Number Of Floquet Modes Research Articles

Hybrid finite element-fast spectral domain multilayer boundary integral modeling of doubly periodic structures

Hybrid finite element (FE)-boundary integral (BI) analysis of infinite periodic arrays is extended to include planar multilayered Green's functions. In this manner, a portion of the volumetric dielectric region is modeled via the FE method whereas uniform multilayered regions are characterized using a multilayered Green's function. As such, thick uniform substrates can be modeled without loss of efficiency and accuracy. The multilayered Green's function is analytically computed in the spectral domain and the resulting BI matrix-vector products are evaluated via the fast spectral domain algorithm (FSDA) without explicit generation of the BI-matrix. Furthermore, the number of Floquet modes in the BI expansion is kept very few by appropriately placing the BI surfaces within the computational unit cell. As a result, the computational cost of the method is very little and the model can easily be adapted to various requirements. Examples of frequency selective surface (FSS) arrays are analyzed with this method to demonstrate the accuracy and capability of the approach.

Frequency downshifting and trapping of an electromagnetic wave by a rapidly created spatially periodic plasma

Experimental and numerical results of the interaction of electromagnetic waves with rapidly time varying spatially periodic plasmas are presented. It is shown that a number of Floquet modes, each with their own oscillation frequency, are created during the interaction. Included among these modes are downshifted waves which will not exist in the single slab case, and also waves with a larger upshifted frequency than one can obtain with a single plasma layer of the same density. In addition, the periodic structure is characterized by pass and stop bands that are different from those of a single plasma layer, and the frequencies of the downshifted modes falling in the stop band of a single plasma layer. Therefore these waves are trapped within the plasma structure until the plasma decays away. To show this phenomenon a chamber experiment is conducted, with the periodic plasma being produced by a capacitive discharge. The power spectrum recorded for waves interacting with the plasma shows vastly improved efficiency in the downshift mechanism, which the numerical calculations suggest is related to the trapping of the wave within the plasma. Reproducible results are recorded which are found to agree well with the numerical simulation.

A modular approach for probe-fed and capacitively coupled multilayered patch arrays

We present a modular technique for analyzing probe-fed, multilayered microstrip phased-array antennas. Each patch layer is assumed to be infinite in extent and represented by its generalized scattering matrix (GSM) with respect to a finite number of Floquet modes. For multilayer patch analysis, the individual GSMs are combined appropriately to yield the overall GSM of the structure. The individual GSM are obtained using the Galerkin method. The probe layer is represented by its generalized impedance matrix (GIM) which is deduced using Floquet modal analysis and the variational method. The GSMs and GIM are combined appropriately to yield the input impedance seen by the probe. Numerical results computed with this technique are shown to agree favorably with available data. Results for two-layered patch arrays and capacitively coupled patches are also presented.