Multimode Solar-Pumped Lasers

Abstract

Milestone multimode solar-pumped laser designs and their laser output performances are introduced in this chapter. Since the knowledge of imaging and nonimaging primary, secondary and tertiary concentrators are vital for successful solar laser designs, Zemax^® and LASCAD™ numerical analysis examples are provided in order to ensure student’s clear understandings of how concentrated solar radiation is optically coupled and absorbed by the laser medium by Zemax^® software and, consequently, how solar laser output power is numerically calculated by LASCAD™ software.

Milestone multimode solar-pumped laser designs and their laser output performances are introduced in this chapter. Since the knowledge of imaging and nonimaging primary, secondary and tertiary concentrators are vital for successful solar laser designs, Zemax^® and LASCAD^™ numerical analysis examples are provided in order to ensure student’s clear understandings of how concentrated solar radiation is optically coupled and absorbed by the laser medium by Zemax^® software and, consequently, how solar laser output power is numerically calculated by LASCAD™ software.

6.1 Solar-Pumped Lasers with Imaging and Nonimaging Primary, Secondary and Tertiary Concentrators

The optical pumping of solar lasers relies on primary, secondary and tertiary concentrators to achieve enough pumping intensity for the lasing threshold [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24]. These solar concentrators can be classified into two types: imaging and nonimaging, depending on whether the image of the sun is focused on the receiver or not [25]. The imaging and nonimaging concentrators responsible for the main advances in solar-pumped lasers will be addressed in the next sections.

6.1.1 Configurations for Solar Energy Collection and Concentration

The Sun appears to move across the sky during the day due to the rotational motion of the Earth. The Sun’s path across the sky also varies seasonally and with geographical location. The Earth’s axial tilt of approximately 23.5° and its elliptical orbit around the Sun ensure that observers at different locations will see the apparent Sun motion differently throughout the year [26]. For these reasons, solar systems (including solar-pumped lasers) require sun-tracking systems for the efficient capture of the solar radiation during the day and along the year. The solar energy collection by these systems can be done in two different ways: through direct tracking or indirect solar tracking by heliostat.

6.1.1.1 Direct Solar Tracking Type

In direct solar tracking systems, the primary concentrator and the receiver (the solar laser head in solar-pumped lasers) are both assembled to the solar tracker with their optical axes aligned with the position of the Sun in the sky, as illustrated in Fig. 6.1. This implicates that all the components of the laser system are movable.

Fig. 6.1

Direct solar energy collection and concentration configuration

In the early stages of solid-state solar lasers, direct solar tracking systems were adopted [1, 2]. In 1966, Young used an equatorial mount mechanism to support the first Neodymium (Nd): Yttrium Aluminum Garnet (YAG) solar laser system with a 0.61 m diameter paraboloidal mirror as primary concentrator [2]. The equatorial tracking, also known as polar or spinning-elevation tracking, is commonly used in telescopes, where the principal axis—the polar axis—is always oriented towards the North Star, by which the Earth’s axis of rotation is oriented. Therefore, this axis tracks the Sun in East–West direction. A secondary axis, named as declination axis and perpendicular to the polar axis, is also needed to correct the solar declination angle that changes along the year, tracking the Sun in North–South direction [27, 28].

Between the middle 1980s and early 2000s, solar laser systems with stationary focus have gained strength with the use of large size mirrors as primary concentrators, for which heliostats were required to redirect the solar radiation towards the static laser head [3,4,5,6,7,8]. Nevertheless, as of 2007, direct solar tracking systems were employed again in solar-pumped lasers with the adoption of the economically competitive Fresnel lenses as primary concentrators [9,10,11,12,13,14]. The low weight of the Fresnel lenses facilitated their assembly on solar trackers, allowing the development of much lighter and more compact solar laser systems and avoiding additional power losses with the use of heliostats. Moreover, unlike the reflective concentrators, the focal spot of Fresnel lenses lies in their rear side. Consequently, the laser head along with the laser resonator and mechanical support are positioned behind the Fresnel lens, as shown in Fig. 6.1, enabling its easy access during the experiments.

6.1.1.2 Heliostat Type

A Heliostat, from helios (the Greek word for Sun) and stat (stationary), is a device composed of one or more mirrors that redirects the solar radiation towards a static receiver [29]. The mirrored surface of the heliostat is kept perpendicular to the bisector of the angle between the Sun’s position in the sky and the stationary receiver, as illustrated in Fig. 6.2.

Fig. 6.2

Indirect solar energy collection and concentration configuration via heliostat

The conventional heliostat configuration is based on the variation of two axes simultaneously [30]: The azimuth axis and the elevation axis. The azimuth axis is vertical relative to the heliostat base, tracking the angle bisector between the Sun and the receiver in the East–West direction. The elevation (or altitude) axis is normal to the azimuth axis, tracking the Sun in North–South direction. The configuration azimuth-elevation is also used in direct solar tracking systems with Fresnel lenses, with the azimuth axis tracking the Sun position [13].

Heliostats begun to be implemented in solar laser systems in the mid-1980s [3, 4]. In order to reach higher solar laser output power levels, large size mirror concentrators were used to pump the laser medium, for which direct solar tracking became inappropriate. The attachment of heavy solar laser systems on a solar tracker structure would lead to higher energy requirements for tracking [27]. Besides, the focusing method of reflective concentrators requires the receiver to be placed in their front (Fig. 6.2), which would make the direct tracking even more troublesome, especially in the daily hours of greatest solar irradiance when the Sun reaches its highest position in the sky, obliging the receiver to be located above the primary concentrator. Therefore, heliostats were needful to redirect the solar radiation towards the laser head [3,4,5,6,7,8].

Despite the progress in solar laser collection efficiency that led to a reduction in primary mirror concentrator area, heliostats are still used in solar laser systems with reflective concentrators, guaranteeing steady solar laser head within the laboratory [15,16,17,18,19,20,21,22, 24].

6.1.2 Parabolic Mirrors and Fresnel Lens as Primary Imaging Concentrators

Solar pumping of lasers requires primary concentrators with high concentration ratios to obtain sufficient gain in the irradiated active medium.

