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Plane harmonic wave propagation along an interface between vacuum and a semi-infinite uniaxial anisotropic medium is considered. It is shown that there is a bulk wave within an anisotropic medium in this case. It is also proved for the first time that a reflected wave must propagate perpendicularly to an interface. Moreover, a reflected wave is absent in the case of ordinary wave propagation.

A phenomenon of plane electromagnetic wave propagation in vacuum parallel to an interface between vacuum and an anisotropic medium has been considered in [

It is obvious that studying behavior of the transmitted and reflected waves when an incident wave propagates parallel to an interface between anisotropic and isotropic media has important theoretical and practical significance. Indeed this issue has not been studied theoretically despite the fact that a similar phenomenon has been described even in hydrodynamics [

In this paper, we consider the ideal case of wave propagation over an infinite interface between free space and a uniaxial dielectric anisotropic medium without frequency dispersion. An orientation of the anisotropy axis is taken arbitrary in our treatment. At the same time, we do not study the problem of the possibility of exciting such a wave and the grounds for this assumption. It is important to note that this particular case cannot be described by using well-known methods [

The behavior of both transmitting in the anisotropic medium and reflecting in vacuum waves is investigated in this paper too. It is shown analytically that a reflected wave should propagate perpendicularly to the interface to satisfying Maxwell’s equations and the boundary conditions simultaneously. The expressions of reflection and transmission coefficients for a semi-infinite medium are obtained and the analysis of these coefficients is carried out.

In this paper, we study the particular case of the uniaxial anisotropic dielectric medium with the scalar permeability

For example, it can be a plasma medium near the resonance region [

It is assumed that the anisotropy axis is orientated in the incidence plane under an arbitrary angle

Geometry of the problem.

In the considered case, a plane harmonic wave with the wavenumber

The solutions of Maxwell’s equations [

The solutions of (

The geometry of the considered problem is shown in Figure

Geometry of the problem of the propagation and reflection of an ordinary wave.

It is important that the normal magnetic field component

Let us find the normal component of the wave vector

Thus the ordinary wave has both the real normal component of the wave vector (

It is seen from (

The geometry of the considered problem is presented in Figure

Geometry of the problem of the propagation and reflection of an extraordinary wave.

It has been shown earlier that a plane harmonic wave propagating parallel to an interface between vacuum and an anisotropic medium can excite a bulk wave propagating under an arbitrary angle within an anisotropic medium. Now it is necessary to describe behavior of a reflected wave in vacuum if it existed.

Let us take into account the fact that the tangential components of the wavenumbers of incident, reflected, and refracted waves must be equal one to other

Moreover a refracted wave has the tangential component of magnetic field for an ordinary wave and the tangential component of the electric field for an extraordinary wave. Therefore such component must be in a reflected wave as this component is absent in an incident wave. But such phenomenon is impossible when a reflected wave propagates along an interface. Based on these considerations, we assume that a reflected linearly polarized wave should propagate perpendicular to an interface between vacuum and an anisotropic medium.

Let us consider the ideal case of plane harmonic wave propagation above an interface between vacuum and a uniaxial anisotropic medium. It follows from (

The geometry of the problem is shown in Figure

Let us write the continuity conditions for the field components at the interface between vacuum and an anisotropic medium [

Thus, if a harmonic plane wave containing the components

The geometry of the problem is given in Figure

The analysis of the obtained expression shows that the parts of an electromagnetic wave transmitting in a medium and reflected from the interface depend on the parameters of the medium and do not depend on frequency. Indeed,

In this section, the numerical example of the extraordinary electromagnetic wave behavior in the considered particular case is presented. We consider the quartz medium with the typical parameters

In Figure

The dependencies of the transmission angles on the inclination angle.

It has been also verified by numerical calculations that there is no frequency dependence of these angles. Dependence can be seen only if frequency dispersion of the constitutive parameters

The dependencies of the transmission and reflection coefficients for the medium parameters given above are presented in Figure

The dependencies of the transmission and reflection coefficients on the inclination angle.

We must also note that

In this paper, we consider the behavior of the harmonic plane wave propagating parallel to the interface between vacuum and a uniaxial anisotropic medium. It is shown that the wave propagating in an anisotropic medium has both the normal component of the wave vector and the normal component of the Poynting vector.

It is also proved that in this case the reflected wave should propagate perpendicularly to an interface. At the same time, the reflected wave is absent for an ordinary wave. Moreover, in this case, the reflection and transmission coefficients do not depend on the frequency if frequency dispersion of material parameters is absent.

It is important to dwell on the practical applications of this phenomenon. In particular, we note that it must be taken into account the calculation and design of microwave and optical communication systems. Furthermore, penetration effect enables the creation of new microwave and optical devices such as a power divider [

The authors declare that there are no conflicts of interest regarding the publication of this manuscript.