Abstract: The electromagnetic analysis of a special class of 3D dielectric lens antennas is described in detail. This new class of lens antennas has a geometrical shape defined by the three-dimensional extension of Gielis formula. The analytical description of the lens shape allows the development of a dedicated semianalytical hybrid modeling approach based on geometrical tube tracing and physical optic. In order to increase the accuracy of the model, the multiple reflections occurring within the lens are also taken into account.

Abstract: The interaction of diatoms with sunlight is fundamental in order to deeply understand their role in terrestrial ecology and biogeochemistry, essentially due to their massive contribution to global primary production through photosynthesis and its e↵ect on carbon, oxygen and silicon cycles. Following the journey of light through natural waters, its propagation through the intricate frustule micro- and nano-structure and, finally, its fate inside the photosynthetic machinery of the living cell requires several mathematical and computational models in order to accurately describe all the involved phenomena taking place at di↵erent space scales and physical regimes. In this chapter, we review the main analytical models describing the underwater optical field, the essential numerical algorithms for the study of photonic properties of the diatom frustule seen as a natural metamaterial, as well as the principal models describing photon harvesting in diatom plastids and methods for complex EM propagation problems and wave propagation in dispersive materials with multiple relaxation times. These mathematical methods will be integrated in a unifying geometric perspective.

Abstract: The interior and exterior Robin problems for the Helmholtz equation in starlike planar domains are addressed by using a suitable Fourier-like technique. Attention is in particular focused on normal-polar domains whose boundaries are defined by the so-called superformula introduced by J. Gielis. A dedicated numerical procedure based on the computer algebra system Mathematica© is developed in order to validate the proposed approach. In this way, highly accurate approximations of the solution, featuring properties similar to the classical ones, are obtained. The computed results are found to be in good agreement with the theoretical findings on Fourier series expansion presented by L. Carleson.

Abstract: The Robin problem for the Helmholtz equation in normal-polar annuli is addressed by using a suitable Fourier-Hankel series technique. Attention is in particular focused on the wide class of domains whose boundaries are defined by the so-called superformula introduced by Gielis. A dedicated numerical procedure based on the computer algebra system Mathematica© is developed in order to validate the proposed methodology. In this way, highly accurate approximations of the solution, featuring properties similar to the classical ones, are obtained.

Abstract: This research study reports the assessment of complementary split ring resonators based on Gielis transformation as basic elements for the design of high‐performance microwave components in printed technology. From the electromagnetic simulation of said structures, suitable equivalent circuit models are extracted and analyzed. Physical prototypes are fabricated and tested for design validation. The obtained results confirm that the adoption of supershaped geometries enables the synthesis of very compact scalable microwave filters.

Abstract: We investigate a promising tunnel FET configuration having a gate on the source only, which is simultaneously exhibiting a steeper subthreshold slope and a higher ON-current than the lateral tunneling configuration with a gate on the channel. Our analysis is performed based on a recently developed 2-D quantum-mechanical simulator calculating band-to-band tunneling and including quantum confinement (QC). It is shown that the two disadvantages of the structure, namely, the sensitivity to gate alignment and the physical oxide thickness, are mitigated by placing a counter-doped parallel pocket underneath the gate-source overlap. The pocket also significantly reduces the field-induced QC. The findings are illustrated with all-Si and all-Ge gate-on-source-only tunnel field-effect transistor simulations.