Primary mirror concentrators of paraboloidal shape have long been exploited by solar laser researchers to stimulate the laser medium, as summarized in Table 6.1. In 1966, Young used a Ø 0.61 m aluminized parabolic mirror to pump the first Nd:YAG solar laser of 1 W in continuous wave (cw) mode [2]. Between the mid and late 1980s, large-size stationary mirror concentrators with apertures up to 10 m were adopted as primary concentrators [3, 4]. This permitted obtaining high solar powers at the focus and cw laser output power levels of more than 60 W [4]. The highest solar laser output power of 500 W cw was further achieved in 1993 by Krupkin et al. [6] using 64 paraboloidal mirrors in the heliostat field of Weizmann Institute (WIS) Solar Tower with total collection area of 660 m². Nevertheless, the solar laser collection efficiency (the laser output power per unit of primary concentrator area) was only 0.76 W/m² [7]. Besides, the solar tower configuration has the drawback of causing astigmatic aberration and focal spot increase [31]. To overcome this problem, Lando and his co-workers built an Astigmatic Corrected Target Aligned (ACTA) solar concentrator [31]. In this device, a segmented primary mirror with 3.4 m aperture was mounted on a two-axis positioner which tracked the solar orbit. The primary concentrator focused the incoming solar radiation towards a plane folding mirror, which in turn deflected the light towards the stationary solar laser head within an enclosure, as shown in Table 6.1. Through this collection and concentration system, with primary concentrator aperture much smaller than the previous ones [3, 4, 6], 6.7 W/m² collection efficiency was reached, constituting a substantial progress in solar laser efficiency at that decade [7]. Since the work of Lando et al. [7], solar laser researchers started to pay more attention to the solar laser efficiency rather than the laser output power for the assessment of the solar laser performance [9,10,11,12,13,14,15,16,17,18,19,20,21,22,23].

Table 6.1 Solar collection and concentration systems of milestone solar lasers with primary mirror concentrators

Significant progress in solar laser collection efficiency and reduction in the collection area have occurred with the adoption of Fresnel lenses as primary concentrators in direct solar tracking systems, as summarized in Table 6.2. Solar laser collection efficiency of 32.1 W/m² with Fresnel lens system was reached in 2018 by Guan et al. using an effective collection area of only 1.03 m² to end-side-pump a bonding Nd:YAG/YAG laser rod [14].

Table 6.2 Solar collection and concentration systems of milestone solar lasers with primary Fresnel lens concentrators

Compared with parabolic mirror systems, Fresnel lens systems reduce complexity, weight, and cost of solar lasers. However, they have chromatic aberration, i.e., spreading the solar radiation spectrum along its focal zone, which may impair the transfer efficiency of the pump radiation to the laser medium. Parabolic mirrors, instead, collect all pumping wavelengths to a small focal spot without dispersion. For these reasons, the solar laser researchers from FCT NOVA have insisted on enhancing the solar laser efficiency using parabolic mirror as primary concentrators. Since 2017, several important milestone solar lasers occurred at the solar facilities of FCT NOVA and PROMES-CNRS (Table 6.1), both composed of an heliostat and a stationary parabolic mirror with 1.5 and 2.0 m maximum diameter, respectively [15,16,17,18,19,20,21,21, 37]. Records in solar-to-laser conversion, collection, and slope efficiencies of 4.64%, 41.3 W/m², and 7.64% were, respectively, attained in 2022 by the simultaneous end-side-pumping of three Cerium (Ce):Nd:YAG laser rods through the NOVA solar facility [20].

6.1.3 Secondary Imaging Concentrators

The concentrated solar intensity of the primary concentrator is limited by the Sun image at the focus, which can lead to a significant mismatch between the sizes of the focal spot and the laser active medium. Thence, for efficient coupling of the solar rays into the laser medium, the focal image must be reduced, which requires secondary optics. In this section, the secondary imaging concentrators that contributed to the most significant advances in solar lasers are presented.

6.1.3.1 Hyperbolic-Cylindrical Reflector for Side-Pumping Scheme

The first 1 W cw Nd:YAG solar laser was pumped through a modified Cassegrain sun-tracking telescope consisting of a 0.61 m diameter paraboloidal primary mirror, a water-cooled hyperbolic-cylindric secondary mirror and a hemicircular cylindric tertiary mirror, as shown in Fig. 6.3 [2]. The aluminized secondary concentrator, as well as the primary concentrator, had an average reflection of 85% in the pump bands.

Fig. 6.3

a Schematic design of the 1 W cw Nd:YAG solar laser system (adapted from [2]) b Assembly of the hyperbolic-cylindric secondary concentrator [2]

In this solar laser system, a side-pumping configuration was adopted, which means that the solar radiation was injected into the laser medium transversely to its optical axis. Thus, to refocus and redistribute the concentrated solar radiation along the 3 mm diameter, 30 mm length, 1.0 at.% Nd:YAG rod, both secondary and tertiary concentrators were two-dimensional. The resultant image at the focus of the hyperbolic-cylindric reflector was 3 mm by 24 mm, which was coincident with the exposed portion of the active medium [2]. The laser resonator was formed by the highly and partially reflective coatings in the laser emission wavelength (1064 nm) deposited on the convex end surfaces of laser rod with 5 cm radius of curvature [2].

6.1.3.2 Meniscus Plus Hyper Hemispherical Aplanatic Refractors for End-Side-Pumping Scheme

An aplanatic lens is free of both spherical and coma aberrations, being widely used in microscope objectives. They are usually made of at least two or three air-spaced lens elements [38].

In 1964 and 1966, Simpson [1] and Young [2] utilized this type of lenses as secondary concentrators in their solar laser experiments with Nd:glass medium, combining a meniscus converging lens with a hyper semispherical lens to pump the laser rod, as shown in Table 6.3. A meniscus converging lens is a convex-concave lens thicker at the center than at the edges, being free from both spherical and comma aberrations [39]. When combined with the hyper hemispherical lens, which has a very wide field of view angle [40], the focal length of the solar laser system is shortened and, consequently, the focal spot is reduced. With this configuration, the more external solar rays could ricochet along the rod, allowing multipass pumping to the thin laser rod.

Table 6.3 Milestone solar lasers with meniscus plus hyper hemispherical aplanat refractors as secondary concentrators

Young succeeded in obtaining Nd:glass solar laser output power of 1.25 W [2]. However, no provisions were made to cool the laser rod in both experiments [1, 2]. Therefore, laser operation lasted less than 1.0 s before cessation owing to excessive temperature.

