Scalable pumping approach for extracting the maximum TEM00 solar laser power Dawei Liang,* Joana Almeida, and Cláudia R. Vistas CEFITEC, Departamento de Física, FCT, Universidade Nova de Lisboa, 2829-516 Campus de Caparica, Portugal *Corresponding author:
[email protected] Received 12 June 2014; revised 28 August 2014; accepted 14 September 2014; posted 15 September 2014 (Doc. ID 214013); published 17 October 2014
A scalable TEM00 solar laser pumping approach is composed of four pairs of first-stage Fresnel lensfolding mirror collectors, four fused-silica secondary concentrators with light guides of rectangular cross-section for radiation homogenization, four hollow two-dimensional compound parabolic concentrators for further concentration of uniform radiations from the light guides to a 3 mm diameter, 76 mm length Nd:YAG rod within four V-shaped pumping cavities. An asymmetric resonator ensures an efficient large-mode matching between pump light and oscillating laser light. Laser power of 59.1 W TEM00 is calculated by ZEMAX and LASCAD numerical analysis, revealing 20 times improvement in brightness figure of merit. © 2014 Optical Society of America OCIS codes: (140.0140) Lasers and laser optics; (140.5560) Pumping; (140.3410) Laser resonators; (140.3530) Lasers, neodymium; (350.6050) Solar energy; (350.6830) Thermal lensing. http://dx.doi.org/10.1364/AO.53.007129
1. Introduction
The conversion of sunlight into laser light by direct solar pumping is of ever-increasing importance. This is because broadband sunlight is converted into laser light, which can be a source of narrowband, collimated, rapidly pulsed, radiations with the possibility of obtaining extremely high brightness and intensity. Nonlinear processes might be used to obtain broad wavelength coverage, including ultraviolet wavelengths, where the solar flux is very weak. Among the potential applications of solar lasers are earth, ocean, and atmospheric sensing; detecting, illuminating, and tracking hard targets in space; and deep space communications. Renewable lasers have a large potential for many terrestrial applications, e.g., high-temperature materials processing, renewable magnesium–hydrogen energy cycle and so on. The direct excitation of large lasers by sunlight also offers the prospect of a drastic reduction in the cost of coherent optical radiation for high average-power 1559-128X/14/307129-09$15.00/0 © 2014 Optical Society of America
applications. Maximizing TEM00 solar laser power to more than 50 W, for example, will most possibly lead to many interesting applications. Moreover, a highpower TEM00 solar laser can greatly reduce CO2 emissions and energy consumption of other electrical lasers powered by non-renewable sources, leading to numerous environmental and economic benefits. Up to now, solar-pumped lasers have not been viewed from this perspective. Since sunlight does not provide enough flux to initiate laser emission, additional focusing systems are usually needed to both collect and concentrate the solar radiation to excite the laser medium. Parabolic mirrors have long been explored by Young [1] and other researchers [2–6] to achieve tight focusing of incoming solar radiation. Large-size Fresnel-lens solar-pumping schemes have only surfaced within the past eight years [7]. Collection efficiency of 19.3 W∕m2 has been achieved by end-side-pumping a 4 mm diameter, 25 mm length Nd:YAG singlecrystal rod [8]. Record-high collection efficiency of 30.0 W∕m2 has been achieved with a 6 mm diameter, 100 mm length Nd:YAG single-crystal rod. However, very large M 2x M 2y 137 factors have also been 20 October 2014 / Vol. 53, No. 30 / APPLIED OPTICS
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associated with this approach [9], resulting in a dismal brightness figure of merit, defined as the ratio between laser power and the product of M 2x and M 2y , of only 0.0064 W. Because of its smooth intensity profile, low divergence, and ability to be focused to a diffraction-limited spot, it is highly desirable to operate a solar-pumped laser in the lowest-mode possible: TEM00 mode. Sidepumping configurations are very suitable for laser power scaling. They allow a more uniform pump absorption profile along the laser rod. The associated thermal loading problems can be significantly reduced. Besides, free access to both rod ends permits the optimization of more laser resonator parameters, enhancing