The solar pumped laser is an important way of utilizing solar energy. A solar pumped laser offers attractive prospects for many applications in the future, including space laser communication, space energy transmission, and magnesium resource recycling [1-3]. The solar laser has attracted more and more attention [4, 5]. The solar concentrating system is very important for a solar pumped laser, and can affect the total conversation efficiency and laser output power directly [6-8].

Fresnel lenses have been used as the primary concentrator of a solar pumped laser because they can offer high concentrating efficiency, along with minimal weight and low cost. In fact, Fresnel lenses have been widely used in the fields of projection display, illumination, and solar-energy utilization [9-11]. The conventional Fresnel lens has a surface consisting of a concentric series of simple lens sections. The material of the Fresnel lens for many solar pumped laser systems is poly(methyl methacrylate) (PMMA). This material is a typical optical plastic that is transparent to most of the wavelengths in the solar spectrum.

Abdel-Hadi reported a laser concentration system including a Fresnel lens and CPC (composite parabolic concentrator) [12]; the area of the Fresnel lens was 60 cm × 60 cm and the focal length 0.75 m. Fang demonstrated a three-stage concentrator system [13], the first stage being a Fresnel lens (0.98 m × 1.2 m, f = 1.3 m). Liang reported a three-stage multi-Fresnel lens that was adopted for a side-pumping solar laser [14]; each part was composed of 32 pairs of narrow plane mirrors and Fresnel lenses. The pumping approach of a scalable TEM₀₀ solar laser was also three-stage system in [15], in which the first-stage had a four-pair Fresnel lens-folding mirror collector. Each Fresnel lens diameter was 1.13 m and the focal length 2 m. Yang used a 1.03 m² Fresnel lens as the primary concentrator for a 28 W solar laser [16].

It is difficult to use a conventional Fresnel lens with large size directly for a solar end-pumped laser, because dispersion and sunlight of divergent angle cause a larger focal-spot size. To enhance concentration efficiency, usually a second concentrator needs to be utilized.

A Fresnel lens 1.4 × 1.05 m² in size and with focal length of 1.2 m was used as a concentrator for a solar pumped laser. The measured full width at half maximum (FWHM) of the focal point was about 11 mm, and a cylindrical cavity was used to enhance the coupling to the laser media [17]. Another Fresnel lens (2 × 2 m², f = 2000 mm) was also adopted as a concentrator for a solar pumped laser with the diameter of the focal point limited to 20 mm. A conical cavity was used to enhance the solar-power absorption by the laser media [18]. A laser output of about 80 W was achieved with a combination of Fresnel lenses 4 m² in area and 2 m in focal length. The FWHM of the Fresnel lens’s focal point was 20.4 mm, and a pumping cavity was used as a secondary power concentrator [19]. A Fresnel lens 0.9 m in diameter acted as a primary concentrator, with a measured FWHM of the focal point of about 12 mm, while a dielectric totally internally reflecting device was employed as a secondary concentrator [20]. A 1-m-diameter Fresnel lens also acted as concentrator, with focal length 1.3 m and FWHM of the focal point 13 mm. A large aspheric lens and a 2D-CPC were used to further compress the concentrated solar radiation [21]. Also, four 800 mm × 800 mm Fresnel lenses were used as a primary concentrator, the FWHM diameter of the focal spot being 12 mm, while aspherical lenses and a fused-silica sphere were used for further concentration [22].

Compared to the side-pumped laser, the end-pumped laser not only has high pump efficiency, but also can easily achieve laser output with good beam quality [23]. If the concentrator for a solar end-pumped laser were a single Fresnel lens without a secondary optical element, the structure would be simpler and adjustment would be more convenient. Thus it is necessary to design a novel Fresnel lens to meet this need.

Figure 1 shows the schematic diagram of a Fresnel lens based on once total internal reflection (OTIR). The prism of the Fresnel lens is composed of two parallel surfaces and one surface that is perpendicular to the emergent light. In this figure, b is the groove pitch, d is the height of the prism, α is the dip angle of two parallel surfaces, and θ is the rim angle. The focal length is F. The distance between the central incident-light ray of the prism and the optical axis is D. H is the height of the current prism, and t is the thickness of the Fresnel lens (3 mm). The groove pitch is 0.33 mm.

Figure 1. Schematic of a Fresnel lens based on OTIR.

The relationship of the parameters is as follows:

The angle α decreases with increasing D in this design, when the focal length is maintained. It causes the two adjacent prisms to overlap, and part of the light will be blocked. To overcome this problem, each prism increases by a step in height relative to the upper prism, and the whole structure is a staircase. According to Eqs. (1) and (2), the structure of this kind Fresnel lens can be given.

