In this talk, I will summarize the recently discovered opportunities of geodesic lenses for producing high-performing antennas for 5G/6G and satellite communications. First, I will explain the operation of geodesic lenses based on Geometrical Optics with rays that are following ``the shortest optical path'' in the geodesic surface. Also, I will explain the connection between geodesic lenses and rotationally symmetric graded-index lenses. Generally, geodesic lenses can be implemented without the need of dielectric materials, resulting in very efficient devices constructed with fully-metallic configurations. When combined with a feeding network and a radiating transition, such as a flare or a leaky-wave, they can produce a multiple-beam lens antenna. Prototypes of these antennas have been recently tested to demonstrate the remarkable performance of geodesic lenses in the Ka-band, part of which is considered for 5G and communications with the new LEO constellations. At high operational frequencies allocated for 5G/6G and radars in vehicles, geodesic lenses offer an opportunity to produce cost-effective antenna solutions with high directivity, high efficiency and spatial diversity through multiple beams.

We give a general description of the mathematical background and a resume of the results about existence and distribution of the spectra of running waves in open and shielded waveguides, including: open and shielded metal-dielectric waveguides with arbitrary cylindrical inhomogeneities and open layered concentric dielectric waveguides of circular cross section and metal--dielectric waveguides (Goubau lines) having layered dielectric covers filled with linear or nonlinear media. The newly obtained results are reported concerning singularities (resonant states) of the transmission coefficient in the problems of the wave scattering by parallel-plate dielectric slabs in a waveguide and free space. The findings are based on recent advances in the spectral theory of open structures.

Fiber optical sensor networks gain interest in the new research area of structural health monitoring (SHM). Different market analysts estimate the market growth (2020 to 2027) in the fields of SHM, Distributed Fiber Optic Sensors or Fiber-Bragg gratings from a compound annual growth rate (CAGR) of 8.4 % up to 25.4 %. It shows the clear necessity of such systems on the market. Fiber optical sensor networks are suitable for fatigue crack detection, internal strain monitoring or temperature surveillance of a whole structure, such as bridges, tunnels, roads, buildings, pipelines, etc. Distributed sensing and quasi-distributed sensing bring their inherit advantages such as immunity to electro-magnetic interference, low weight, small size, or their multiplexing capability to SHM systems. In distributed sensing, the optical fiber itself is used as the sensing element. It allows a continuous measurement of several fiber kilometers. Quasi-distributed sensing is based on Bragg-gratings that are inscribed into the optical fiber. Different multiplexing techniques, known from communication systems, are used to distinguish several thousands of serial sensing points. The presentation addresses the questions: How to interrogate large fiber optical sensor networks? Where to apply these networks in SHM?