considerably laser-beam quality. Therefore, their brightness figure of merit can be much higher than that of end-pumping approaches. A 0.29 W solar laser-beam brightness figure of merit has been achieved by side-pumping a 4 mm diameter Nd:YAG rod through the heliostat-parabolic mirror system in PROMES-CNRS [10]. This has remained as a record-high value until recently. A 1.9 W solar laser-beam brightness figure of merit has been reported by side-pumping a 3 mm diameter, 30 mm length Nd:YAG rod by a first-stage Fresnel lens, a second-stage fused silica aspheric lens, third-stage two-dimensional compound parabolic concentrators (2D-CPC) concentrator, and finally a V-shaped pumping cavity [11]. This result has surpassed the previous record value [10] by 6.6 times. Unfortunately, only 2.3 W solar laser power operating in the lowest fundamental mode (TEM00 ) has been produced. The TEM00 solar laser power collection efficiency is also limited to 2.93 W∕m2 . To substantially improve solar laser-beam brightness, a scalable TEM00 mode-pumping approach is proposed in this paper. Incoming solar radiation is first collected and concentrated by four Fresnel lenses. Each lens is then followed by its plane folding mirror, which redirects the concentrated solar light toward the 3 mm diameter, 76 mm length Nd:YAG rod by a series of solar energy concentrators. Uniform pump-radiation distributions are achieved at the light-guide rectangular output ends. Consequently, the absorbed pump flux along the thin rod is evenly spread, alleviating considerably thermal loading problems. Cooling water ensures both an effective heat removal and, not less importantly, an efficient light coupling from the light guide to the thin rod. Optimum pumping conditions and asymmetric laser resonator parameters are found through ZEMAX and LASCAD numerical analysis, respectively. On one hand, 90.4 W multimode solar laser power is attained by a 4.5 mm diameter, 76 mm length Nd:YAG rod, reaching 22.6 W∕m2 solar laser-power collection efficiency. On the other hand, high TEM00 mode solar laser power of 59.1 W is numerically achieved with the 3.0 mm diameter, 76 mm length Nd:YAG rod, resulting in an excellent brightness figure of merit of 38 W, being 20 times higher than the previous record [11] and 5938 times more than that of the most 7130
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powerful Nd:YAG laser [9]. TEM00 mode laser power collection efficiency can significantly be boosted to 14.8 W∕m2 . 2. Fresnel Lens-Folding Mirror Solar Energy Collection and Concentration System
The scalable solar energy collection and concentration system, as shown in Fig. 1, is formed by both four Fresnel lenses (F1 –F4 ) for collecting and concentrating the incoming solar radiation and four plane folding mirrors (M1 –M4 ) for reflecting solar radiation from the Fresnel lenses toward the laser head. The detailed description of the laser head will be given in both Figs. 3 and 5 in later sections. Each Fresnel lens has 1.13 m diameter, 3 mm thickness, and 2 m focal length. With four Fresnel lenses, we have 4 m2 total collection area. The center of each Fresnel lens is positioned d 1350 mm away from their common center point C, which is located h 586 mm above the center of the laser head, as shown in Fig 1. The plane folding mirrors are placed 586, 602, 618, and 634 mm, with 16 mm shifts between neighboring mirrors, below their respective Fresnel lenses, making 45° angle with the Fresnel lens optical axis. The 16 mm shift ensures the correct light coupling from each Fresnel lens to its respective large spherical input face of the secondary concentrator, as shown in Figs. 1, 3, and 4. The Fresnel lenses are made of polymethyl methacrylate (PMMA) material, which is transparent at visible and near infrared wavelengths and cuts undesirable solar radiation beyond 2200 nm and below 350 nm. An averaged transmission efficiency of 78% is numerically calculated for each Fresnel lens. By considering each Fresnel lens with 1 m2 collection area, 950 W∕m2 terrestrial solar irradiance, 95% reflectance for each plane folding mirror, 700 W solar power can be focused to the focal zone. For the 4 m2 area collection system, 2800 W solar power is assumed to reach
Fig. 1. 4.0 m2 area Fresnel lens and folding mirror solar laserpumping approach, easily scalable to 11.7 m2 area Fresnel lens; folding mirror scheme by four 1.73 m diameter Fresnel lenses.
