Fig. 1. (Color online) The graded refractive-index structure of an N-layer anti-reflective coating system. A plane wave is incident from the air with the refractive index of n₀ and incident angle of θ. Every layer of the coating is characterized by the thickness d_i with the refractive index n_i, i = {1, 2, …, N}. The entire absorption layer is assumed to be in the bottom layer with refractive index n_ab without the back surface reflectance. The right curve shows the numerical value of the graded change of refractive index and the thickness of each anti-reflective layer.

Fig. 2. (Color online) The dependence of the incident photon flux density on the wavelength and the incident angle on the day of the spring equinox for (a) Quito, (b) Beijing and (c) Moscow, respectively. At noon of the day of the spring equinox, the sunlight is vertically incident on the equator. The incident angle at noon of the day of spring equinox for Quito, Beijing and Moscow is 0, 40, and 55 degrees, respectively. At sunrise or sunset, the incident angles of these three cities are the same 90 degrees. (d) The comparison of the spectrum of the incident photon flux density of three cities at noon on the day of the spring equinox. The incident photon flux density spectra are totally different Earth due to the atmosphere scatter and absorption at different location with different incident angle and latitude.

Fig. 3. (Color online) The optical transmittance spectrum with λ = [300, 1100] nm and θ = [0°, 90°] for two-layer AR coating optimized by (a) ACA without SPCTRL2, and with SPCTRL2 of (b) Quito (c) Beijing and (d) Moscow. The detail structures are presented in Table 2. The areas with transmittance above 80% and 98% are marked by white lines. The incident quantum efficiency at Quito, Beijing and Moscow optimized by ACA with SPCTRL2 incorporated is 0.26%, 1.37% and 4.24% larger than that optimized without SPCTRL2 incorporated for two-layer AR coating, respectively. Comparison of the actual solar spectrum and incident quantum efficiency η_in (λ), for (e) Quito (f) Beijing and (g) Moscow with and without SPCTRL2 incorporated. When considering the solar spectrum in different cities and setting η_in as the evaluation function in the AR coating optimization, the peak of the quantum efficiency spectrum moves towards around 700 nm, which is the peak of the actual solar spectrum and fits the actual solar spectrum very well for all three cities.

Table 1. Input parameters used in SPCTRL2 program.

Table 2. Detail structures of two-layer antireflective coating optimized by ant colony algorithm with and without SPCTRL2 incorporated.