Scattering and propagation of electromagnetic waves in planar and curved periodic structures - applications to plane wave filters, plane wave absorbers and impedance surfaces

Abstract: The subject of this thesis is scattering of electromagneticwaves from planar and curved periodic structures. The problemspresented are solved in the frequency domain.Scattering from planar structures with two-dimensionalperiodic dependence of constitutive parameters is treated. Theconstitutive parameters are assumed to vary continuously orstepwise in a cross section of a periodically repeating cell.The variation along a longitudinal coordinate z is arbitrary. Ageneral skew lattice is assumed. In the numerical examples, lowloss and high loss dielectric materials are considered. Theproblem is solved by expanding the .elds and constitutiveparameters in quasi-periodic and periodic functionsrespectively, which are inserted into Maxwell?s equations.Through various inner products de.ned with respect to the cell,and elimination of the longitudinal vector components, a linearsystem of ordinary di.erential equations for the transversecomponents of the .elds is obtained. After introducing apropagator, which maps the .elds from one transverse plane toanother, the system is solved by backward integration.Conventional thin metallic FSS screens of patch or aperturetype are included by obtaining generalised transmission andre.ection matrices for these surfaces. The transmission andre.ection matrices are obtained by solving spectral domainintegral equations. Comparisons of the obtained results aremade with experimental results (in one particular case), andwith results obtained using a computer code based on afundamentally di.erent time domain approach.Scattering from thin singly curved structures consisting ofdielectric materials periodic in one dimension is alsoconsidered. Both the thickness and the period are assumed to besmall. The .elds are expanded in an asymptotic power series inthe thickness of the structure, and a scaled wave equation issolved. A propagator mapping the tangential .elds from one sideto the other of the structure is derived. An impedance boundarycondition for the structure coated on a perfect electricconductor is obtained.Keywords:electromagnetic scattering, periodicstructure, frequency selective structure, frequency selectivesurface, grating, coupled wave analysis, electromagneticbandgap, photonic bandgap, asymptotic boundary condition,impedance boundary condition, spectral domain method,homogenisation