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**BIE model of periodic diffraction problems in optics.**
*(English)*
Zbl 07478518

Summary: Optical diffraction on a periodical interface belongs to relatively lowly exploited applications of the boundary integral equations method. This contribution presents a less frequent approach to the diffraction problem based on vector tangential fields of electromagnetic intensities. The problem is formulated as the system of boundary integral equations for tangential fields, for which existence and uniqueness of weak solution is proved. The properties of introduced boundary operators with singular kernel are discussed with regard to performed numerical implementation. Presented theoretical model is of advantage when the electromagnetic field near the material interface is studied, that is illustrated by several application outputs.

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### References:

[1] | Bao, G.; Cowsar, L.; (eds.), W. Masters, Mathematicall Modelling in Optical Science, Frontiers in Applied Mathematics 22. SIAM, Philadelphia (2001) · Zbl 0964.00050 |

[2] | Bonnet, M.; Guiggiani, M., Tangential derivative of singular boundary integrals with respect to the position of collocation points, Int. J. Numer. Methods Eng. 41 (1998), 1255-1275 · Zbl 0922.73073 |

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