Analytically design of multicycle broadband AR coatings

Normal-incidence multicycle broadband AR coatings on glass with low residual over the wavelength region 400 nm to 800 nm are theoretically discussed. Using the method of effective interfaces and the concept of equivalent index layers a 4-layer design sub(AHBL)air is expanded into the designs sub [AHC2LCBL]air and sub[AH(C2LC)2BL]air were A, B, C, H, and L are quarter-wave layers with refractive indices nH = 1.38, nL = 2.35, and nL<nL,nB, NC<nH. These designs represent 1-cycle, 2- cycle, and 3-cycle broadband AR coatings and perform a residual reflectance of 0.20 percent, 0.14 percent, and 0.10 percent, respectively. Four other designs demonstrate the approach at other wavelength regions. In one example, all quarter-wave layers with refractive indices in-between nL and nH are analytically substituted using equivalent index layers to get two-material multilayers suitable for practical applications. After this, the design is refined with respect to the optical thickness whereby the layer number is fixed. The resulting design consists of 18 layers and performs an average residual reflectance 0.085 percent over the region 400 nm to 800 nm.