Implementation of a numerical needle method for thin-film design

A variant of the powerful thin-film needle design technique, which was first described by Tikhonravov and his co-workers, is described. In this method thin layers are introduced at optimum positions within the refractive-index profile of a given multilayer system. In the original method the optimum locations for the layer insertions are calculated analytically, whereas in this variant of the method they are determined numerically. This approach, although somewhat slower, is very flexible. With the numerical needle method it is easy to define a merit function that consists of quite complex spectral quantities, such as Commission Internationale de l'Eclairage color coordinates or custom spectral properties that are defined at run time. In the program described, three different absorbing or nonabsorbing materials can be used for the needle layers and one or more needles can be inserted into the system at any given time. Multilayer solutions can also be sought in which the system is defined in terms of repeating groups of layers. It is also possible to calculate automatically a series of solutions to a particular problem with increasing overall thicknesses or to perform simultaneous calculations on several different systems. Examples are given that illustrate these various points.