on. Highly efficient solar-pumped laser with ultrahigh brightness thus become essential to the success of these applications.
The first solar-pumped laser was reported by Young in 1966 . Since then, researchers have been exploiting parabolic mirrors and Fresnel lenses to attain enough concentrated solar radiation at focal point, and several pumping schemes have been proposed for enhancing solar laser output performance [3–11]. The progress with Fresnel lenses and chromium codoped Cr:Nd:YAG ceramic laser medium  has revitalized solar laser researches. collection efficiency has been reported in 2011  by utilizing an economical Fresnel lens and the most widely used Nd:YAG single-crystal rod. The most recent solar-pumped laser with a liquid light-guide lens and a Nd:YAG rod has produced collection efficiency in 2012 .
Ultrahigh brightness renewable solar laser beams can be focused to heat magnesium oxide (MgO) to more than 4000 K and thus create pure magnesium [8,9]. Magnesium can be easily stored and transported in the form of “pellets” and, when necessary, reacts with water to produce both hydrogen and thermal energy for fuel cell vehicle applications. Laser beam brightness is given by the laser power divided by the product of the beam spot area and its solid angle divergence. This product is proportional to the square of the beam quality factor . The brightness figure of merit is then defined  as the ratio between laser power and the product of and . Most recently, a large improvement in solar-pumped laser beam brightness has been achieved by side-pumping of a thin Nd:YAG single-crystal rod. A record-high figure of merit of 0.29 W has been registered .
In rod geometries, however, the heat is removed on the circumferential surface of the cylinder, thereby generating a radial thermal gradient [12,13]. The change in temperature within a laser rod causes a thermal distortion of the laser beam. This imposes a limit to the extraction efficiency and energy scaling of lasers. The thin-disk laser concept, initially developed for diode-pumped laser systems [14,15], is one of the most suitable approaches when high power, high efficiency, and good beam quality are required simultaneously. Due to small volume-to-surface-area ratio, the gain medium can be cooled very efficiently. The direction of the heat flow is hence mainly parallel to the laser cavity axis, which in combination with short optical path length through the active medium, results in a reduction of the thermal lensing effect and thermally induced aberrations by orders of magnitude compared to typical high-power rod lasers. Valuable experiences have been gained by our research team in building a fiber optic pump beam shaping system for the high-power thin-disk laser . We therefore propose a new concept of applying thin-disk laser technology to solar-pumped lasers in this paper. It can expand significantly the frontier of solar laser beam brightness, while alleviating the thermal management problems that have hampered solar-pumped lasers. Solar energy collection and concentration is achieved through the combination of plane mirrors and Fresnel lenses, symmetrically aligned around the Nd:YAG laser disk. The concentrated solar radiation from each Fresnel lens is then focused to the lateral face of the disk through a toroidal fused silica lens. Optimum pumping conditions and solar laser beam parameters are found through ZEMAX and LASCAD numerical analysis, respectively, for different Nd:YAG single-crystal disks. The solar laser performances of core-doped ceramic Nd:YAG disks with -doped YAG cladding isstudied and compared to that of single-crystal disks. 53 W figure of merit is numerically calculated, which surpasses the record-high figure of merit for solar laser  more than 180 times, and the strong thermal effects that have hampered the progress of rod-type solar-pumped laser can be drastically alleviated.
2. Description of Ultrahigh Brightness Nd:YAG Disk Laser Pumping Scheme
The solar-pumped disk laser scheme in Fig. 1 is composed of 12 Fresnel lenses () and 12 plane mirrors (), radially mounted for side-pumping of the Nd:YAG disk.
