Methods and algorithms of computational mathematics and their applications

Inverse Sturm–Liouville Problem and its application to inverse problems in thin film optics

A. V. Tikhonravov^a, A. A. Shkalikov<sup>b

a</sup> Lomonosov Moscow State University, Research Computing Center
^b Lomonosov Moscow State University, Mechanics and Mathematics Department

Abstract: The application of the results of the inverse Sturm–Liouville problem for the development of the theory and numerical methods for solving inverse problems in thin film optics is shown. A brief overview of the most effective methods for designing optical coatings is given. It is shown that with the help of developed methods the most demanding types of coatings with a large number of optimized parameters can be designed. The unique spectral properties of these coatings are achieved on the basis of the developed theory.

Keywords: inverse problem, Sturm-Liouville problem, transformation operators, optical coatings, spectral characteristics.

UDC: 535.4

Received: 29.10.2024

DOI: 10.26089/NumMet.2024s01