Modeling and Analysis of Transient Processes in Open Resonant Structures

Preface.- Numerical analysis of transient processes: fundamental results of the theory, methods and problems. Introduction. Main equations and fundamental results of the theory. Methods of solving initial boundary problems on the basis of space-time representations. Time domain methods.- Waveguides and periodic structures: exact ‘absorbing’ conditions on virtual boundaries in cross section of a regular wave guiding structures. Introduction. Compact waveguide units. 2-D scalar problems in cylindrical coordinates. Vector problems of the theory of open waveguide resonators. Problems of the electromagnetic theory of gratings.- Compact inhomogeneities in free space: virtual coordinate boundaries in scalar and vector problems of wave scattering theory. Introduction. Exact conditions for artificial boundaries in cylindrical (polar) coordinates. Exact conditions for artificial boundaries in Cartesian coordinates. Vector problems: spherical coordinates. Axially symmetric problems: spherical and cylindrical coordinates.- The simplest modifications of the ‘Exact ABCs’ approach and the associated numerical tests. Introduction. Radiators with infinite flanges. Wave radiation from a plane-parallel waveguide of arbitrary aperture. The problems of strong and remote field sources. Evolutionary basis of outgoing waves in the domains LQ with homogeneous and inhomogeneous filling. Numerical tests of the new exact conditions.- Transform operators in space of signal’s evolutionary basis: a time domain analogue of generalized scattering-matrix method. Introduction. Evolutionary signal basis and transform operators. Canonical problems of time domain. Algorithms for calculating transient characteristics of resonant inhomogeneities. Signals in the floquet channel: the transform operators and some canonical initial boundary-value problems.- Open periodic resonators and waveguides: novel results in electromagnetic theory of gratings. Introduction. Essential qualitative results inthe spectral theory of gratings. Dynamic patterns of spectral points in the frequency domain. Gratings in transient wave fields. Establishing of regularities. Pulse deformations by free propagation in regular section of the floquet channels.- Model synthesis of resonance quasi-optical devices: dispersive open resonators, absorbing coatings, pattern-forming structures. Introduction. Model synthesis of structures including grating dispersive elements (Frequency Domain). Inverse problems in electromagnetic theory of gratings (Frequency domain). Open dispersive resonators. Transient processes in the near zone of pulsed waves radiators.- References.- Appendix A.