6.1.3.3 Fused Silica Aspheric Lens for Both End- and Side-Pumping Schemes

Aspherical lenses encompass any lens with rotational symmetry that has a non-spherical surface, in which the radius of curvature varies radially from the center to the edge. These lenses can focus all the incident light on the same focal region, reducing spherical aberration and providing true diffraction-limited spot sizes. The concentrated solar radiation can hence be collected and compressed efficiently from the focal zone of the primary concentrator into the laser medium. For these reasons, fused silica aspherical lenses have been used as secondary concentrators in several solar-pumped laser systems with either side-pumping or end-side-pumping configurations [15,16,17,18,19,20], summarized in Table 6.4. Fused silica material is suitable for solar-powered lasers since it has a wide transparency range over the laser media absorption spectra. Furthermore, it is very resistant to high temperature and thermal shock [41].

Table 6.4 Milestone solar lasers with aspherical lenses as secondary concentrators

The curvature surface of the aspheric lenses (z) utilized in these solar laser systems followed Eq. (6.1) [19]:

$$z = \frac{{RoCr^{2} }}{{1 + \sqrt {1 - (1 + k)RoC^{2} r^{2} } }} + \alpha_{1} r^{2}$$

(6.1)

where RoC is the radius of curvature, r is the radial aperture, k the conic constant, and α₁ the aspheric coefficient.

The most efficient Nd:YAG solar laser with parabolic mirror as primary concentrator was obtained with the use of a secondary aspherical lens in an end-side-pumping scheme [17]. In end-side-pumping configurations, most of the concentrated solar radiation is directly focused onto the end face of the laser rod, i.e., parallel to the laser beam. Therefore, the optical path of solar rays within the laser medium is much longer than that of side-pumping scheme, enabling higher pumping efficiency. Nevertheless, end-side-pumping can lead to severe thermal loading issues in single solid-state laser media of cylindrical geometry [42, 43], due to the non-homogenous pumping light distribution along the laser rod’s length, precluding these laser systems to scale to high power. To attenuate this drawback, the potential of multirod solar laser systems based on the simultaneous pumping of several laser media has been recently investigated [18, 20]. In these systems, each rod absorbs only a portion of the concentrated solar radiation incident on the pumping cavity, reducing significantly the thermal induced effects. The records in solar-to-laser conversion, collection, and slope efficiencies of 4.64%, 41.3 W/m², and 7.64%, respectively, were attained through the simultaneous pumping of three Ce:Nd:YAG laser rods using an aspherical lens as secondary concentrator (Table 6.4) [20].

Side-pumping configuration is also suitable for laser power scaling once it spreads the solar radiation along the laser rod, hence improving the thermal performance. The most efficient side-pumped Nd:YAG solar laser with 2.43% solar-to-laser power conversion efficiency, 17.7 W/m² collection efficiency and 5.4% slope efficiency had also an aspheric lens as secondary concentrator (Table 6.4) [15].

6.1.3.4 Liquid Light Guide Lens for End-Side-Pumping Scheme

The liquid light guide lens can be considered as a laser flow tube. Nonetheless, it can also work as a lens due to the difference of refraction index n between the air (n_air = 1) and the coolant (usually water, n_water = 1.33), as shown in Fig. 6.4.

Fig. 6.4

Liquid light guide lens configuration. Adapted from [11]

In 2012, Dinh and his co-workers utilized a liquid light guide lens to improve the performance of an end-side-pumping solar laser system, composed of a Fresnel lens primary concentrator and a secondary conical mirror (Fig. 6.4) [10, 11]. In this case, the liquid light guide lens worked essentially as a tertiary concentrator, helping to refocus the reflected solar rays by the conical cavity into the laser rod. With this configuration, 120 W cw laser power was produced from a 6 mm diameter, 100 mm length Nd:YAG rod, resulting in 30 W/m² collection efficiency. Such result was 2 times higher than that without the glass tube, i.e., with the conical cavity flooded with water [10, 11].

In 2018, Guan et al. [14] and Liang et al. [21] developed liquid light guide lenses with hemispherical front surfaces to end-side-pump a bonding Nd:YAG/YAG [14] and a Cr:Nd:YAG rod [21], respectively, within a conical cavity. The curved front surface allowed the concentrated solar rays to be more efficiently focused on the top region of the laser rod, so the light guide lens acted as a secondary concentrator. These pumping configurations led to the records in solar laser collection efficiencies of 32.1 and 32.5 W/m² with Nd:YAG [14] and Cr:Nd:YAG laser materials [21], respectively, as summarized in Table 6.5. Similar configuration with liquid light guide lens as a secondary concentrator was also adopted for the first Ce:Nd:YAG solar laser [22].

Table 6.5 Milestone solar lasers with liquid light guide lens as secondary concentrators

6.1.4 Secondary Nonimaging Concentrators

Nonimaging concentrators can be considered as a funnel for light, sacrificing the image of the source in order to concentrate the light to intensities approaching the theoretical limit [44]. They have played an important role in the advancement of solar-pumped lasers, acting as secondary and/or tertiary concentrators. In this section, the secondary nonimaging concentrators that contributed to the most significant advances in solar lasers are presented.

6.1.4.1 Three-Dimensional Compound Parabolic Concentrator (3D-CPC) for Side-Pumping Scheme

One of the most representative nonimaging type concentrators is the compound parabolic concentrator (CPC), also known as Winston-type collector [45]. The three-dimensional (3D) CPC shape is derived from the CPC design principle for a flat receiver, represented in Fig. 6.5. It is based on the intersection of two parabolas facing each other, the axes of which are inclined at angles ± θ_a with respect to optical axis of the collector. The angle θ_a is the acceptance angle of the concentrator, i.e., the angle at which the incoming sunlight can be captured by a concentrator and reflected to the absorber. Because of the CPC shape, all the incident solar rays within the maximum concentration angle θ_a can be transmitted to a small output aperture emitting into a larger angle. This implies that irradiance is larger at the output aperture than at the entrance aperture, leading to a net concentration of the pump radiation [46].

Fig. 6.5

Schematic design of a compound parabolic concentrator (CPC) for a flat receiver

The use of secondary 3D-CPCs concentrators has contributed to the advances of solar lasers in the 90’s and early 2000s [6, 7], as summarized in Table 6.6.