The Fresnel lenses are evenly distributed along the 0.8 m radius circumference around the center of the laser disk. The formation has 12-fold symmetry. To redirect the incoming solar radiation towards the Fresnel lenses, each plane mirror is mounted beside the Fresnel lens at a 45° angle, as shown in Fig. 1. Each Fresnel lens has area and 0.8 m focal length. It is made of Polymethyl Methacrylate (PMMA) material, which is transparent at visible and near infrared wavelengths, but absorbs the infrared radiation beyond 2200 nm and cuts undesirable UV solar radiation below 350 nm. Solar tracking can be achieved by mounting the whole laser system onto a two-axis heliostat that follows the Sun continuously in direct tracking mode. Incoming solar radiation is focused to the laser disk, firstly through the Fresnel lenses and secondly through the toroidal fused silica lens, which further compresses the concentrated solar radiation from the focus of each Fresnel lens to the lateral face of the disk, as shown in Figs. 1 and 2.
Fused silica is an ideal optical material for Nd:YAG laser pumping since it is transparent over the Nd:YAG absorption spectrum. It has a high softening point and is resistant to scratching and thermal shock. High optical quality (99.999%) fused silica torus lenses can be manufactured by optical machining and polishing . The back and lateral surfaces of the Nd:YAG laser disk are directly cooled by water, which also helps to eliminate some UV and IR radiation, which does not contribute to lasing. The cooled back surface of the disk is 1064 nm HR coated, while the front surface is 1064 nm AR coated. The laser resonant cavity is formed by both the 1064 nm HR mirror and the output coupler, as shown in Fig. 2. The optimized output coupler reflectivity, usually varying between 90% and 98%, can be achieved by LASCAD analysis. A circular plane reflector is also placed below the cooled surface of the disk for a more efficient pump light coupling to the disk.
3. Numerical Analysis of Laser Output Performances of Single-Crystal Nd:YAG Disks
ZEMAX nonsequential ray tracing is used to find the optimum pumping parameters and the mounting positions of all optical elements. The standard solar spectrum for one-and-a-half air mass (AM1.5)  is used as the reference data for consulting the spectral irradiance () at each wavelength. The terrestrial solar irradiance of is considered in ZEMAX software. The effective pump power of the light source takes into account the 16% overlap between the absorption spectrum of the Nd:YAG medium and the solar spectrum . The solar half-angle of 0.27° is also considered in the analysis. The absorption spectrum of Polymethyl Methacrylate (PMMA), fused silica, and water materials are included in ZEMAX numerical data to account for absorption losses. The above materials play an important role in preventing UV solarization and IR heating to the Nd:YAG medium.
Nd:YAG is the most widely used solid-state laser material and is a promising candidate in high-power thin-disk lasers. It has been demonstrated as the best material under solar pumping because of its superior characteristics on thermal conductivity, high quantum efficiency, and mechanical strength compared to other host materials [3–11]. For 1.1% Nd:YAG laser medium, 22 absorption peaks are defined in ZEMAX numerical data [9,11]. All the peak wavelengths and their respective absorption coefficients are added to the glass catalogue for Nd:YAG material in ZEMAX software. Solar irradiance values for the above-mentioned 22 peak absorption wavelengths could be consulted from the standard solar spectra for AM1.5 and saved as source wavelength data. In ray tracing, the laser disk is divided into a total of 18,000 zones. The path length in each zone is found. With this value and the effective absorption coefficient of 1.1% Nd:YAG material, the absorbed power within the laser medium can be calculated by summing up the absorbed pump radiation of all zones. The absorbed pump flux data from the ZEMAX analysis is then processed by LASCAD software to study the laser beam parameters and quantify the thermal effects applied in the active medium.
In LASCAD analysis, the optical resonator is comprised of two opposing parallel mirrors at right angles to the axis of the laser disk. One end mirror is high reflection coated (HR, 99.98%) and corresponds to the HR-coated surface of the disk. The output coupler is partial reflection coated (PR). The amount of feedback is determined by the reflectivity of the mirrors. Different disk heights give rise to different round-trip losses for LASCAD analysis. The round-trip resonant cavity loss is the sum of the absorption and scattering losses for laser emission wavelength within the laser medium and imperfect HR and AR losses. For , for example, a round-trip loss of 0.90% is assumed. All the technical parameters and data used in both ZEMAX and LASCAD numerical analyses have already been confirmed by our previous experimental results [9,11]. For correct parameterization of the laser system, the laser output performances of different diameter () and height () disks are studied. For each case, the curvature radius , ranging typically between 10 and 14 mm, of the toroidal lens is optimized to obtain the maximum absorbed pump power within the Nd:YAG medium.
