Sidorov D. Bragg resonances in layered structures with linear and nonlinear elements

The object is the processes of resonance reflection and transmission of electromagnetic waves in layered Bragg structures caused by constructive interference. The aim is to identify new physical regularities of reflection and transmission of electromagnetic waves and space-time wave packets in quasiperiodic apodized structures and Bragg resonators with nonlinear layers. The methods of investigation are the transmission matrices method, the method of decomposition into plane harmonic waves, digital spectral analysis methods with multi-frequency broadband microwave measurement techniques using the principle of Fourier holography. The thesis is devoted to the investigation of resonance phenomena in periodic and quasiperiodic apodized layered Bragg structures with linear and nonlinear elements. The advantage of the apodized Bragg resonators with respect to frequency selectivity has been demonstrated by analyzing the values of eigenfrequencies of layered structures. The possibility of apodization of the Bragg reflectors through variation the thickness of thin contrast layers has been theoretically proved and experimentally validated. The pseudoinverse method for calculation the field at boundaries of the structures has been proposed. This method is the combination of the transmission matrix method and the Jacobi iterative procedure. The presence of several nonlinearities in the resonant layer of Bragg structure leads to a complex hysteretic behaviour of the frequency characteristics due to the redistribution of the field between the parts of the resonance layer with different types of nonlinearity. Scope: Radiophysics, microwave engineering, the learning process.