Table 6.6 Milestone solar lasers with secondary three-dimensional compound parabolic concentrators (3D-CPCs)

In 2003, Lando et al. reached 6.7 W/m² by using a 3D-CPC combined with a 2D-CPC tertiary concentrator to side-pump a Nd:YAG laser rod [7]. Similar archetype has been previously utilized by Krupkin et al. in 1993 to side-pump an array of laser rods at the WIS solar tower, reaching 500 W cw solar laser power [6].

6.1.4.2 Two-Dimensional Compound Parabolic Concentrator (2D-CPC) for Side-Pumping

The CPC can take a variety of shapes depending on the receiver geometry [47]. For solar-pumped lasers, the classical two-dimensional (2D) CPC profile is based on the design principle for tubular receivers, illustrated in Fig. 6.6. This CPC type has two different segments that smoothly join at point B(B’) related to θ_a. The lower segment, from the bottom of the receiver, A, to point B (B’) is an involute of the receiver’s cylindrical cross-section. The upper segment, from point B(B’) to C(C’), is of parabolic shape.

Fig. 6.6

Cross-section of a two-dimensional compound parabolic concentrator (2D-CPC) classical design for a tubular absorber. Adapted from [48]

A light ray entering the 2D-CPC with an angle ${\theta }_{i}$ = ${\theta }_{a}$ will strike the tubular receiver of radius r tangentially. The distance along the tangent from the receiver (P’) to the last intersection point of the ray with the concentrator (P) is represented by $\rho$, which is given by the following equation for the two CPC segments [48], where $\theta$ is the angle between the radius to the bottom of the receiver and the radius to the tangential point P’:

$$\rho = \left\{ {\begin{array}{*{20}l} {r\theta } \hfill & {{\text{if}}\,\left| \theta \right| \le \theta_{a} + \pi /2} \hfill \\ r[{\frac{{\theta + \theta_{a} + \pi /2 - \cos \left( {\theta - \theta_{a} } \right)}}{{1 + \sin \left( {\theta - \theta_{a} } \right)}}}] \hfill & {{\text{if}}\,\theta_{a} + \pi /2 \le \left| \theta \right| \le 3\pi /2 - \theta_{a} } \hfill \\ \end{array} } \right.$$

(6.2)

As observed in Eq. (6.2), the classical 2D-CPC profile only depends on the acceptance angle ${\theta }_{a}$ and on the absorber radius $r$. With $\overline{{CC^{\prime } }}$ being the 2D-CPC entrance width, the rod radius is given by Eq. (6.3),

$$2\pi r = \overline{{CC^{\prime } }} \sin \left( {\theta_{a} } \right)$$

(6.3)

The 2D-CPC was first implemented in solar-pumped lasers as a secondary concentrator in 1988 by Weksler and Schwartz, to increase the coupling of solar rays from the WIS concentrator into the Nd:YAG rod in a side-pumping configuration [4], as shown in Table 6.7. This has contributed to more than 60 W of solar laser power, the highest to that date. Later, Lando et al. has also utilized this concentrator type at the focus of the ACTA solar concentrator for side-pump Nd:YAG solar laser experiments, achieving 6.7 W/m² collection efficiency, which constituted a record in 2003 [7].

Table 6.7 Milestone solar lasers with secondary two-dimensional compound parabolic concentrators (2D-CPCs)

6.1.4.3 Conical Pump Cavity for End-Side-Pumping Scheme

In the previous works, non-imaging secondary CPCs were used to further concentrate and redistribute the sunlight from primary mirror concentrators along the laser rods in side-pumping configurations [4, 6, 7]. However, the pump radiation passes through the active medium only once in a CPC chamber. Besides, the optical path in side-pumping configuration is less than that in end-pumping configuration, resulting in lower pumping efficiency. These concerns became even more challenging with the introduction of Fresnel lens as primary concentrator [9], due to the dependence of the focal length on the solar spectrum wavelength. To overcome this issue, in 2007 Yabe et al. adopted a secondary conical mirror to end-side-pump a Cr:Nd:YAG rod at the focus of a 1.3 m² Fresnel lens [9], as illustrated in Fig. 6.7.

Fig. 6.7

Schematic design of a secondary conical pump cavity for end-side-pumping, with Fresnel lens primary concentrator (adapted from [10])

This type of concentrator provided the confinement of light by multiple reflections inside the pumping cavity, enhancing the absorption efficiency. The solar laser collection efficiency was boosted to 18.7 W/m², representing a 2.8 times enhancement over the previous record of 6.7 W/m² by Lando et al. [7]. Since then, the conical cavity has been widely used by solar laser researchers, either as a secondary [9,10,11,12] or tertiary concentrator [13, 14, 17,18,19,20,21,22].

6.1.4.4 Dielectric Totally Internally Reflecting Secondary Concentrator (DTIRC) for End-Side-Pumping Scheme

Dielectric totally internally reflecting concentrator (DTIRC) was originally designed for photovoltaic applications with the goal of reducing the cost of electricity generated through photovoltaic conversion [49]. DTIRCs combine the front surface refraction with total internal reflection from the sidewall to achieve concentrations close to the theoretical limits [50]. Unlike dielectric CPCs, which has a flat front surface, the curved front surface of the DTRICs works like a lens, concentrating the solar rays before their reflection on the sidewalls. Therefore, the more curved the front surface, the shorter the DTRIC [50].

In 2011, Liang and Almeida employed a modified version of the DTIRC with an aspherical front surface and a conical section to efficiently concentrate the solar radiation from a 0.636 m² Fresnel lens primary concentrator to the upper end-region of the 25 mm length Nd:YAG laser rods with either 3 or 4 mm diameter [13], as illustrated in Fig. 6.8. The previous progress in solar-pumped laser with economical Fresnel lens has revitalized solar laser researches [9]. However, chromatic aberration of the Fresnel lens hinders the coupling of the different solar pump wavelengths into a small laser rod by a conventional lens. The modified DTIRC was therefore designed to overcome this difficulty [13]. For end-pumping, one part of the radiation was directly focused onto the upper end-face of the laser rod through the curved surface of the DTRIC, represented by ray A, while another part was focused indirectly through total internal reflection from the conical section of the DTIRC, represented by ray B. The solar radiation that does not hit the end face of the rod, represented by ray C, was guided into the small conical cavity, ensuring a multi-pass side-pumping to the rod.