Figs. 3 and 4 represent the behavior of both multimode laser power and brightness figure of merit for single-crystal disks with different and . The resonator cavity length is optimized according to the different disks to attain the highest laser beam brightness. The radius of curvature of the output coupler (RoC) is assumed as .
Maximum multimode laser power of 29.6 W is numerically achieved by pumping the disk with . collection efficiency is hence calculated. By reducing the disk height to 6 mm, multimode laser power of 28.7 W is calculated for the same disk diameter. For the disk, multimode laser powers between 26 W and 28 W can also be achieved.
Brightness figure of merit can be easily improved by pumping disks with small height and large diameter. High figure of merit of 36 W is then numerically measured for the Nd:YAG disk. This result is 124 times higher than the current brightness figure of merit for solar-pumped laser with rod geometry . The lowest figure of merit of 1.8 W is found for the Nd:YAG disk with and . This value is still 6.2 times higher than the record figure of merit .
4. Numerical Analysis of Laser Output Performances of Core-Doped Nd:YAG Ceramic Disks and its Comparison to Single-Crystal Nd:YAG Disks
Polycrystalline ceramic Nd:YAG laser material can act as host material and enables new possibilities in designing the laser medium with respect to dopant concentration as well as distribution, size, and geometry. A single-crystal undoped YAG cap and an doped active medium can be bonded together for slab geometries. However, it is not a viable concept to bond a cladding layer around a single-crystal rod. Using the ceramic technology instead, an undoped cladding around a doped core can be realized for the rod geometry. The core-doped ceramic mediums are laser active in the -doped core only, and bonded with the same host material, either undoped or doped, with a different element that effectively absorbs light at the signal wavelength. This technology has been applied in diode-pumped arrangements with rod geometries and has shown potential to provide better laser beam brightness when compared to conventional single-crystal rods [20,21]. Since the medium cross-section is widened by the cladding, wider Gaussian intensity distributions can be accommodated in the laser active region without truncating its wings. This will lead to a more efficient use of the built-up inversion as the average intensity in the doped part of the laser medium becomes higher.
Among various absorber materials, is found to be the best candidate to Nd:YAG laser, due to its spectroscopy properties. It is also effective in suppressing parasitic oscillations that occur at the disk edges which limit extraction efficiency and energy scaling of lasers [22–24]. For this reason, the influence of core-doped Nd:YAG disks with cladding on laser performance is studied. The laser performance of the Nd:YAG single-crystal disks, analyzed in section 3, is compared to that of core-doped Nd:YAG disks with same height and Nd:YAG diameter , as represented in Fig. 5.
The absorption spectrum of 5.0% at has five strong peaks in the NIR region at the central wavelengths of 1070, 1220, 1350, and 1460 nm. For the laser wavelength of 1064 nm, the absorption coefficient of reaches , while low absorption coefficients of about are detected for the absorption peaks of Nd:YAG . Therefore, the remaining IR radiation can be strongly absorbed, reducing the thermal effects within the Nd:YAG medium. The absorption spectrum of is added to the glass catalogue in ZEMAX software. The numerical simulations show that the absorption efficiency depends on the cladding diameter . An optimized is then found for each core diameter .
The heat load within both the single-crystal and the core-doped Nd:YAG disks with the same is given in Fig. 6, for three different disks . Red means near maximum heat load for these plots, whereas blue means little or no heat generation. The absorbed pump power is also given in each case.
