Broadband High-Reflection Coating at 50 Degrees [ Contents ] [ Index ] [ Home ] In the paper, Konstantin V. Popov, J.A. Dobrowolski, Alexander V. Tikhonravov, and Brian T. Sullivan, "Broadband high-reflection multilayer coatings at oblique angles of incidence," Applied Optics, Vol. 36, No. 10, 1 April 1997, pp. 2139-2151. the authors examine the problem of creating broadband dielectric reflectors using contiguous quarter-wave stacks. It is an interesting paper -- well worth reading if you need to design this type of coating. The following example is taken from the paper. The goal is to design a high reflector which operates in the wavelength range 400-800 nm at a 50 degree angle of incidence. Because this coating is at 50 degrees, the reflectance of S polarization will be much higher than P. Hence, we can concentrate on controlling the reflectance for P polarization. The coating, composed of layers of L (index 1.45) and H (index 2.35), is to be deposited on glass G (index 1.52). The incident medium is air (index 1.0). The formulas in the paper lead to a 3-stack (7 periods/stack) design whose stacks are centered at wavelengths 705, 555, and 437 nm. To increase the reflectance, the authors add one additional H layer next to the substrate. The result is a 43-layer coating whose average P reflectance is 98%. TFCalc can be used to design and refine this type of coating. The starting design is a 43-layer coating with the stack formula G a(HL)^7 b(H(LH)^7) c(LH)^7 air where H and L represent 1 QWOT (quarter-wave optical thickness) at a reference wavelength of 550 nm and incident angle of 50 degrees, and the factors a, b,and c must be determined using "group" optimization. (This is called group optimization because we vary the thickness of a group of layers; all layers in the same group keep the same relative thickness to the other layer in the group.) Using one continuous target (Rp=100% for 400-800 nm at 50 degrees) and starting values of a = 1.2000, b = 1.0000, c = 0.8000, group optimization finds a = 1.3260, b = 1.0171, c = 0.7855. These values correspond to stacks centered at 729, 559, and 432 nm. The average P reflectance is about 98%. The performance for P polarization is displayed below. If all layers are optimized to improve the reflectance, the average P reflectance stays approximately the same; however, the minimum reflectance is substantially higher, as shown below. Here is the last design, with the first layer closest to the substrate and thickness given in nm. ``` H 97.87 L 171.35 H 80.56 L 152.15 H 74.35 L 154.04 H 83.10 L 178.45 H 72.02 L 129.75 H 85.36 L 141.64 H 82.96 L 141.89 H 71.17 L 137.71 H 69.96 L 104.04 H 55.42 L 113.89 H 71.53 L 121.61 H 63.21 L 111.11 H 61.47 L 121.69 H 63.51 L 101.69 H 56.86 L 101.16 H 52.26 L 82.60 H 46.62 L 94.22 H 53.49 L 90.92 H 46.16 L 86.62 H 51.59 L 91.80 H 45.96 L 80.64 H 49.35 ```