We investigated the process of propagation of the surface waves in the chiral meta-spectrum with gradient dielectric, magnetic and magnetoelectric permittivities in our work. We have found a condition for the existence of nonclassical plane electromagnetic waves in it. We have proved that the dispersion equation for the gradient chiral medium leads to four roots for the normalized wave vector. Thus, in this artificial environment, as in a homogeneous chiral medium, in general, four waves can propagate, differing in the direction of propagation. We took into account an anomalous propagation of waves in such an environment, when there can be more or less than two counter modes. So, we solved the most important mathematical problems of uncertainty or lack of solution (an unusual combination of signs of the transverse and longitudinal components of the wave vector) in our decision. Dependences of the component of the normalized propagation vector on the chirality parameter of the meta-environment and the components of the normalized wave vector on the parameters of the gradient of the spatial profiles of the material characteristics of the artificial medium were obtained.

Keywords: gradient chiral meta-medium, compositional structure, plane electromagnetic waves, gradient tensors of material characteristics, normalized wave vector

The results of an analytical study of diffraction of surface waves in anisotropic gradient open planar structures were presented in this work. The solutions of the wave equation and the possible values ​​of the constants of propagation for waves in the complex plane transverse wave numbers were found. We obtained a graphical expression of the reflection coefficient of the first guided magnetic modes from the given size of the cross-structure for different values ​​of the gradient parameters in the transverse profiles of the elements of the dielectric tensor of waveguide layer. We finally showed the possibility of practical applications of all results.

Keywords: compositional structure, waves of the discrete spectrum, the gradient tensor of the dielectric suseptibulity, the reflection coefficient of the first magnetic modes

We presented theoretical studies which were related with a compositional system consisting of two regular anisotropic gradient planar structures in this article. The principal axes of tensors of the dielectric permittivity were coincided with axes of the Cartesian coordinate system when their components were generalized by the spatial distribution. We used a representation of a set of related fields for the surface waves by mixed spectrum of the regular symmetrical gradient anisotropic waveguides. We also used the system of coupled equations for the quasi-amplitude coefficients of the interacting modes, which was received in our previous work. Then we analyzed the effect of anisotropy, inhomogeneity in the transverse and longitudinal dependence of modal transformation. It was possible to trace the transformation of modes with maintaining of polarization and take into account the phase relations between the interacting modes and functions of changing of all material characteristics in connected structures and their dependence on parameters of the gradient components of the dielectric tensor in waveguide media. The possibility of effective control to the interaction between modes of the continuous spectrum due to changes in parameters and characteristics of compositional artificial medium was found out. A comparison of the losses in the casing and in the usual coupled system was done. The high reliability of all results was marked.

Keywords: connected regular anisotropic gradient structures, surface waves, parameters of the gradient components in the tensor of the dielectric permittivity, losses of directed waves

Distribution of surface waves in open nonlinear anisotropic and gradient planar compositional structures was considered. The planar waveguide structure consisted of four layers which dielectric susceptibility of the internal environment contained additive components. One of the components was depended on the module of electric field under sedate laws. Other components were represented by a tensor of dielectric permeability which main axes were coincided with axes of the Cartesian system of coordinates, then were turned on some corner of rather longitudinal coordinate of Oz, and finally were turned round the cross coordinate of Oy. Elements of a tensor of dielectric susceptibility depended on spatial coordinates under the generalized laws. From Maxwell's equations we received the wave equations for the cross working-out electric and magnetic vectors. New solutions of these quasi-differential equations which special cases could be presented by the set of known special functions were found. Cross and longitudinal components of electric and magnetic fields were found on this basis. In the end of our research we showed the possibility of practical applications of all results.

Keywords: non-linearity, non-linear optics , layered structure , surface waves , discrete spectrum , dielectric waveguides complex structure .

The theoretical research of the compositional system consisting of two irregular anisotropic gradient-planar structures was done. The main axes of the dielectric tensor rotated around the y-axis in case of their elements had different spatial distributions. The system of coupled integro-quasidifferential equations for the amplitude coefficients of the interacting modes was achieved taking into account the substitution of the field for the required system by the related set of surface and pseudosurface electric and magnetic waves in mixed spectrum for regular asymmetrical inhomogeneous anisotropic waveguides. Creating this system, we considered the irregular boundary components of structures, as well as anisotropy, heterogeneity, transverse and longitudinal dependence of modal transformation. The solution of this system allowed to trace the transformation of modes with persistence of polarization and took into account the phase relations between the interacting modes and functions of border changing for related structures and their dependence on the parameters of the gradient components of the dielectric transmittivity tensor of waveguide environment. An ability to manage the transformation of modes of the continuous spectrum by changing the parameters and characteristics of compositional simulated media and its non-reciprocity was proved.

Keywords: related irregular compositional structures, the system of coupled integro-quasidifferential equations, pseudosurface electric and magnetic waves, parameters of the gradient components of the dielectric transmittivity tensor.