Vol. 95

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues
2021-01-21

New Theoretical Floquet Modal Analysis to Study 3-D Finite Almost Periodic Structures with Coupled Cells

By Bilel Hamdi and Taoufik Aguili
Progress In Electromagnetics Research Letters, Vol. 95, 163-169, 2021
doi:10.2528/PIERL20110406

Abstract

This research letter offers a generalization character to our previous work [4, 5] to examine a 3-D almost periodic phased array antenna excited by arbitrarily located sources. An original modal formulation based on the Floquet analysis procedure is proposed utilizing the periodic walls along x, y, and z-axes, where the analysis region in the spectral domain is reduced to the Brillouin zone. Here, a good idea is provided to enforce the given boundary conditions for obtaining an integral equation formalism developed through Galerkin's method for solving periodic volumic structure (e.g. 3-D regular structure in the cubic grid). The interaction between cells in 3-D geometry (lattice) could be deduced using a novel expression of mutual coupling. However, it is possible to obtain it explicitly by the mean of Fourier transform and its inverse. Then, it is proven how Floquet analysis can be employed to study a 3D-finite array configuration with arbitrary amplitude and linear phase distribution along x, y, and z directions, including mutual interaction effects. To deal with the real hole 3D array configuration, a superposition theorem is suggested to describe the electromagnetic behavior in the spatial domain. For modeling the given 3D antenna array, one numerical method is adopted: The moment method combined with an equivalent circuit (MoM-GEC). An important gain in the running time and memory used would be achieved using Floquet analysis in comparison with other spatial conventional methods (especially, when the number of cells increases by adding the second and third directions).

Citation


Bilel Hamdi and Taoufik Aguili, "New Theoretical Floquet Modal Analysis to Study 3-D Finite Almost Periodic Structures with Coupled Cells," Progress In Electromagnetics Research Letters, Vol. 95, 163-169, 2021.
doi:10.2528/PIERL20110406
http://jpier.org/PIERL/pier.php?paper=20110406

References


    1. Ona, R., R. Tascone, and R. Zich, "Three-dimensional periodic arrays of thin conductors," Electromagnetics, Vol. 7, No. 2, 185-203, 1987 (Published online: Feb. 01, 2007).
    doi:10.1080/02726348708908178

    2. Neto, A., S. Maci, G. Vecchi, and M. Sabbadini, "A truncated floquet wave diffraction method for the full-wave analysis of large phased arrays — Part II: Generalization to 3-D cases," IEEE Transactions on Antennas and Propagation, Vol. 48, No. 3, Mar. 2000.

    3. Yaghjian, A. D., "Definition of an EM continuum and boundary conditions for electric quadrupolar continua," Proceedings of the 2013 International Symposium on Electromagnetic Theory, 2013.

    4. Hamdi, B., T. Aguili, N. Raveu, and H. Baudrand, "Calculation of the mutual coupling parameters and their effects in 1-D planar almost periodic structures," Progress In Electromagnetics Research B, Vol. 59, 269-289, 2014.
    doi:10.2528/PIERB14021105

    5. Hamdi, B., T. Aguili, and H. Baudrand, "Floquet modal analysis to modelize and study 2-D planar almost periodic structures in finite and infinite extent with coupled motifs," Progress In Electromagnetics Research B, Vol. 62, 63-86, 2015.
    doi:10.2528/PIERB14111602

    6. Mekkioui, Z. and H. Baudrand, "2-D bi-periodic centered-fed microstrip Leaky-Wave Antenna (LWA) analysis by a source modal decomposition in spectral domain," IET Microwaves, Antennas and Propagation, Vol. 3, No. 7, Oct. 2009.

    7. Baudrand, H., M. Titaouine, N. Raveu, and G. Fontgland, "Electromagnetic modeling of planar almost periodic structures," SBMOI/IEEE MTT-S International Microwave and Optoelectronics Conference, 2009.

    8. Bhattacharyya, K. A., Phased Array Antennas: Floquet Analysis, Synthesis, BFNs, and Active Array Systems, Wiley and Sons, Mar. 2006.

    9. Nader, B. L., H. Bilel, and A. Taoufik, "Electronically steerable radiation pattern of coupled periodic antenna used floquet analysis," ACES Journal, Vol. 34, No. 2, Feb. 2019.

    10. Craeye, C. and D. G. Ovejero, "A review on array mutual coupling analysis," Radio Science, Vol. 46, RS2012, 2011.
    doi:10.1029/2010RS004518

    11. Shore, R. A. and A. D. Yaghjian, "Traveling waves on two- and three-dimensional periodic arrays of lossless scatteres," Radio Science, Vol. 42, RS6S21, 2007.

    12. Campione, S. and F. Capolino, "Ewald method for 3D periodic dyadic Green’s functions and complex modes in composite materials made of spherical particles under the dual dipole approximation," Radio Science, Vol. 47, RS0N06, 2012.

    13. Campione, S., M. B. Sinclair, and F. Capolino, "Effective medium representation and complex modes in 3D periodic metamaterials made of cubic resonators with large permittivity at midinfrared frequencies," Photonics and Nanostructures — Fundamentals and Applications, Vol. 11, No. 4, 423-435, 2013.
    doi:10.1016/j.photonics.2013.07.013

    14. Campione, S. and F. Capolino, "Electromagnetic coupling and array packing induce exchange of dominance on complex modes in 3D periodic arrays of spheres with large permittivity," Journal of the Optical Society of America B, Vol. 33, No. 2, 261, 2016.
    doi:10.1364/JOSAB.33.000261

    15. Sultan, K. S., H. H. Abdullah, and E. A. Abdallah, "Method of moments analysisforantennaarrays with optimum memory and time consumption," PIERS Proceedings, 1353-1356, Kuala Lumpur, Malaysia, Mar. 27–30, 2012.

    16. Ammar, N., T. Aguili, and H. Baudrand, "Analysis of multilayered cylindrical structures using a full wave method," Progress In Electromagnetics Research, Vol. 85, 425-438, 2008.
    doi:10.2528/PIER08091803

    17. N'Gongo, R. S. H. Baudrand, "Application of wave concept iterative procedure in planar circuits," Recent Res. Devel. Microwave Theory and Technique, Vol. 1, 187-197, 1999.