However, d increases rapidly when D decreases. This leads to the design becoming inappropriate. This design is suitable for the outer part of the Fresnel lens, where the radius is 300 to 600 mm. To compensate for the defects of this design, we propose another design for the inner part as follows.

Figure 2 shows the Fresnel lens design based on twice total internal reflection (TTIR). The prism consists of surfaces of a fixed tilt angle β, a gradient angle α, and a plane perpendicular to the emergent light. Angle β was set to π/4. The thickness of the Fresnel lens t is set to 3 mm.

Figure 2. Schematic of a Fresnel lens based on TTIR.

The height of each prism also increases relative to the upper prism, for the same reason as in the outer part of the Fresnel lens. The parameters’ relationship is as follows:

According to Eqs. (3)-(6), the structure of this kind Fresnel lens can be given. This method is used to design the inner part of the Fresnel lens.

The structure of the hybrid Fresnel lens is shown in Fig. 3. This hybrid Fresnel lens includes two parts, the inner part and the outer part. The radius of the inner part is 300 mm, and the radius of the outer part is from 300 to 600 mm. The inner part is a twice-total-internal-reflection and vertical-transmission lens. The outer part is a once-total-reflection and vertical-transmission lens. The material of the Fresnel lens is PMMA. The concentrating performance of the Fresnel lens was studied using the TracePro optical software.

Figure 3. Schematic diagram of the hybrid Fresnel lens.

To optimize the design, the relationship between concentration efficiency and the Fresnel lens’s focal length is demonstrated in Fig. 4, when the receiver radius is 3 mm. Figure 4 shows that the concentration efficiency changes when the focal length varies from 700 to 1200 mm. The maximum efficiency of 73.2% is reached when the focal length is 750 mm, so the hybrid Fresnel lens’s focal length is set to that value.

Figure 4. Relationship between efficiency and focal length

Figure 5 shows the irradiation of the hybrid Fresnel lens’s focus spot. The wavelength of incident light also ranges from 374 to 1642 nm in the simulation.

Figure 5. Irradiation of the hybrid Fresnel lens’s focus spot.

Figure 6 shows that the efficiency changes as the receiver radius ranges from 0 to 40 mm. The curvature of the hybrid Fresnel lens increases more sharply than that of the conventional Fresnel lenses mentioned earlier in refs. 24 and 25. Focal length, groove pitch, thickness, and diameter of the conventional Fresnel lens that is compared are respectively 750 mm, 0.33 mm, 3 mm, and 1200 mm [24, 25]. The concentration efficiencies of the hybrid and conventional Fresnel lenses are 37.3% and 9.7% respectively when the receiver radius is 2 mm, and are 73.2% and 19.1% respectively when the receiver radius is 3 mm. This means that collection of the sun’s energy by the hybrid Fresnel lens is 3.7 times as great as by the conventional Fresnel lens, if the radius of laser rod is 3 mm and end pumping is adopted. The maximum efficiency of the hybrid Fresnel lens is 92.1%, when r is 6.5 mm; that of the conventional Fresnel lens is 80.8%, when r is 37.5 mm.

The inset of Fig. 6 demostrates that the total concentrator efficiency is 40.2% when a CPC is at the focal plane of the Fresnel lens. After optimizing the position of the CPC, the maximum concentration efficiency can reach 50.4% [24]. Even when a dielectric-filled CPC is used to improve the efficiency, the total concentrating efficiency of the secondary concentrating system is only 64.1% [26].

Figure 6. Relationship between concentration efficiency of the system and receiver radius.

The FWHM of the hybrid Fresnel lens’s focal point is 5.6 mm. This result also has advantage over that for the Fresnel lenses in refs. 17-22.

In this paper, a novel hybrid Fresnel lens for a solar end-pumped solid-state laser was reported. The new hybrid Fresnel lens includes two parts, the inner part and the outer part. The inner part is a twice-total-internal-reflection and vertical-transmission lens. The outer part is a oncetotal-reflection and vertical-transmission lens. The focal length of the Fresnel lens is 750 mm, the radius of the inner part is 300 mm, and the radius of the outer part is from 300 to 600 mm. The concentration efficiency of this hybrid Fresnel lens is 73.2%, when the receiver radius is 3 mm. This means that collection of the sun’s energy by the hybrid Fresnel lens is improved greatly, so a secondary concentrator becomes unnecessary, and the concentrator system can be simpler. This kind of Fresnel lens can also be used in other fields, such as concentrated photovoltaics and solar thermal utilization.