An Analytical Investigation For The Electromagnetic Properties Of Periodic Structures With Electromagnetic Band-Gap

Recently, artificial electromagnetic surfaces, such as spiral-shaped elements, mushroom structures, Jerusalem crosses form grids, surfaces filled with Peano Curve and Hilbert Curve, and so on, could be treated as Electromagnetic Band-Gap periodic structures. In theory, electromagnetic properties of such structures have been concluded as dimensional distribution of reflection electromagnetic field for bianisotropic electromagnetic surfaces. The former investigations are always focusing on reflection properties based on the incidence of equal plane waves, so the gained results couldn't be generalized, for example, the surface waves couldn't be represented. In this paper, the dimensional distribution of reflection electromagnetic field aroused by a dipole source for such surfaces has been investigated. By using Fourier-Bessel integral transformation, the reflection electromagnetic field was expressed as an integral form in terms of the cylindrical wave function in continuous spectrum, that is, Sommerfeld type integral, so the reflection characteristic caused by any dipole source, theoretically, could be gained by using sum. As we all know, in complex plane, Sommerfeld type integral contains singularities including polar points and branch points, the bad property of convergence, as well as the solution of the integral equation has no closed form, so how to simplify and solve the integral efficiently are a difficult question in electromagnetic theory since it has been first derived by A Sommerfel for more then one hundred years.In this paper, a generic analytical model for the electromagnetic properties of such structures was developed in spectral domain, and the influence of parameters for the model was analyzed. By using spectral domain method, the impedance and reflection effects of periodic structures with Electromagnetic Band-Gap have been investigated, and then the expressions of surface impedance and reflection coefficient have been deduced. By using reflection coefficient method in spectral domain, the exact spectral impedance expressions which contained portrait wave number in rational fraction of index function with complex argument have been concluded, that is, exact impedance boundary condition of such structures. By using rational approximately, the exact...