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the large input faces of the fused silica secondary concentrators. The focal length of the Fresnel lens is highly dependent on solar spectrum wavelength, especially in UV and visible region and becomes nearly saturated in the NIR region, as shown in Fig. 2. On the one hand, the strong variation of focal length between 1.842 and 2.036 m in 300–900 nm region causes large dispersions of the concentrated solar radiations along the optical axis of the Fresnel lens. This explains the reason why our large area fused silica secondary concentrators should be used to concentrate nearly all the useful solar pumping radiations within 500–900 nm range (very valuable for pumping the Nd:YAG rod) into the rectangular light guide, and finally to the laser rod via the hollow 2D-CPC concentrator and the V-shaped cavity, as shown in Figs. 3–5. On the other hand, the approximation of the NIR focal spots from 2.036 m to more than 2.042 m for wavelengths above 900 nm leads to a strong undesirable focal hot spot, which can be partially avoided by deviating this spot away from the input face of the light guide in ZEMAX analysis. The refractive index of PMMA material varies from 1.533 to 1.482 as the solar wavelength increases from 300 to 1100 nm, as shown in Fig. 2. This wavelength dependent refractive index is programmed also in ZEMAX numerical data. It is worth noting that it is possible to scale the 4 m2 area approach to an even more powerful 11.7 m2 area pumping scheme, corresponding to using four 1.73 m diameter Fresnel lenses. The large spaces between the Fresnel lenses, as indicated in Fig. 1, allow the mounting of four 1.73 m diameter Fresnel lenses, and hence, about 8000 W solar power can be expected in their focal zones. Nevertheless, we choose the 4 m2 area pumping approach in this paper, due principally to the easy commercial availability of 1 m2 area Fresnel lens, and also the easy comparability with the previous literature [9]. Solar tracking can be achieved by mounting the whole optical system onto a two-axis solar tracker that
Fig. 3. Detailed view of the laser head, composed of the fusedsilica secondary concentrators with rectangular light guide, the hollow 2D-CPC concentrators, and the V-shaped pumping cavities, all symmetrically mounted around the 3.0 mm diameter, 76 mm length Nd:YAG rod.
Fig. 4. Example of the machining process of the 70 mm length fused silica light guide with 15 mm × 10 mm rectangular crosssection, directly from a 90 mm diameter, 155 mm length fused silica rod, already with 45 mm radius spherical input face machined from the cylindrical rod.
follows the sun continuously in direct tracking mode. The two stepper motors of the tracker are controlled by both an electronic control unit with global positioning system guidance for quick solar orientation and a photo-sensing unit for accurate solar tracking. 20 October 2014 / Vol. 53, No. 30 / APPLIED OPTICS
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Fig. 5. Detailed pumping scheme from the light-guide output ends to the long and thin laser rod through the hollow 2D-CPC concentrators. Four V-shaped cavities are mounted around the laser rod.