Fig. 6.8

The Nd:YAG laser head composed of the secondary DTIRC and the tertiary conical concentrator where a 3–4 mm diameter rod is efficiently pumped. RoC, radius of curvature; H₁, height of the aspherical section of the DTRIC; H₂, height of the conical section of the DTRIC; D₁, DTIRC input diameter; D₂, DTIRC output diameter. HR, high reflection; PR, partial reflection

As shown in Fig. 6.8, the end face of the DTRIC was in direct contact with cooling water, which ensured an efficient light coupling to the rod. The laser resonator was formed by the high reflection (HR) coating at 1064 nm on the upper end-face of the laser rod and the partial reflection (PR) coating on the concave output mirror. This solar laser system permitted to obtain 12.3 W cw laser power from a Ø 4 mm × 25 mm laser rod, corresponding to a record solar laser collection efficiency of 19.3 W/m² at that time.

6.1.5 Tertiary Imaging and Nonimaging Concentrators

Tertiary concentrators are indispensable for increasing the solar laser pumping efficiency since they can either compress or wrap the solar radiation from the secondary concentrator to the laser medium. The imaging and nonimaging tertiary concentrators that played a key role in the solar laser advances are addressed in this section.

6.1.5.1 Semi-Cylindrical Mirror as an Imaging Tertiary Concentrator

Semi-cylindrical tertiary mirrors have been implemented in some solar laser systems with side-pumping configuration to both redirect and refocus the transmitted solar radiation from imaging secondary concentrators back to the laser rod [2, 3, 15], as summarized in Table 6.8.

Table 6.8 Milestone solar lasers with semi-cylindrical mirror as tertiary concentrators

This tertiary concentrator was first adopted by Young in 1966 for the first Nd:YAG solar laser emission [2]. To prove the advantage of using the semi-cylindrical mirror, Young decided to compare the output performance of the Nd:YAG solar laser system with and without it. This experiment has revealed 1.5 times increase in the laser output power over that obtained with the hyperbolic cylindric secondary concentrator alone.

In 1984, Arashi et al. placed a semi-cylindrical concentrator just behind the secondary cylindrical lens to refocus the transmitted solar radiation to the side-pumped Nd:YAG laser rod [3]. With this combination, 18 W cw solar laser power was measured, the highest at that time.

In 2019, Liang et al. used a water-cooled semi-cylindrical tertiary concentrator for the most efficient side-pumped solar laser [15]. This pump cavity showed great usefulness in both refocusing and reflecting the pump rays from the secondary aspherical lens towards the Nd:YAG rod. One part of the concentrated solar radiation from the parabolic mirror was directly focused onto the laser rod by the secondary lens, but the pump rays were only partially absorbed. Double-pass pumping was possible by the semi-cylindrical mirror, once it could refocus the transmitted pump rays from the secondary lens back to the laser rod. Besides, a significant part of the pump rays exiting the aspherical lens did not pass directly through the laser rod. Therefore, the tertiary concentrator had also a fundamental role in redirecting those pump rays to the laser rod.

6.1.5.2 Two-Dimensional Compound Parabolic Nonimaging Concentrator (2D-CPC)

Tertiary concentrators with 2D-CPC shape were also used in conjunction with either secondary 3D-CPCs [6, 7] or rectangular fused silica light-guide homogenizers [23] to side-pump the laser rod, as summarized in Table 6.9.

Table 6.9 Milestone solar lasers with two-dimensional compound parabolic concentrators (2D-CPCs) as tertiary concentrators

In 1993 and 2003, Krupkin et al. [6] and Lando et al. [7] combined the 3D-CPC secondary concentrators with 2D-CPC tertiary concentrators for side-pumping of Nd:YAG laser rods. The experimental results from these solar laser systems constituted records in solar laser power [6], collection efficiency [7] and brightness figure of merit [7].

Later, in 2012, Almeida et al. resort a modified version of the classic 2D-CPC as a tertiary concentrator in combination with a secondary fused silica rectangular light guide to improve the absorbed pump distribution along a Nd:YAG laser rod [23].

The classic 2D-CPC design is based on the edge ray principle, which requires the extreme incident rays at the entrance aperture to be tangent to the tubular receiver [44], as demonstrated in Fig. 6.6 (Sect. 6.1.4.2). In a solar laser system, this prevents the most extreme solar rays from being absorbed by the laser medium, impairing the absorption efficiency. The modified 2D-CPC was designed to overcome this drawback, allowing the coupling of the pump rays with high incidence angles coming from the light guide into the laser rod [23]. This design configuration contributed to multimode solar laser beam brightness figure of merit of 0.29 W, which was three times higher than that of the previous solar-pumped Nd:YAG laser by a Fresnel lens [13] and nine times more than that from the previous side-pumped Nd:YAG solar laser with 2D-CPC as tertiary concentrator [7].

6.1.5.3 Conical Nonimaging Concentrator for End-Side-Pumping Scheme

Tertiary concentrators with conical shape have been the most widely used in end-side-pumping solar laser systems since the utilization of this type of concentrators in 2007 by Yabe et al. [9]. Conical reflectors of different dimensions have been attached to different secondary concentrators, such as DTRIC [13], aspheric lenses [17,18,19,20] and liquid light guide lenses [14, 21, 22], with the common purpose of increasing the absorption efficiency by enabling multi-pass pumping to the laser medium, as shown in Fig. 6.9.

Fig. 6.9

a Schematic design and b front image of the laser head of the most efficient single-rod Ce:Nd:YAG solar laser with primary parabolic mirror concentrator (adapted from [19]). c Front image of the laser head of the most efficient solar laser with three Ce:Nd:YAG rods simultaneously pumped (adapted from [20]). Both solar laser prototypes had an aspheric lens and a conical cavity as secondary and tertiary concentrators, respectively

Most of these tertiary concentrators consisted of a silver-coated aluminum foil of 94% reflectivity [13, 17,18,19,20,21,22] that covered the inner walls of the conical pump cavity. Except the solar laser schemes with a liquid light guide lens as secondary concentrator, which had a dry tertiary conical cavity [14, 21, 22], the remaining prototypes had a water-flooded conical cavity [18,19,20], as demonstrated in Fig. 6.9.

