Modeling the reflection of the electromagnetic waves at a diffraction grating generated on a curved surface

This article describes mathematical tools that allow one to simulate the reflection at diffraction gratings generated on an arbitrary surface. To solve this problem an analog of the Kirchhoff method was used. As an example, we considered reflection at a grating generated on a spherical surface. For modelling such systems we developed a program that allowed us to carry out a numerical experiment. We discussed a possibility of generalization of the results onto arbitrary diffractive optical elements.