3. Nd:YAG Solar Laser Head with a Series of Light Concentrators
The solar laser head is composed of four fused-silica secondary concentrators with rectangular light guides, four hollow 2D-CPC concentrators, and four V-shaped pumping cavities within which the 3 mm diameter, 76 mm length Nd:YAG single-crystal rod is efficiently pumped, as shown in Fig. 3. The laser resonant cavity is formed by two opposing mirrors. One is 1064 nm high reflection coated (HR1064 nm) while the other is 1064 nm partial reflection coated (PR1064 nm). For extracting maximum multimode solar laser power, a symmetric laser resonant cavity with 476 mm length can be employed (not shown in Fig. 3 or Fig. 5.) For extracting maximum TEM00 solar laser power, the asymmetric laser resonant cavity of 1041.8 mm length is employed, as indicated in Figs. 3, 5, and 8 in the following sections. Fused silica is an ideal optical material for solar 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, which also makes it very suitable for ultra-high power solar-pumping applications. High optical-quality fused silica (99.999%) concentrators can be manufactured by optical machining and polishing. The large spherical input face, the dimensions of the rectangular light guide, the hollow 2D-CPC concentrator, and finally the V-shaped pumping cavity are all optimized by both ZEMAX and LASCAD numerical analysis to efficiently concentrate the incoming solar radiations from the Fresnel lens to the thin laser rod. Since fused silica secondary concentrator with a rectangular light guide plays a crucial role in attaining highly efficient TEM00 mode solar laser emission, 7132
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experimental research, as shown in Fig. 4, has been carried out to validate our novel pumping approach. To manufacture the large spherical input face, as shown in both Figs. 3 and 4, a 90 mm diameter, 155 mm length fused silica rod of 99.999% optical purity from Beijing Kinglass Quartz Co., Ltd. is machined and ground to the required semi-spherical dimensions. The spherical input face with a 45 mm radius is centered at O1 in Fig. 4. The light guide with 15 mm × 10 mm rectangular cross-section, 70 mm length is then cut and ground directly from the same fused silica rod, shown in Fig. 4. The 40 mm central section from O1 to O2 of the 90 mm diameter rod can be finally ground to conical shape in order to reduce the weight of the concentrator, as shown in Fig. 3 (unfinished in Fig. 4). The fused-silica secondary concentrator with the rectangular light guide, produced all in one piece, accomplishes the functions of both solar energy concentration and homogenization. It is therefore inherently much more efficient than other schemes since it avoids large optical losses associated with the possible combination of both spherical lens and light guide. In solar-pumped laser researches, the laser resonator stability depends on how well the sun is tracked. Solar tracking errors move the center of the absorption distribution inside the laser rod, resulting both in less output power and a non-uniform beam profile. The use of the light guide with a rectangular cross-section is essential to overcoming this problem [12]. The focal position of the secondary concentrator is designed to coincide with the center position O2 at the 15 mm × 10 mm input face of the light guide, as indicated in Fig. 4. Each light guide serves as a beam homogenizer by transforming the near-Gaussian profile of the concentrated light spot, incident on the 15 mm × 10 mm input face, into a uniform light distribution exiting its 15 mm × 10 mm output end face. Longer length means better output beam uniformity, but results in less transmission efficiency. 70 mm light guide length is sufficient for achieving good uniformity from the output face, while at the same time, maintains high transmission efficiency. As a result, tracking error may shift the focal spot at the input face of the light guide, causing only slight reduction in power intensity at its output end. The output radiation distribution still remains uniform. The absorbed pump distribution profile along the laser rod is therefore not seriously affected. Its laser output power can usually be more stable than other pumping schemes without pump light homogenization measures [10]. Each third-stage hollow 2D-CPC concentrator has a 16 mm × 12 mm large rectangular input aperture, a 14 mm × 8.5 mm rectangular output aperture, and a 6 mm height, as shown in Fig. 5. The hollow 2D-CPC is used to convert the rays from the 16 mm × 12 mm large-aperture emitting into a small angle, less than 40° for example, to the 14 mm × 8.5 mm small-aperture emitting into a large angle, 65° for example, thus the source étendue is preserved. This
preservation implies that irradiance is larger at output aperture than at the entrance aperture, leading to a net concentration of the pump radiation. Efficient optical coupling between the 15 mm × 10 mm output ends of the light guide and the laser rod are obtained by cooling water. The V-shaped cavity is finally used to achieve double-pass absorption of the highly concentrated pump radiation emitting from the 14 mm × 8.5 mm output aperture of the 2D-CPC concentrator. The V-shaped cavity is in close contact with the concentrator. It has a 16 mm length, a 9 mm depth, and there is a 3 mm separation between the output end aperture of the concentrator and the laser rod optical axis. The inner walls of both the hollow 2D-CPC concentrator and the V-shaped pumping cavity are bonded with a protected silvercoated aluminum foil with 94% reflectivity. As shown in Fig. 5, cooling water with 6 L∕ min flow rate first cools the thin laser rod within the V-shaped cavities, then passes through the hollow 2D-CPC concentrators and finally exits the laser head from the spaces between the fused silica light guides and the input apertures of the hollow concentrators. All the above optimized design parameters are found by both non-sequential ZEMAX raytracing and LASCAD laser cavity design code. As already explained, the asymmetric laser resonant cavity, as shown in both Figs. 3 and 5, is employed to extract the maximum TEM00 solar laser radiation from the laser head. 4. Numerical Optimization for Extracting the Maximum TEM 00 Laser Power A.
