Optimization

The method

The multidimensional optimization method is based on the approach suggested by Davidon (1959), and further developed by Fletcher and Powell. The Davidon–Fletcher–Powell method [14] is a Quasi-Newton Method also known as a Variable Metrics Method. Almost every incident wave, and structure parameters, including refractive indexes, can be set as variables. There isn't any restriction on optimization search area except a physical meaning of the variable parameters (for example a layer thickness can not be negative).

In the ideal case of parabolic behaviour of the criterion function, the process converges after N iterations for N variables; in many real cases it takes more, and after the defined number of iterations the code continues from the position reached in the direction of steepest descent. The Optimization page sets the iterations, the accuracy of the numerical derivatives and the size of the region searched.

The criterion function

The objective is the minimum mean-square deviation between user-defined target values and the calculated ones. The Criterion Function is a set of completely independent criterion points, each targeting the power of a given diffraction order — or, in the collinear codes, the angular position of a resonance of the structure — at its own wavelength, angle and polarization, with a weight. Several methods of a criterion function construction allow solving variety of design and inverse structure reconstruction problems.

The variables

The Variable Parameters page selects what varies: wavelength, period and angles, and the structure parameters exported from the Settings dialog; media with identical refractive indices can be grouped so that one variable moves them together. Optimization is available in all six Full-edition codes; the Optimization dialog topic describes the controls.

Examples

• The rear mirror of a 914 nm Nd:YVO₄ microlaser: transparent at the 808 nm pump, reflecting at 914 nm; step-by-step example 4.2.
• Step-by-step example 1.1.2 and its neighbours use the Optimize button on resonant waveguide gratings.

Optimization is a Full-edition feature. In demo mode refractive indices, being fixed at multiples of 0.5, cannot be variables.