Refining and optimization in multilayers

An important aspect of modern thin film design work is the use of computers to match the multilayer parameters to a set of optical specifications such as a desired reflectance curve. Following a brief historical survey we discuss modern optimization algorithms as they apply to thin film design. Optimization is an active research field in present-day applied mathematics, and it is important to use recently developed techniques. Without going into mathematical detail we compare the operation of two algorithms that have proven successful-a modification of the damped least squares method common in lens design, and a gradient (steepest descent) method using several different merit functions. Examples of designs obtained by optimization techniques are given, including some in which the process achieved the known theoretically optimum design starting from arbitrary or simple quarterwave initial designs. Optimization techniques have other applications in thin films and we mention briefly two of these: determination of dispersion characteristics of single layers and design of masks for coating tanks.