Optical Design Parameters of the Solar Laser System
The standard solar spectrum for a1.5 air mass (AM1.5) [13] is used as the reference data for consulting the spectral irradiance W∕m2 ∕nm at each wavelength. The terrestrial solar irradiance of 950 W∕m2 is considered in ZEMAX software. The effective pump power of the light source takes into account the 16% overlap between the Nd:YAG absorption spectrum and the solar spectrum [14]. The half angle of 0.27° subtended by the sun is also considered in the analysis. The absorption spectrum and the wavelength dependent refractive indexes of PMMA, fused silica and water materials are included in ZEMAX numerical data. Despite the small overlap between the Nd:YAG absorption spectrum and the solar spectrum, Nd:YAG has been demonstrated as the best material under solar pumping because of
its superior characteristic on thermal conductivity, high quantum efficiency, and mechanical strength compared to other host materials. For 1.1 at. % Nd3 -doped YAG single-crystal medium, 22 absorption peaks are defined in ZEMAX numerical data. All the peak wavelengths and their respective absorption coefficients are added to the glass catalogue 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. During ray-tracing, the active medium is divided into a total of 18000 zones. The path length in each zone is found. With this value and the effective absorption coefficient, 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 laserbeam parameters of the Nd:YAG single-crystal rods. The absorbed pump-flux distributions along eight transversal and one central longitudinal crosssections of the 3 mm diameter, 76 mm length Nd:YAG rod are shown in Fig. 6. Red means near maximum pump absorption, whereas blue means little or no absorption. Absorbed pump-light distributions still present non-uniform distribution along the thin rod, as shown by the central longitudinal absorbed pump-flux distribution along the laser rod. Nevertheless, this is the distribution that gives the maximum TEM00 laser power. It is also worth noting that a uniform pump-absorption profile along the rod can also be achieved by using other 2D-CPC with different dimensions in ZEMAX and LASCAD numerical analysis. However, the total laser output TEM00 power will be considerably reduced. When the absorption profile is centrally peaked, the temperature on the rod axis increases further, resulting in stronger thermal lensing at the center, higher-order aberrations at the periphery, and larger stress in the laser rod as compared with those of uniform excitation [15]. Consequently, to scale a solarpumped rod laser to higher average power, it is very important to start with a smoother deposition profile, having a slight minimum at the center of the laser rod, as shown by both the eight transversal absorbed pump-flux distributions and also the central longitudinal distribution in Fig. 6. Compared to the previous TEM00 pumping approach [11], the absorbed pump power is more evenly spread along the longitudinal cross-section of the 3 mm diameter, 76 mm
Fig. 6. Absorbed pump-flux distribution along both eight transversal cross-sections and one longitudinal central cross-section along the 3.0 mm diameter, 76 mm length Nd:YAG rod. The maximum absorbed pumped solar flux (about 16% of the whole solar spectrum) within the rod can reach 0.87 W∕mm3 , corresponding to about 14°C temperature increase in LASCAD analysis. 20 October 2014 / Vol. 53, No. 30 / APPLIED OPTICS
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B.
