Modification of transfer-matrix method for electromagnetic waves in layered superconductor in presence of dc magnetic field
In the present paper, we modify the transfer-matrix method to study the dissipation-free transition of electromagnetic waves of terahertz range through a plate of layered superconductor embedded in the dielectric environment in the presence of external direct current (dc) magnetic field. In this work, we сonsider TM-polarized electromagnetic waves. The setup is arranged in such a way that the dielectric and superconducting layers in the plate are perpendicular to its interface, and the external magnetic field is directed along the plate and parallel to the layers. We consider the case of a weak external dc field at which magnetic vortices do not penetrate the plate. Due to the nonlinearity of the Josephson plasma formed in the layered superconductor, the dc magnetic field penetrates non-uniformly into the plate and affects the electromagnetic wave. Hence, the magnitude of the external dc magnetic field can be used as a variable parameter to tune various phenomena associated with the propagation of an electromagnetic waves in layered superconductors. In the presence of the external homogeneous dc magnetic field, linear electromagnetic waves in the layered superconductor turn out to be non-exponential. Therefore we cannot directly apply the transfer matrix method, in which the amplitudes of the corresponding exponents are compared. However, in the present paper, it is shown that for a sufficiently thick plate, the matrices describing the wave transfer through the plate can be introduced. The analytical expressions for these matrices are derived explicitly in terms of special Legendre functions. The obtained transfer-matrices can be used for the further study of the wave transfer through the layered superconductor in the presence of an external dc magnetic field.