For both the single-crystal and the core-doped disks, the heat load inside the active medium is reduced with increased diameter, despite the increase of absorbed pump power, as observed in Fig. 6. This largely alleviates the thermal lensing effects, and the achievement of high-brightness laser beam becomes possible, as already demonstrated in Fig. 4. When the absorption profile is centrally peaked, the temperature on the axis increases further, resulting in stronger thermal lensing at the center, higher-order aberrations at the periphery, and larger stress in the laser medium compared with those of uniform excitation. At high average output power, even a uniform gain distribution in a water-cooled laser medium, as shown in the single-crystal Nd:YAG disk in Fig. 6, has been shown to induce a nonparabolic heat distribution as a result of the temperature dependence of the thermal conductivity . This results in a radially dependent refractive power of the thermal lens, which has a maximum on the medium axis. Consequently, to achieve ultrahigh beam brightness, we should start with a low power deposition at the center of the medium, which can be easily achieved by the core-doped ceramic Nd:YAG disk, as shown in Fig. 6. Moreover, the absorbed pump power is also 118% more than that of single-crystal with the same Nd:YAG diameter. The influence of the core-doped disks on both multimode laser power and laser beam brightness is analyzed in Figs. 7 and 8, respectively.
The multimode laser power is largely favored by the implementation of the core-doped Nd:YAG disks, as analyzed in Fig. 7. The highest multimode laser power of 34 W is numerically calculated for the core-doped disk, corresponding to 124% improvement over that of the single-crystal disk with the same . Collection efficiency of is hence calculated. An optimized of 16 mm is calculated in this case.
As shown in Fig. 8, solar laser beam brightness figure of merit is increased with the use of core-doped disks, especially for larger diameters. 53 W ultrahigh figure of merit can be reached by pumping the core-doped disk. This corresponds to an improvement of 147% over the figure of merit of the single-crystal disk with same and surpasses the record figure of merit by more than 180 times. Therefore the introduction of core-doped ceramic technology to solar-pumped disk laser can be an effective choice in achieving more laser beam brightness.
For achieving the highest solar-pumped laser beam brightness, a multi-Fresnel lens scheme is proposed for side-pumping either the single-crystal Nd:YAG or the core-doped ceramic Nd:YAG disk. Optimum laser system parameters are found through ZEMAX and LASCAD numerical analysis. The production of 34 W multimode solar laser power can be expected, corresponding to collection efficiency. 53 W figure of merit can be reached, surpassing by more than 180 times the record brightness figure of merit for Nd:YAG solar laser with rod geometry. Significant reduction in thermal lensing effects is predicted. Laser beam brightness can still be improved by pumping small height and large diameter laser disks.
As shown in Table 1, maximum solar laser power and collection efficiency are given by . However, the large factor of 135 degrades largely the beam brightness figure of merit to only 0.0066 W. For , , are obtained. High laser beam figure of merit is achieved. With the proposed pumping scheme, LASCAD simulation leads to beam quality factors slightly less than unity. The very low pump power deposition at the center of the medium in Fig. 6 has resulted in a thermal lens with very large focal length. Near diffraction-limited laser beam can hence be extracted by a large -shaped resonant cavity. Significant improvement in brightness figure of merit over the previous setups is therefore achieved. Even though, in recent years, a series of laser beam with has been realized experimentally [26,27], we still have some reservations regarding the LASCAD numerical calculation accuracy of the factors from the unusual non-Gaussian absorbed pump flux profiles, as given in Fig. 6. Experimental research of the proposed scheme will be carried out by us to validate the results of numerical analysis in the next step.
With the proposed approach, solar-pumped solid-state lasers can benefit largely from the advantages of thin-disk laser geometry. The frontier of solar laser beam brightness can be significantly expanded, while the thermal management problems that have plagued present-day solar-pumped lasers can be drastically reduced. Highly efficient solar-pumped laser with ultrahigh brightness can thus become possible.
This research project (PTDC/FIS/103599/2008) was funded by the Science and Technology Foundation of the Portuguese Ministry of Science, Technology and Higher Education (FCT-MCTES).
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