Extracting the Maximum Multimode Solar Laser Power
The absorbed pump-flux data from the ZEMAX analysis is then processed by LASCAD software. The stimulated emission cross-section of 2.38 × 10−19 cm−1, the fluorescence life time of 220 μs, and a typical absorption and scattering loss of 0.003 cm−1 for the 1.1 at. % Nd:YAG medium are adopted in LASCAD analysis. An averaged solar pump wavelength of 660 nm is also used in the analysis. The optical resonator is comprised of two opposing parallel mirrors at right angles to the axis of the laser medium. The amount of feedback is determined by the reflectivity of the mirrors. One end mirror is high-reflection (HR) coated, corresponding to the HR-coated surface of the active medium. The output coupler is partial-reflection coated, with reflectivity variable between 70%–99% according to different rod diameters. Output couplers of different reflectivity are tested individually to maximize the multimode laser power. The sum of absorption, scattering, and diffraction losses for laser emission wavelength within the active medium constitute the most important part of round-trip resonant cavity loss. Imperfect (HR) and anti-reflection (AR) coating losses of both laser medium and cavity mirrors are also an important part of the round-trip loss. For example, for a L 7.6 cm length laser rod with the typical absorption and scattering loss of α 0.003 cm−1, we have the total round-trip absorption and scattering losses of 2Lα 2 × 7.6 cm × 0.003 cm−1 4.56%. If 0.4% imperfect HR and AR coating loss is assumed, we then have 4.96% round-trip loss. The diffraction loss depends on rod diameter, cavity length, and the radius of curvatures (RoC) of cavity mirrors. Usually the diffraction loss of a large diameter rod within a short resonant cavity is nearly negligible. For example, for the 4.5 mm diameter, 76 mm length rod pumped within the symmetric resonator with L1 L2 200 mm, LT L1 L2 L 476 mm, RoC −12 m cavity mirrors, LASCAD beam propagation method (BPM) gives only 0.034% diffraction loss, finally resulting in the total round-trip loss of 5.0% for calculating the laser multimode output laser power, as given in Fig. 7. The laser output power is dependent on the rod diameter and reaches its maximum value of 90.4 W for 4.5 mm diameter rod, corresponding to a very satisfactory solar-laser collection efficiency of 22.2 W∕m2. M 2x 5.0 and M 2y 4.9 are also calculated in LASCAD analysis. The laser-beam brightness figure of merit is hence calculated as 3.7 W, corresponding to 160% enhancement over the previous record [11]. 7134
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Multimode laser power (W)
length rod, hindering the creation of strong hot spots within the crystal. Also, compared to other highpower end-pumping schemes [9], the laser-beam divergence of this approach is found to be significantly reduced in LASCAD analysis, due principally to the relatively uniform absorbed pump distributions in Fig. 6.
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Two 3 mm diameter laser rods with 70 and 82 mm length, respectively, are also tested individually with slightly scaled pumping schemes as shown in Fig. 5. The 70 and 82 mm rods are pumped through light guides with 12 mm × 10 mm, 16.5 mm × 10 mm cross-sections, respectively, while the dimensions of the large aspheric input concentrators can remain unchanged. The dimensions of the 2D-CPCs, the V-shaped cavities are also slightly scaled accordingly in order to spread the pump radiation efficiently along the 3 mm diameter rod. For the same input solar power, the multimode laser output powers from these two rods are calculated numerically with LASCAD code. Figure 7 compares the multimode laser output power levels of the 70, 76, and 82 mm length rods for different diameters ranging from 2.5 to 5 mm. The 70 mm rod requires the rectangular light guide with a 12 mm × 10 mm cross-section, which inevitably introduces more transmission losses from the focal spot to the rod. The output laser power is therefore not as high as that of the 76 mm rod. The 82 mm rod means using the guide with 16.5 mm × 10 mm cross-section, the optical coupling efficiency can be increased accordingly. However, large absorption and scattering losses along the 82 mm rod for 1064 nm laser wavelength can cause more round-trip loss within its relatively large rod volume, resulting therefore in the reduced laser power level, as compared to that of the 76 mm rod. C.
Extracting the Maximum TEM00 Solar Laser Power
The asymmetric optical resonator, as shown in Figs. 3, 5, and 8, is already found to be an excellent configuration for achieving fundamental mode laser operation [11,16]. The absorbed pump-flux data for each rod diameter, ranging 2.5–4.5 mm from the ZEMAX analysis is processed individually by LASCAD software. As shown in Fig. 9, there exists a very strong dependence of the TEM00 mode laser power on the RoCs of both HR and PR mirrors. It is very important
Fig. 8. Asymmetrical laser resonant cavity for the efficient production of TEM00 solar laser power.
