Using a method based on mathematical operations with Maxwell’s equations in vector form, it is proved that electromagnetic waves propagating in an arbitrary direction in a bi-gyrotropic medium are always characterized by the collinear orientations of the Poynting vector and the group velocity vector. It is shown that the corresponding Cartesian components of these vectors are proportional to each other, which confirms the collinearity of these vectors. It is found that for all types of electromagnetic waves propagating in an unbounded ferromagnetic medium (which is a special case of a bi-gyrotropic medium), these vectors are always codirected.

The spatial-frequency distributions of spin waves in a magnon crystal and their dispersion characteristics were experimentally investigated. In spite of the weak energy contrast of the crystal, the formation of a number of Brillouin zones and the existence of two types of wave nonreciprocity were detected. Of the two types, one is due to the asymmetry of dispersion dependences with respect to the direction of wave propagation, and the other is due to the difference between the spatial distributions of the waves propagating in opposite directions. The magnon crystal made it possible to detect and measure these types of nonreciprocity.

Maxwell’s equations without using the magnetostatic approximation were used to derive a dispersion equation for spin waves in a tangentially magnetized ferrite plate one of the surfaces of which adjoins a perfect magnetic wall, and the isofrequency dependences of these waves were calculated. It was found that the wave distribution along the plate thickness is described by two wavenumbers, and the isofrequency dependences of different modes of spin waves smoothly pass one into another and have sections corresponding to the volume–volume, volume–surface, and surface–surface wave distributions.

The problem of arbitrary propagation of electromagnetic waves in a tangentially magnetized one-side metallized bigyrotropic layer is solved without using the magnetostatic approximation. It is shown that, in this problem, Maxwell’s equations are reduced to a differential equation corresponding to a biquadratic characteristic equation with four roots kx21, ‒kx21, kx22, and –kx22 describing the distribution of the wave in the layer cross section. A dispersion equation for describing waves with real kx21 and kx22 values is obtained. Using this equation, the characteristics of spin waves in a one-side metallized ferrite plate (a special case of a bigyrotropic layer) are calculated for the frequencies above the ferromagnetic resonance frequency. It is found for these waves that quantity kx21 can take both real and imaginary values, while quantity kx22, only real ones. It is found that, at a certain frequency, the spin wave has an isofrequency curve almost identical to a straight line.

Based on an analysis of statistical data on railway and road traffic, as well as laboratory studies, mathematical models are developed that describe the “human–monitoring system–vehicle–traffic system” system. The issues of classifying operators according to their tendency to fall asleep and create emergency situations are explored. A statistical analysis of the accident rate of vehicle drivers was carried out based on their susceptibility to accidents. The degree of effectiveness and safety of monitoring systems is taken into account, as well as the influence of psychological factors caused by drivers excessive trust in the monitoring system. The risks associated with system malfunctions and insufficient efficiency of its operation are calculated. The use of an ineffective driver monitoring system does not reduce, but increases the likelihood of an accident. The design and principles of operation of a driver vigilance telemechanical control system (DVTCS) are described. The device is designed for continuous monitoring of the drivers vigilance and attentiveness while driving rolling stock. The work of DVTCS is based on scientific results according to which episodic changes in skin resistance reflect the level of alertness and wakefulness. It has been shown that due to more reliable, continuous, and nondistracting monitoring of the drivers physiological state the DVTCS provides a higher level of traffic safety than its “Safety Handle” counterpart. Statistical data from operational and laboratory data have been analyzed, indicating a high level of operational safety of the DVTCS. A comparison of Russian and international requirements for the safety level of DVTCS has been carried out. Methods for further improvement of the device are noted.

A study is performed of the general nonreciprocal characteristics of a surface spin wave and a backward spin wave in a tangentially magnetized plane-parallel ferrite plate. The rule governing the interdependence between the localization of a spin wave across the thickness of the ferrite plate and directions of its group and phase velocities is established.

Purpose of this paper is to give an overview of various experimental methods for investigation of spin waves characteristics. Methods. The paper presents a description of a number of experimental techniques, such as the probing method, the phase shift method, the method of measure of equiphase dependences, the method of intersecting wave beams, and the use of Fourier analysis of the complex transfer coefficient of spin waves to determine their spatial spectrum. The conditions for using the listed methods and the characteristics of spin waves that one can measure by means of these methods are discussed in detail. Results. The paper presents a number of fundamental results that have been obtained on the basis of described methods. For example, the probing method was successfully used to visualize the amplitude and phase distribution of spin waves in the ferrite film plane and, in particular, it was used to experimentally confirm the previously predicted appearance of super-directed propagation of surface and backward volume spin wave beams. The phase-shift measurement method made it possible to measure the dispersion dependence of spin waves in ferrite structures such as ferrite – metal and ferrite – dielectric – metal, where measurements cannot be made by the probing method. The method of measuring equiphase dependences of spin waves made it possible, in particular, to measure for the first time with great accuracy the value of an external magnetic field magnetizing an yttrium iron garnet film to saturation in various crystallographic directions. The method of intersecting wave beams has made it possible to clarify the mechanism of parametric instability of surface spin waves. Fourier analysis of the complex transfer coefficient of spin waves allowed to determine the spatial spectrum of these waves; in particular, dispersion dependences of higher modes of the backward volume spin wave were first measured using this method. Conclusion. The methods described in this paper may continue to be successfully used for investigations of spin waves characteristics in various magnon crystals, ferrite structures and meta-structures.

