Method for approximate analytical calculation of electromagnetic wave reflection coefficients from a layer of inhomogeneous non-reciprocal chiral metamaterial taking into account dispersion of material parameters

Background. Modern research in the field of metamaterials opens up new horizons in the development of materials with unique electromagnetic properties that can be used in various applications, from telecommunications to medical diagnostics. Inhomogeneous non-reciprocal chiral metamaterials are of particular interest due to their ability to control the polarization of electromagnetic waves and alter their properties. However, such electrodynamic problems are often solved using numerical methods that require significant computational resources and time, which limits their practical application. Therefore, there is a need to develop approximate analytical methods for estimating reflection coefficients and understanding the physical mechanisms underlying these processes. Aim. Development of a method for approximate calculation of reflection coefficients of a flat homogeneous electromagnetic wave from a planar layer of an inhomogeneous non-reciprocal chiral metamaterial, taking into account the dispersion of material parameters. An analytical approach has been proposed that will allow obtaining solutions of different approximation orders and provide a deeper understanding of the physics of reflection processes. Methods. An analytical approach to calculating reflection coefficients based on field theory methods is used. Inhomogeneity and non-reciprocity of chiral metamaterial are taken into account. A number of approximate solutions have been developed to analyze the behavior of electromagnetic waves under various conditions of incidence and polarization. Results. The proposed analytical method makes it possible to efficiently calculate reflection coefficients for plane waves under various conditions of interaction with inhomogeneous non-reciprocal chiral metamaterials. Conclusion. New approach to calculation of reflection coefficients of plane electromagnetic wave from planar layer of inhomogeneous non-reciprocal chiral metamaterial is presented taking into account dispersion of material parameters. The developed analytical method provides faster and more efficient solutions compared to numerical methods and contributes to a better understanding of the physics of reflection processes in complex materials. The results obtained can be useful for further research in the field of metamaterials and their application in modern technologies.