TEM 00 Mode Laser Power (W)
to note that different RoC means different diffraction loss, even though absorption loss, scattering loss and imperfect coating loss remain the same (4.96% as analyzed in the previous section) for the asymmetric resonator. The total round-trip loss has to be analyzed individually for different RoCs and rod diameters. For example, for the 3 mm diameter rod, if we choose the −12 m RoC mirrors, LASCAD BPM analysis will give 0.84% diffraction loss. The total round-trip loss of 4.96% 0.84% 5.8% is hence calculated. By considering 5.8% round-trip loss in LASCAD analysis, 59.1 W TEM00 solar laser power is numerically attained. In conclusion, the resonant cavity with a −12 m RoC rear mirror (HR 99.8%) positioned at L1 165.8 mm and another −12 m RoC output mirror (with 85% reflectivity) positioned at L2 800 mm, total cavity length LT L1 L2 L 1041.8 mm can extract the maximum TEM00 laser power for the 3 mm diameter, 76 mm length rod, as shown in Fig. 8. For the same 3 mm diameter rod, however, if we choose the −2 m RoC mirrors, LASCAD BPM analysis gives only 0.05% diffraction loss, then 4.96% 0.05% 5.1% round-trip loss is used to calculate the TEM00 laser power of only 22.6 W. Optimized cavity parameters for extracting 65 60 55 50 45 40 35 30 25 20 15 10 5 0
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22.6 W TEM00 laser power with R1 R2 −2 m RoC are: L1 162 mm, L2 800 mm, and LT L1 L2 L 1038 mm. The TEM00 laser power is considerably reduced despite the low diffraction loss of only 0.05%. We attribute the significant laser power reduction to the following reason. Small RoC mirror results in small laser-oscillation mode volume along the central core region of the laser rod, causing a large mismatching with the large absorbed pumpradiation mode volume, as shown in Fig. 6. For the maximum extraction of TEM00 solar laser power from all the available absorbed solar pump power within the rod, it is preferable to establish a large oscillation mode volume by adopting large RoC mirrors. Finally, as the RoC increases, the maximum TEM00 laser power also becomes saturated, starting from −8 m to infinite RoC (flat mirror, not possibly shown in Fig. 9) at about 59.1 W power level for the 3 mm diameter rod. This result is 25.7 times more than the previous record in solar laser power. 14.67 W∕m2 TEM00 solar laser collection efficiency is also five times more than the previous record [11]. A strong influence of RoC on M 2x , M 2y factors is demonstrated in Fig. 10. On one hand, the output laser beam profile for −12 m RoC approaches a nearly perfect TEM00 Gaussian distribution, corresponding to M 2x 1.08 and M 2y 1.43, on the other hand, M 2x 1.32 and M 2y 2.2 are achieved for −2 m RoC, leading to a less favorable Gaussian profile, as shown in Fig. 10. The relatively large discrepancy in M 2x and M 2y factors are believed to be caused by the non-symmetric absorbed pump profiles in Fig. 6 and the LASCAD cavity analysis also reveals the difference in spot sizes and laser beam divergence along both X-axis and Y-axis, as shown in Fig. 8. Finally, both the laser output powers for the 3 mm diameter rod in Fig. 9 and the M 2x , M 2y factors in Fig. 10 are used to calculate the laser beam brightness figure of merit at different RoCs. From Fig. 13, the brightness figure of merit for the 76 mm rod is found to be dependent on the RoC of the resonant cavity mirrors. Small RoC means low figure of merit, while large RoC leads to a higher value, which also becomes saturated at 38 W level for the RoC of more than 12 m. Therefore, it is 20 October 2014 / Vol. 53, No. 30 / APPLIED OPTICS
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Fig. 12. M 2 factors dependency on both the rod length and the RoC of the cavity mirrors.
