Multi-domain Analysis And Computable Modeling Of Time Reversal Electromagnetic Systems

Time reversal(TR) possesses never-fading charms and classical electromagnetism likewise holds lasting fascinations. Theoretical researches of TR electromagnetism(TR-EM) may help motivate us a deeper understanding of the symmetries of the electromagnetic fields; for instance, the relations between symmetries in different domains and the new phenomenons, new rules and new methods arising therefrom. The realistic significance of TR-EM researches is to propose a series of questions, propositions and projects; for instance, what is TR electromagnetic fields, TR analysis methods are particular, and the computable modeling and comprehensive application of TR electromagnetic system(TREMS). Because of the profoundness of TR symmetry in physics and the extensiveness of classical electromagnetism in applications, TR-EM researches have been revealing vast prospects. Our team first carried out a series of works on TR-EM in China. The competitions on TR-EM researches have created a virtuous circle between several teams worldwide. My trend investigations show that TR-EM researches are poised for the second round, so I take advantage of the opportunity to re-discuss the basic theory of TR-EM deeply and re-develop computable models of TR-EM generally. These are just the backgrounds, significance, and motivation of this dissertation.Around the theoretical and realistic significances of TR-EM researches, three progressive aims are set in the course of this dissertation: to systematically analyze the multi-domain symmetries of classical electromagnetic fields and establish the realizable theory of TR electromagnetic fields and the general theory of TREMS; to achieve the computable models of the relationships between spatial symmetries of electromagnetic boundaries and the focus patterns of TR electromagnetic fields; based on TR analysis methods, to explore new scheme of far-field subwavelength-target recognition in dense multipath scattering environments. To accomplish the first aim, firstly, this dissertation discusses a necessary condition and a sufficient condition of TR symmetry of electromagnetic fields; secondly, the symmetries of electromagnetic fields are investigated in time domain, frequency domain, coordinate space, and k space, the dual-combination multiplication table about chiral operation, conjugation operation, negative frequency operation, time reverse operation, space vector centrosymmetry operation, and k space vector centrosymmetry operation are derived, and the appropriate combination between these operations and four domains are illustrated; thirdly, the definition, realization process, and classification of TR electromagnetic fields are discussed; lastly, the general framework of TREMS, the quantitative description of TR electromagnetic fields, and the physical constraints and intrinsic stability of TREMS in the general theory of TREMS are studied. To accomplish the second aim, firstly, this dissertation analytically models the spatial focus characteristics of TR electromagnetic fields in a rectangular cavity and a parallel plate waveguide; secondly, the effects of the focus patterns of TR electromagnetic fields from mirror symmetry and rotation symmetry of electromagnetic boundaries are investigated; lastly, the geometric mechanism from the symmetries are discussed. To accomplish the third aim, firstly, this dissertation points out the physical fact that ‘the uncertainty principle limits the spatial focus of electromagnetic fields, namely Rayleigh limit, but it does not limit the precision of the phase measurement at the receiving end’; secondly, after combining TR technology with time frequency analysis, this dissertation calculates ‘TR phase-prints’ of different folded states of subwavelength structures; lastly, mathematical and physical mechanisms of this scheme are discussed. These are the aims, methods and processes of this dissertation.Primarily, we made efforts to construct the theory foundation of TREMS; in the process it was found that there were at least eleven dual-combination operations which would show the symmetries of electromagnetic fields and therefore some new ideas could be advanced to equivalently achieve TR electromagnetic fields. Secondly, we proposed the concept of TR planning which could help the quantitative design of focus characteristics of TREMS and proposed the concept of TR polarization stream which could help the computable modeling of polarization properties of TREMS. Moreover, we found the effects of polycentric focus and continuous focus of TR electromagnetic fields, from which the new phenomenons would motivate a deeper understanding than previous. Finally, we combined TR technology with statistical analysis of grid network on Ising model, then found the inverse U-shape relationship between the interaction strength in Ising network and the focusing performance of TREMS and TR symmetry breaking of TREMS due to noises, which would contribute to the quantitative design of TREMS, but also contribute to a deeper understanding about noises; we combined TR concept with super resolution concept, then summarized the physical mechanisms of TR super resolution phenomenons and sketched the phenomenological classification of them, which would lay a theoretical foundation to design super-resolution TREMS; we utilized the phase flatness of TR electromagnetic fields and the phase non-flatness of subwavelength perturbation synthetically and combined with time frequency technology, then proposed the concept of TR phase-prints which broke through the challenge of far-field subwavelength-target recognition in dense multipath scattering environment successfully. In summary, this dissertation hopes to increase some theoretical momentum for a new round of TR-EM researches and to accelerate the engineering-application transformation of TR technology. These are the conclusions, contributions and outlooks of this dissertation.