DISPERSION ANALYSIS OF DOUBLE-SIDED OPEN PERIODIC MEDIA USING INHOMOGENEOUS PLANE WAVE EXCITATION

Abstract

Double-sided open periodic structures are analyzed using inhomogeneous plane wave scattering. The leaky and surface wave modes of several unit cells of different structures are computed using the poles of generalized reflection and transmission coefficients of inhomogeneous plane waves in the spectral domain. It is shown that the reflection and transmission coefficients of the zeroth order Floquet mode contain the poles of the Green's function of the complex stratified periodic structure. The properties of evanescent mode amplification as well as super resolution near field imaging in a wire medium are addressed. A balanced leaky wave antenna unit cell with double-sided radiation feature is introduced and it is shown that, in contrast to grounded structures, total absorption in lossless non- chiral double-sided open unit cells is not feasible as long as the behavior of the unit cell is well described by its fundamental mode. In homogeneous open dielectric structures, the spectral representation of the Green's function leads to a series of propagating discrete surface wave modes, together with a continuous integral representation indicating the branch cut in the Riemann sheet (1). By introducing possibly inhomogeneous periodicities into these structures, the analysis of the whole configuration can be reduced to the analysis of one period known as unit cell. This unit cell has open boundaries at the unbounded sides, and periodic boundary conditions are assumed at its side walls, see Fig. 1. In homogeneous layered dielectric media, the spectral domain Green's functions have closed form (2). However, inhomogeneous complex objects do not have any closed form Green's function. Therefore, numerical methods are employed to compute the eigenvalues of these structures. In the numerical computation of open boundary structures, often perfectly matched layers (PML) are chosen as absorbing boundary condition (3). As a result, the spectral domain Green's function can be expressed in terms of the summation of three different groups of modes namely Berenger modes, leaky modes and surface wave modes (4). Among these modes, Berenger modes are complex modes which are more concentrated in the PML layer, while leaky modes are complex modes more concentrated in the guiding structure (5). For the analysis of complex objects immersed in or placed on top of a layered medium, the computation of leaky complex modes is possible with several methods. The most common approach is based on eigenvalue decomposition of the system matrix resulting from a numerical model (6-8). Another robust method is trying to find the stationary points of stored energy derived from physical observations. Since eigenvalue decomposition is a numerically expensive procedure, a physics based method for the computation of complex and surface wave modes of planar periodic configurations was addressed in (9, 10). This method was based on the scattering of inhomogeneous plane waves from grounded unit cells and the eigenmodes were explored by exciting the poles of the reflection coefficient.