understandable for researchers to use flat-flat (infinite RoC) cavity mirrors for the maximum extraction of TEM00 laser power [16]. Based on the same process for extracting the maximum TEM00 mode laser power from the 3 mm diameter, 76 mm length rod, as shown in Fig. 9, we also find a strong dependence of TEM00 mode laser power on the RoCs of the cavity mirrors for the 3 mm diameter, 70 mm and the 82 mm length rods, as shown in Fig. 11. Due to the relative short rod length of 70 mm, therefore, small rod volume and less round-trip loss, 61.0 W TEM00 mode laser power is achieved with RoCs of more than 10 m, which compares favorably with the 59.1 W laser power for the 76 mm rod. Due to the large rod volume and high round-trip loss, the 82 mm rod offers the lowest fundamental mode laser power of 57.0 W for the RoC of more than 9 m, which is 3.5% less than that of the 76 mm rod. For different rod lengths, the strong influence of RoC on M 2x , M 2y factors is demonstrated in Fig. 12. The output laser beam profile for large RoC result in
average laser beam quality factors of M 2x 1.10 and M 2y 1.45. Relatively large average M 2 values of M 2x 1.33 and M 2y 2.21 are found for small RoC. The 70 mm rod present relatively large M 2 factors while the 82 mm rod offers similar values as that of the 76 mm rod. Based on the numerically calculated results in Figs. 11 and 12, the beam brightness figure of merit for 70, 76, and 82 mm are finally compared, as given in Fig. 13. The 76 mm rod presents the highest laser-beam figure of merit of 38 W, while the 70 and 82 mm rods presents slightly reduced values. Despite the highest TEM00 mode power of 61.0 W, achieved by using the 70 mm rod in Fig. 11, its brightness figure of merit of 36.3 W is less than that of the 76 mm due to the relatively higher M 2 values of the 70 mm rod in Fig. 12. The reduced TEM00 mode power level of the 82 mm rod is, however, compensated by its relatively low M 2 values, leading to a satisfactory brightness figure of merit of 36.8 W. The easy commercial availability of
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RoC (mm) Fig. 11. Laser output power is dependent on both the rod length and the RoC of the cavity mirrors. 7136
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RoC (m) Fig. 13. Laser beam brightness figure of merit for different rod length is strongly dependent on the RoC of the cavity mirrors.
the 76 mm (3 in.) rod constitutes another good reason for us to finally choose the 3 mm diameter, 76 mm length Nd:YAG rod for extracting the TEM00 mode laser power with the highest beam-brightness figure of merit of 38.0 W. 5. Conclusions
A scalable solar-pumped TEM00 mode laser pumping configuration is put forward in this paper. It is composed of the four Fresnel lens with four folding mirrors, the four secondary fused-silica concentrators with rectangular light guides, four hollow 2D-CPC concentrators, and finally the four V-shaped reflectors for the efficient pumping of the 3 mm diameter, 76 mm length Nd:YAG single-crystal laser rod. Optimum optical pumping conditions are found through ZEMAX software. Optimized laser resonator parameters are found through LASCAD numerical analysis. On one hand, high-multimode solar laser power of 90.4 W is numerically attained with the 400 mm symmetric laser cavity, leading to the high solar laser collection efficiency of 22.6 W∕m2. On the other hand, 59.1 W TEM00 mode laser power is also numerically deduced with the asymmetric laser resonant cavity, where a good matching between the pump mode volume and 1064 nm laser oscillation mode volume are ensured by the cavity mirrors of large RoCs. The record-high solar laser-beam brightness figure of merit of 38 W is therefore predicted for the 3.0 mm diameter, 76 mm length Nd:YAG rod, corresponding to 20 times enhancement over the previous record. Due to the introduction of the novel secondary concentrator with light guide of rectangular cross-section, stable solar-laser emission is now possible at its lowest mode: the TEM00 mode. The proposed solar-laser pumping approach provides an effective solution to reaching high TEM00 mode laser power with super beam quality. This is essential for the success of many applications such as space-based solar-power transmission and laser-power beaming to off-grid locations such as spacecraft. This research project PTDC/FIS/122420/2010 was funded by the Science and Technology Foundation of
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