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Four section of thematic supplementals

Full-wave numerical approaches for the analysis of leaky modes propagating in Electromagnetic-Bandgap (EBG) waveguides composed by multilayered arrays of two-dimensional (2D) cylindrical inclusions have been proposed. A first method based on the lattice sums technique for periodic structures with inclusions of circular section has been suitably adapted to the analysis of modes with complex propagation wavenumbers. The self-contained formulation uses a fast and accurate calculation of the lattice sums, which allows for an appropriate choice of the spectral determination for each spatial harmonic. A further full-wave modal method based on the Fourier Series Expansion in conjunction with perfectly matched layers (PMLs) has been developed, which can take into account cylindrical inclusions with arbitrary geometry of the transverse section. Real and imaginary parts of the propagation wavenumber are calculated with the two proposed approaches for a typical EBG waveguide and a very good agreement is observed in a wide frequency range.

International audience; The efficient calculation of the Lattice Sums (LSs) for evaluating the free-space periodic Green's function (PGF) of an infinite phased array of line sources is addressed here and is extended for the first time to leaky waves. The method is based on the Graf's addition theorem for the 0-th order Hankel function that leads to an expansion in terms of Bessel functions of the relevant PGF. The coefficients of the expansion, called LSs, are slowly convergent series involving higher-order Hankel functions. Their efficient computation is performed by resorting to an extension of the standard Ewald method, in terms of spectral and spatial series having Gaussian convergence even in the case of complex waves and improper harmonics. The adopted approach allows for the analysis of a wide class of periodic waveguides supporting leaky modes, and it is particularly suitable for the treatment of infinite array of dielectric fibers and rods.