The use of the conical cavity as a tertiary concentrator contributed to the most important milestone solar lasers in multimode regime:

• The most efficient Nd:YAG solar lasers with parabolic mirror [17] and Fresnel lens [14] as primary concentrators;

• The most efficient Cr:Nd:YAG solar laser  [21];

• The most efficient single-rod Ce:Nd:YAG solar laser with primary parabolic mirror concentrator [19], in Fig. 6.9a, b;

• The most efficient simultaneous solar laser emissions with Ce:Nd:YAG as laser media [20], in Fig. 6.9c.

6.2 Examples of Numerical Analysis of Milestone Solar-Pumped Lasers

In this section, examples of the modelling and numerical analysis of some milestone solar-pumped lasers are given. The design parameters of the solar laser prototypes here presented were first optimized in Zemax^® ray-tracing software in non-sequential mode. LASCAD™ laser cavity analysis software was then used to find out the optimum laser resonator parameters.

6.2.1 Zemax^® and LASCAD™ Numerical Analysis of 12.3 W Solar Laser with DTIRC Secondary and Conical Tertiary Concentrators

The layout from Zemax^® of the 12.3 W solar laser [13] is represented in Fig. 6.10. It was composed of the 0.9 m diameter Fresnel lens primary concentrator, the DTIRC secondary concentrator and the conical tertiary mirror, within which the 4 mm diameter, 25 mm length, 1.0 at.% Nd:YAG laser rod was end-side-pumped. This design configuration contributed to the record in solar laser collection efficiency of 19.3 W/m² with Nd:YAG laser medium in 2011 [13].

Fig. 6.10

Shaded model layout of the 12.3 W solar laser components [13]: a Solar laser system; b Laser head with the fused silica modified DTIRC and the conical tertiary mirror

For modeling the solar laser system, its components are defined by the non-sequential objects of Zemax^® in the Non-Sequential Component Editor window, as explained in Sect. 2.1.1.1 of Chap. 2. The list of Zemax^® non-sequential objects utilized to design the 12.3 W solar laser system, as well as the respective materials, are given in Fig. 6.11.

Fig. 6.11

List of Zemax^® objects in the non-sequential component editor to simulate the components of the 12.3 W solar laser [13]

For the light source, 22 peak absorption wavelengths of the Nd:YAG material were added in the source wavelength data: 527, 531, 569, 579, 586, 592, 732, 736, 743, 746, 753, 758, 790, 793, 803, 805, 808, 811, 815, 820, 865, and 880 nm. The weight of each wavelength was defined based on its spectral irradiance value in the standard direct solar spectrum for one-and-a-half air mass (AM1.5 D) [51]. The absorption coefficients of each of those wavelengths [52] were defined in the glass catalog data for the 1.0 at.% Nd:YAG (see Sects. 2.1.1.2 and 2.1.1.4 of Chap. 2 for more details). The absorption spectra and wavelength-dependent refractive indices of PMMA, fused silica and water [19] were also included in the glass catalog data to account for absorption losses in those media. For the conical tertiary concentrator, 94% reflectivity was assumed [13], using the coating I.06 in the section Coat/Scatter of the object properties (see Sect. 2.1.1.3 of Chap. 2 for more details).

The X, Y, Z positions and directions (Tilt About X, Y and Z) of the 12.3 W solar laser components in Zemax^® space are indicated in Fig. 6.12. The optimal parameters of the 12.3 W solar laser [13] components defined in Zemax^® are indicated in Table 6.10.

Fig. 6.12

Example of the position and rotation of the 12.3 W solar laser [13] components in Zemax^® non-sequential component editor

Table 6.10 12.3 W solar laser [13] components defined in Zemax^® non-sequential component editor

For the ray-tracing analysis of the absorbed pump power and light distribution within the active medium, detector volumes divided into several voxels were used. The number of analysis rays in the source and the number of voxels in the detectors were adjusted in order to attain accurate results and good image resolution. To estimate the absorbed pump power by the laser rod, the radiation absorbed in each voxel was summed up.

Figure 6.13 shows the absorbed pump flux distributions along seven transversal cross sections and one longitudinal central cross section of the 4 mm diameter, 25 mm length, 1.0 at.% Nd:YAG laser rod. Red color means near maximum pump absorption, whereas blue means little or no absorption. The 4 mm diameter, 25 mm length 1.0 at.% Nd:YAG rod absorbed a maximum power of 48.6 W. Due to the rotational symmetry of the end-side-pumping configuration, a symmetric absorbed pump profile was attained. In the central region of the laser rod, maximum absorbed pump intensity of 0.436 W/mm³ was detected.

Fig. 6.13

Absorbed pump flux distributions along the longitudinal central cross-section and seven transversal cross sections of the 4.0 mm diameter, 25 mm length, 1.0 at.% Nd:YAG rod of the 12.3 W solar laser [13], obtained through Zemax^® numerical analysis

The absorbed pump flux data from the Zemax^® analysis was then processed by LASCAD™ to quantify the thermal effects applied in the active medium, previously defined in LASCAD™ (see Sects. 2.2.3 and 2.2.4 of Chap. 2 for more details). A fluorescence lifetime of 230 µs [42] and the mean absorbed and intensity-weighted solar pump wavelength of 660 nm [4] were considered. These values were used for the LASCAD™ numerical analysis of all the solar laser schemes [13, 17, 20, 23]. The reported values of the Nd:YAG stimulated emission cross-section range from 2.7 to 8.8 × 10⁻¹⁹ cm² [53]. Therefore, the value of the stimulated emission cross-section used in LASCAD™ depended on the values given by the laser rod manufacturers. In the present case, a stimulated emission cross-section of 2.8 × 10⁻¹⁹ cm² was assumed [13].

Based on the information from the Finite Element Analysis (FEA) of LASCAD™, the optimal laser resonator beam parameters, represented in Fig. 6.14, were found.

Fig. 6.14

Schematic design of the 12.3 W solar laser resonator [13]. The image is not at scale

The high reflection (HR 1064 nm) coating on the end face of the laser rod and the partial reflection (PR 1064 nm) coating on the output mirror, together with the Nd:YAG laser rod, formed the laser resonator. L_ROD represents the rod length and L represents the separation length between the antireflection (AR 1064 nm) coating on the end face of the rod and the PR 1064 nm output mirror. In the experiments, maximum laser power of 12.3 W was extracted from a PR mirror with 98% reflectivity (R) and −0.5 m radius of curvature (RoC).

