The thesis is devoted to magnetic metamaterials operating in the frequency range of 10 MHz 1 GHz. Mechanisms of tailoring the properties of metamaterials are developed and a number of linear and nonlinear applications is proposed.In Chapter 1, the introduction to the field of metamaterials is given and the main goal of the thesis is defined as the search for possible applications of low-frequency metamaterials. The main motivation is the potential of magnetic metamaterials in Magnetic Resonance Imaging (MRI).Chapter 2 briefly summarizes the near-field properties of magnetic metamaterials. Magnetic coupling between a pair of metamaterial elements is described and magnetoinductive (MI) waves propagating on the metamaterials arrays are introduced.In Chapter 3, the magnetic coupling between the elements is studied in more detail. Based on the analogy between MI waves and acoustic waves in solids, "diatomic" metamaterial arrays having two elements per unit cell are introduced. It is shown that by changing the resonant frequencies of the elements and the coupling between them it is possible to acquire additional freedom in tailoring the dispersion properties of MI waves compared to simple "monatomic" configurations.In Chapter 4, various linear applications of metamaterials are discussed. They are shift-dependent transmission, subwavelength imaging and focusing, and rotational resonance of MI waves. It is shown that the microscopic model based on taking the interaction between the elements into account allows for reliable explanation of the phenomena studied.In Chapter 5, a nonlinear application, parametric amplification of MI waves, is discussed. It is shown that parametric amplification can lead to the compensation of loss in metamaterials and to increase of the power extracted from an MRI detection system.Conclusions are drawn and possible directions for future work are determined in Chapter 6.

The thesis discusses the dynamic electromagnetic field on periodic structures. The author focuses on three principal types of resonant structures, considering their application possibilities. In general, these types can be individually defined as follows: materials exhibiting a negative refractive index of the incident electromagnetic wave; structures with gradual changes in impedance, characterised by their usability as reflectionless surfaces; and periodic structures able to conveniently shape the magnetic field distribution. Materials of the third group within the above-shown short list facilitate the fabrication of magnetoinductive lenses for nuclear magnetic resonance. The presented analysis of the properties of periodic resonant structures is mainly based on numerical models utilising the finite element method, and this approach is combined with both the derivation of the corresponding analytical relations and an experimental measurement of the non-radiating component of the electromagnetic field. The thesis includes a physical description of the basic elements of periodic resonant structures. Physical properties of the elements were examined in detail via numerical analysis. In the course of the research, the data acquired through this analysis and the related experimental measurement enabled the author to propose a method for optimising the most widely used resonant structures. Moreover, several new versions of resonant elements, structures, and fabrication techniques were also designed. The results obtained from the numerical analyses carried out to examine the central physical properties of the fabricated structure samples were all verified via the designed method for measuring the non-radiating component of the magnetic field.