An integral equation method in the problem of electromagnetic wave propagation in a space filled with a locally inhomogeneous medium with a graphene layer at the boundary of the inhomogeneity region

Abstract

Background. The purpose of the study is to obtain a hybrid integro–differential equation in the case of an inhomogeneous volumetric graphene-covered obstacle to an electromagnetic wave. Material and methods. The Green tensor and the tensor analogue of the Green integral formula are used to derive the equation. Results. The transmission problem for the Maxwell equations is reduced to a hybrid integro-differential equation. Conclusions. A new equation is obtained to describe the propagation of a monochromatic electromagnetic wave in the three-dimensional locally inhomogeneous space with a graphene layer; collocation method is proposed to solve the hybrid equation numerically.

Keywords

• electromagnetic wave propagation
• graphene layer
• maxwell's equations
• green's tensor
• green's formula
• hybrid integro-differential equation
• collocation method