Diffraction of a backward volume spin wave on a through hole in a ferrite plate is investigated experimentally and theoretically for when the length of the spin wave is greater than the diameter of the hole and the linear transducer exciting the wave is perpendicular to an external uniform magnetic field. It is found that in one direction of the possible super-directional propagation of the wave, a distinct shadow of the hole is observed at a considerable distance from the latter. Good agreement between the experimental and theoretical results is obtained.

A study is performed of the characteristics of a surface spin wave propagating perpendicular to the direction of a uniform magnetic field in a tangentially magnetized plane-parallel metal–ferrite–dielectric–metal structure. It is established that at certain parameters of the structure, quasilinear portions appear in the dispersion dependence of this wave which can ensure the undistorted transmission of a useful signal modulating the surface spin wave.

The influence of the boundary conditions of “perfect metal” and “perfect magnetic wall” being established in various combinations near or on every surface of a tangentially magnetized ferrite plate, on the possibility of undistorted transmission of useful signal through the use of surface spin waves in this structure, is theoretically studied. It was found that, depending on parameters of the structure and boundary conditions, the quasi-linear regions occupying the range of frequencies with a width from 75 to 220 MHz and the range of wave numbers width from 40 to 200 cm –1 can occur in the dispersion characteristic of spin waves. It was demonstrated that, for undistorted transmission of the useful signal modulating the spin wave, using of the spin waves that parameters correspond to the mentioned quasi-linear regions is necessary.

A study is performed of the Bragg diffraction of a weakly diverging beam of the first mode of a backward bulk spin wave on a low-contrast magnon crystal. Effects are noted of the broadening and stratification of beams of the zero and first orders of diffraction into filamentary rays, and the beams of the zero and first orders of diffraction not passing through the magnon crystal in one band of frequencies.

A magnetic system is developed to generate a stationary uniform magnetic field in a relatively large region between the poles of a magnet that is used in a setup for the study of characteristics of spin waves. The calculations and subsequent measurements show that the application of ring terminals with certain parameters in the magnet allows a several-fold increase in the size of the region with a high uniformity of the magnetic field. The Fourier analysis of the distribution of the amplitude of spin waves is used to show that improvement of the uniformity of the magnetic field in the system due to the application of the ring terminals leads to a several-fold increase in the accuracy of measurement of the wave number. It is found that the first mode of the backward volume spin wave is split into satellite modes that are excited in the ferrite film due to the presence of several layers with similar magnetic parameters.

The analysis of the need to use devices for monitoring the state of the driver in transport is carried out. It is noted that the driver may not notice short-term attention gaps. It is necessary to exclude such failures that may lead to serious consequences on the road. On the basis of a mathematical model, it is shown that it is important to take into account both the reliability of the monitoring system to recognize the loss of the driver's efficiency, and its ability to quickly initialize the driver if necessary. It is shown that the use of systems that detect a decrease in the level of vigilance with a sufficiently high reliability will provide an increase in the overall level of road safety. An example of such a system is given.

Analytical formulas are obtained for all components of the high-frequency field, Poynting vector $$\overrightarrow P $$ , and group velocity vector $$\overrightarrow U $$ of electromagnetic waves propagating in an arbitrary direction in an unbounded bi-gyrotropic medium described by the Hermitian permittivity and permeability tensors. It is proven that the corresponding components of vectors $$\overrightarrow P $$ and $$\overrightarrow U $$ are proportional to each other (therefore, these vectors are parallel) and the ratio between these components is the volume density of the wave energy. The change in the absolute value and orientation of vector $$\overrightarrow U $$ and orientation of vector $$\overrightarrow P $$ depending on the orientation of the wave vector for different types of electromagnetic waves propagating in a ferromagnetic medium (a particular case of a bi-gyrotropic medium) is calculated. It is found that vectors $$\overrightarrow U $$ and $$\overrightarrow P $$ are always identically oriented for waves of all types in a ferromagnetic medium.

The orientations of the Poynting and group velocity vectors are calculated, depending on the orientation of the wave vector for different types of electromagnetic waves propagating in an infinite ferromagnetic medium. The Poynting and group velocity vectors are found to be codirectional for all the types of waves in this medium.