Automatic Designing of Multilayer Dielectric Films (II)

• Published in: Oyo Buturi Vol. 32; no. 3; pp. 199 - 212
• Main Author: KIMURA, Nobuyoshi
• Format: Journal Article
• Language: Japanese
• Published: The Japan Society of Applied Physics 10.03.1963
• ISSN: 0369-8009; 2188-2290
• DOI: 10.11470/oubutsu1932.32.199

In the present paper, two subjects are mainly studied. One is the development of the designing method studied in the previous paper (I). When the merit function of the system is a many variable function of multi-vectors, general formulae for determining the optimum values of system parameters are derived by using generalized maximum step method and generalized secondary approximation theory. By applying this method to multi-layer films (a many variable function of two vectors), optimum values of both thicknesses and refractive indices can be determined simultaneously. The other is the investigation of the convergency of the merit function to an extremum. Although the weakness of the steepest ascent method is that the converging speed is very slow if the hyper surface of the merit function is distorted along a direction of any system parameter, in maximum step method it can be eliminated by testing the signs of components of a direction cosine of the position vector conceived by the line that connects a corrected point on the hyper surface with the next corrected point. Contours of equal merit function of antireflection monolayer are drawn in a diagram taking thickness and refractive index as abscissa and ordinate. A band pass filter consisting of eleven layer films is designed by the generalized maximum step method. As an example of the distorted hyper surface of the merit function, anti-reflection films of triple layer, the weighing function being taken into consideration, are designed also by using the same method. Anti-reflection films of double layer are designed by using the generalized secondary approxi-mation theory.