There are a number of design considerations to ensure a lens efficiently focuses light rays onto a focal point. The two relevant for this discussion are geometry and material selection. Design considerations include the geometric shape, the wavelength with the highest quantum efficiency for the PV cell, and the refractive index of the materials used for the lens.
Fresnel lenses are the most common geometry designed for CPV concentrators . A Fresnel lens is composed of a number of Fresnel zones visualized as a series of prisms with different steps in thickness cut around the lens circumference. The expected concentration factors in the assembly are typically modeled using ray tracing, specifically the edge-ray principle . The edge-ray principle solely considers the trajectory of edge rays from the source through the lens and to the target. This modeling is available in a number of optical design programs, such as ZEMAX®. The concentration factor typically ranges from 5 to 500x depending on if the lens is planar or circular. A planar Fresnel lens utilizes one-axis tracking, and a circular requires dual-axes tracking.
The material requirements for polymeric lenses are based on optical and thermal properties. The material class must have high optical transmission. In Chapter 2, the wavelength dependency of polymeric refractive indices was discussed. As discussed, the material choice is dependent on the wavelengths that need to be focused. For PV cells, the relevant wavelengths are always
in the visible spectrum. This requires a limited dispersion of visible wavelengths of light, as measured by the Abbe number. The Abbe number (VD) defines how much the refractive index changes over the visible spectrum. It is the ratio of the difference between the refractive index of green-yellow (nD = X = 589 nm) light minus 1 and the difference between the refractive index at blue-green (nF = X = 486 nm) and red (nC = X = 656 nm) light.
In addition, the optical design is sensitive to the polymeric lens thickness and the radius of curvature. As a result, the polymeric material must have a low coefficient of thermal expansion (CTE) to ensure the focus point does not change during thermal cycling.
Historically, polyacrylates have been the favored material selection for Fresnel lenses due to their high optical transmission, low wavelength dispersibility (Abbe number 50 to 60), and comparatively good weathering characteristics . Because concentrators are most efficient under sunny conditions, most of the weathering of polymethylmethacrylate (PMMA) lens has been performed in arid environments. Rainhart and coworkers found a 10% drop in transmission over a 17-year exposure period and significant decreases in mechanical strength due to crazing . Reports issued by 3M indicate similar decreases for optical transmission after 13 years of weathering in Minnesota with the largest decreases occurring between 350 and 500 nm.
These decreases in performance were due to poor mechanical and soiling durability. Polymethylmethacrylates are susceptible to crazing, in part, because they are amorphous with an above ambient glass transition temperature. Crazes are small microvoids on the polymer surface created by thermal or mechanical stresses. They severely decrease the mechanical strength of the polymer and readily form cracks under applied stress. Rainhart and coworkers noted there was a significant increase in embrittlement due to crazing in weathered samples. The samples also suffered mechanical scratches during soiling. This accounted for a 7% optical transmission loss . To avoid this decreased performance, abrasion-resistant polyacrylates have been proposed for these applications. Abrasion-resistant polyacrylates are formulated with a cross-linked polysiloxane topcoat; a commercial example is Spartech’s (Clayton, Missouri) Polycast SAR.