For accurate calculation of the laser power in LASCAD™, a simulation of the laser beam profile, based on the beam propagation method (BPM), was performed to find the correct laser beam width at the output mirror. The following procedure (also explained in Sect. 2.3.2 of Chap. 2) was adopted:

• 1. Accounting for apertures in the laser resonator (Fig. 6.15).

  Fig. 6.15

  

  Accounting for apertures in the 12.3 W solar laser resonator [13] in LASCAD™ Parameter Field

• 2. Starting BPM analysis (see Sect. 2.2.5 of Chap. 2 for more details).

• 3. Finding the beam waist, W, of the laser beam profile. It is calculated by multiplying the half width of the BPM computational window (4080 μm) by the quotient between the number of squares of the grid representing the maximum oscillating laser modes in X, Y directions (~20 squares) and the total number of squares in the grid (42 squares), illustrated in Fig. 6.16.

  Fig. 6.16

  

  Top-view of the 12.3 W solar laser beam profile from BPM analysis of LASCAD™

• 4. Modifying the M_x², M_y² factors in the Parameter Field window until the spot sizes are coincident with the beam waist from BPM analysis, as illustrated in Fig. 6.17.

  Fig. 6.17

  

  Correction of the beam waist in LASCAD™ Parameter Field by changing the M_x², M_y² factors

• 5. Calculating multimode laser power in the Laser Output Power window, with account for apertures unchecked, as indicated in Fig. 6.18.

  Fig. 6.18

  

  Numerically calculated laser output power in LASCAD™ as a function of the absorbed solar power, for the output mirror reflectivity (R) of 98%

For accurate calculation of the laser power, the total roundtrip losses (given by Eq. (2.7) in Chap. 2) must be defined in this window. By considering a typical absorption and scattering loss α of 0.002 cm⁻¹, a two-way loss of 1% was found for the 4.0 mm diameter, 1.0 at.% Nd:YAG rod with 2.5 cm length. Assuming 0.4% of imperfect HR and AR coatings, the total round-trip loss increased to 1.4%. The diffraction losses depend on rod diameter, resonator length and radius of curvature (RoC) of the resonator mirrors. For the present solar laser resonator, 0.04% of diffraction losses was calculated by LASCAD™ BPM analysis. A total round-trip loss of 1.404% was hence defined in the Laser Output Power window (Fig. 6.18).

Based on this procedure, 12.26 W was numerically obtained from an output mirror with R = 98% and RoC = −0.5 m, matching well with the experimental solar laser power value with similar PR mirror characteristics [13].

6.2.2 Zemax^® and LASCAD™ Numerical Analysis of 28 W Solar Laser with a Fused Silica Light Guide Homogenizer and a 2D-CPC Pump Cavity

The layout from Zemax^® of the 28 W solar laser [23] is represented in Fig. 6.19. The fused silica light guide of 14 mm × 22 mm rectangular cross-section was used to both transmit and homogenize, through total internal reflection, the concentrated solar radiation from the focal zone of the 2.0 m diameter parabolic mirror to the entrance aperture of a modified 2D-CPC water-flooded pump cavity, within which the 4 mm diameter, 30 mm length, 1.1 at.% Nd:YAG laser rod was side-pumped. This design configuration contributed to record solar laser brightness figure of merit of 0.29 W in 2012 [23].

Fig. 6.19

Shaded model layout of the 28 W solar laser components [23]: a Solar laser system; b Laser head with the fused silica light guide homogenizer and the 2D-CPC pump cavity; c Detailed view of the modified 2D-CPC pump cavity

The list of Zemax^® non-sequential objects utilized to design the 28 W solar laser components, as well as the respective materials, are given in Fig. 6.20.

Fig. 6.20

List of Zemax^® objects in the non-sequential component editor to simulate the components of the 28 W solar laser [23]

The X, Y, Z positions and directions (Tilt about X, Y and Z) of the 28 W solar laser components in Zemax^® space are indicated in Fig. 6.21.

Fig. 6.21

Example of the position and rotation of the 28 W solar laser [23] components in Zemax^® non-sequential component editor

The optimal parameters of the 28 W solar laser [23] components defined in Zemax^® are indicated in Table 6.11.

Table 6.11 28 W solar laser [23] components defined in Zemax^® non-sequential component editor

All the solar laser components were parameterized using objects existent in the Zemax^® list, except for the 2D-CPC pump cavity, which was designed in AUTOCAD and imported to Zemax^® (see Sect. 2.1.3.2 of Chap. 2 for more details). The solar wavelength data and the media materials were defined in the same way as in the previous example in Sect. 6.2.1. For the primary concentrator, 64% reflectivity was assumed, which accounted for the absorption losses in both the heliostat and parabolic mirrors [23]. Therefore, the coating I.36 was defined in the section Coat/Scatter of the object properties. For the 2D-CPC, 94% reflectivity (I.06) was considered [23].

The absorbed pump flux distributions along one central transversal cross section and one central longitudinal cross section of the 4 mm diameter, 30 mm length, 1.1 at.% Nd:YAG laser rod is shown in Fig. 6.22. The rectangular fused silica light guide behaved like a beam homogenizer by transforming the near-Gaussian profile of the concentrated light spot from the parabolic mirror, incident on its input face, into a uniform rectangular light distribution at its output end [23], enabling a homogeneous absorbed pump light distribution along the Nd:YAG laser rod, as demonstrated in Fig. 6.22. This helps to reduce the thermal induced effects in the laser rod and meliorate the laser beam quality. Therefore, the output laser beam brightness can be higher compared to solar lasers with no light homogenizer [7, 13].

Fig. 6.22

Absorbed pump flux distributions along the central transversal and longitudinal cross-sections of the 4.0 mm diameter, 30 mm length, 1.1 at.% Nd:YAG rod of the 28 W solar laser [23], obtained through Zemax^® numerical analysis

The modified 2D-CPC also played a crucial role in improving the absorbed pump distribution by coupling efficiently the pump rays into the center of the laser rod, as shown by the transversal cross-section (Fig. 6.22).

