Floquet Modal Analysis to Modelize and Study 2-D Planar Almost Periodic Structures in Finite and Infinite Extent With Coupled Motifs

Abstract

Abstract-Studying of mutual coupling parameters between the antenna elements in an array environment has been considered as the subject of feature research. That is why, in this paper, we present a new Floquet modal analysis procedure for analyzing almost periodic structures. Accurate evaluation of the mutual coupling could be achieved by this analysis. It is shown how Floquet analysis can be exploited to study a finite array with arbitrary amplitude and linear phase distribution in both x-y directions including mutual coupling effects. Two different calculation methods of coupling coefficients between the array elements are presented, in spectral and spatial domains, to solve the suggested problem. For modeling the given structures, the moment method combined with Generalized Equivalent Circuit (MoM-GEC) is proposed. High gain in the running time and memory used is given using Floquet analysis. To validate this work, several examples are shown.

Radiation Pattern Synthesis of the Coupled Almost Periodic Antenna Arrays Using Artificial Neural Network ANN Model

“…This section takes up the main expression of the radiation pattern related to the proposed almost periodic planar structures (see figure (1) of the periodic antenna array example) [6][7][8] which is discussed in our previous work [5,9,11]. To resolve this problem, it is claimed that an integral method based on the method of moments combined with the generalized equivalent circuit (MoM-GEC) [6,7,10] is implemented.…”

“…To restraint the electromagnetic calculation on one unit cell, the dependence on Floquet modes (α or (α, β)) is taken into account [9,11,14,32]. Then, the field components can be therefore expressed in the generalized Fourier series expansions, and the analysis region can be reduced to only one periodicity cell bounded by the known periodic walls, as presented in the figure (2).…”

“…Today, the synthesis of the radiation pattern of almost periodic planar structures is the subject of various scientific researches, mostly in space and defense applications, communication systems and electronic devices such as phased array radar systems, frequency selective surface (FSS) applications [28], millimeter waves, and optical wave regions (for other examples: reflection gratings, phased arrays, and electromagnetic bandgap structures, leaky wave antennas, etc.) [9,11,14]. In general, smart antenna arrays involve intelligent systems including genetic algorithms and neural networks to synthesize the radiation pattern [2,3].…”

Light Scattering From Two-Dimensional Periodic Arrays of Noble-Metal Disks and Complementary Circular Apertures

“…jγ 00 z (6) and the scattered field is expressed in the form of a superposition of the Floquet modes as [12][13][14][15][16][17][18] …”

“…If this periodic nature is violated, we must deal with the whole structure governed by infinite space Green's functions. Still in some cases having partial periodicity, transformation process may be be valid [16]. The coefficients in (5)- (7) are explained as follows.…”