Extension of the Method of Single Expression for Analysis of Materials with Complex Permittivity and Permeability

An extension of the method of single expression (MSE) for analysis of materials with complex permittivity and permeability is presented. Along with the real and imaginary parts of permittivity both the real and imaginary parts of permeability are taken into account in the MSE without any approximations. Any combination of signs (positive or negative) for complex permittivity and permeability can be easily treated by the MSE. Normal incidence of plane electromagnetic wave on a layer with complex permittivity and permeability for some combination of their signs including doubly positive and doubly negative media is considered and analysed. Reflection and transmission coefficients of the layers, as well as distributions of electric and magnetic fields amplitudes and power flow density along the layers are obtained via numerical simulation by the MSE. A "magnetic" metallic layer and doubly lossy and "gain-loss" layers with simultaneously positive and negative permittivity and permeability are considered and discussed