A symmetric concave-concave laser resonator of 320 mm length was adopted in this case, as illustrated in Fig. 6.23. The HR coated mirror with RoC =–5 m, the Nd:YAG laser rod and the PR mirror formed the laser resonator. The PR mirror with R = 94% and RoC = –0.8 m led to the maximum measured laser output power of 27.7 W [23].

Fig. 6.23

Schematic design of the 28 W solar laser resonator [23]. The image is not at scale

In the present case, a stimulated emission cross-section of 2.8 × 10⁻¹⁹ cm² was assumed for LASCAD™ analysis [23]. Based on the procedure described in 6.2.1, multimode laser output power of 29.48 W was numerically extracted from the PR mirror with R = 94% and RoC = –0.8 m at maximum absorbed pump power of 121.2 W, as shown in Fig. 6.24, which agrees reasonably well with the experimental value [23].

Fig. 6.24

Numerically calculated laser output power from the 4 mm diameter, 30 mm length, 1.1 at.% Nd:YAG rod in LASCAD™ as a function of the absorbed solar power, for the output mirror reflectivity (R) of 94%

6.2.3 Zemax^® and LASCAD™ Numerical Analysis of Simultaneous Solar Laser Emissions from Three Ce:Nd:YAG Laser Rods Within a Single Pump Cavity

The design of the 16.5 W solar laser [20], composed of the 0.8 m diameter parabolic mirror as primary concentrator, the secondary aspheric lens and the conical tertiary mirror, within which the three 2.5 mm diameter, 25 mm length, 0.1 at.% Ce: 1.1 at.% Nd:YAG laser rods were end-side-pumped, is represented in Fig. 6.25. This design configuration contributed to the current records in solar-to-laser conversion, collection and slope efficiencies of 4.64%, 41.25 W/m² and 7.64%, respectively [20].

Fig. 6.25

Design of the three-rod Ce: Nd:YAG laser head, composed of the fused silica aspheric lens, the conical pump cavity and the Ce:Nd:YAG rods, actively cooled by water [20]

The list of Zemax^® non-sequential objects utilized to design the 16.5 W three-rod Ce:Nd:YAG solar laser system, as well as the respective materials, are given in Fig. 6.26.

Fig. 6.26

List of Zemax^® objects in the Non-Sequential Component Editor to simulate the components of the most efficient solar laser from three Ce:Nd:YAG rods [20]

In this case, two sources were defined. Source 1 represents the relevant solar emission wavelengths that overlaps with the Nd³⁺ ion absorption spectrum, as well as those correspondent to the Ce³⁺ non-radiative transfer to Nd³⁺ by quantum cutting down conversion. Source 2 is related to the solar wavelengths corresponding to the radiative transfer from Ce³⁺ to Nd³⁺ (see Sect. 4.5 of Chap. 4 for more details). For such, the wavelength data was defined in two spectrum files, one for each source. The spectrum file for source 1 is similar to the wavelength data of the previous examples, i.e., with 22 peak absorption wavelengths of Nd³⁺, whose weight is decided by the solar spectral irradiance value. For source 2, six wavelengths were defined in the spectrum file, corresponding to the most relevant Nd³⁺ peak absorption wavelengths that matches with the Ce³⁺ fluorescence spectrum: 527, 531, 569, 579, 586, and 592 nm [19, 20]. In this case, the weight of each wavelength was defined based on its spectral irradiance in the Ce³⁺ fluorescence spectrum [54]. It is worth noting that the Nd³⁺ material programmed in the glass catalog data in Zemax^® software can also be used to represent the Ce:Nd:YAG material. This is possible thanks to the energy transfer mechanism from Ce³⁺ to Nd³⁺ ions in Ce:Nd:YAG medium.

For the primary concentrator, 75% reflectivity was assumed, which accounted for the absorption losses in both the heliostat and parabolic mirrors [20]. Therefore, the coating I.25 was defined in the section Coat/Scatter of the object properties. For the conical pump cavity, 94% reflectivity (I.06) was considered [20].

The X, Y, Z positions and directions (Tilt about X, Y and Z) of the simultaneous 16.5 W solar laser system in Zemax^® space are indicated in Fig. 6.27. The optimal parameters of the simultaneous 16.5 W solar laser [20] components defined in Zemax^® are indicated in Table 6.12.

Fig. 6.27

Example of the position and rotation of the most efficient solar laser emissions from three Ce:Nd:YAG rods [20] in Zemax^® Non-Sequential Component Editor

Table 6.12 Components of the most efficient solar laser emissions from three Ce:Nd:YAG rods [20] defined in non-sequential component editor

The absorbed pump flux distributions along five transversal cross-sections of the three Ce:Nd:YAG rods are given in Fig. 6.28. Non-uniform distributions along the end-side-pumped laser rods were numerically calculated with a peak absorbed pump flux of 0.68 W/mm³. Nevertheless, these were the distributions that ensured the maximum absorbed solar power by the three rods.

Fig. 6.28

Absorbed pump-flux distributions along five transversal cross-sections (1, 2, 3, 4 and 5) of the three 2.5 mm diameter, 25 mm length Ce:Nd:YAG rods, obtained through Zemax^® numerical analysis [20]

In the present case, a stimulated emission cross-section of 2.8 × 10⁻¹⁹ cm² was assumed for LASCAD™ analysis [20]. The laser resonator configuration for maximum multimode solar laser extraction from one of the three Ce:Nd:YAG laser rods is illustrated in Fig. 6.29, which is similar for all the three laser rods. PR mirrors with 97.5% reflectivity and RoC = –0.5 m were adopted. Each one was optically aligned with its respective laser rod 15 mm away from the AR1064 nm output face.

Fig. 6.29

Schematic design of the laser resonator for multimode solar laser extraction from one of the three Ce:Nd:YAG rods [20]

With this laser resonator configuration, maximum multimode laser power of 5.64 W was numerically calculated for each one of the Ce:Nd:YAG rods, as shown in Fig. 6.30, corresponding to 16.92 W (3 × 5.64 W) total multimode solar power, which is close to the experimental value of 16.5 W.

Fig. 6.30

Numerically calculated laser output power from one of the three Ce:Nd:YAG rods in LASCAD™ as a function of the absorbed solar power, for the output mirror reflectivity (R) of 97.5%