A solution to the complement of the generalized Luneburg lens problem

Lenses are of interest for the design of directive antennas and multi-optics instruments in the microwave, terahertz and optical domains. Here, we introduce an optical problem defined as the complement of the well-known generalized Luneburg lens problem. The spherically symmetric inhomogeneous lenses obtained as solutions of this problem transform a given sphere in the homogeneous region outside of the lens into a virtual conjugate sphere, forming a virtual image from a real source. An analytical solution is proposed for the equivalent geodesic lens using the analogy between classical mechanics and geometrical optics. The refractive index profile of the corresponding inhomogeneous lens is then obtained using transformation optics. The focusing properties of this family of lenses are validated using ray-tracing models, further corroborated with full-wave simulations. The numerical results agree well with the predictions over the analyzed frequency bandwidth (10–30 GHz). This virtual focusing property may further benefit from recent developments in the fields of metamaterials and transformation optics.

Antenna array with switching scanning in elevation plane

It is known that the most reliable communication in hard-to-reach places such as the Arctic, Tundra, Taiga is satellite communication [1-5]. Therefore, for satellite communications, it is necessary to develop your own antenna arrays. This article discusses a waveguide-slot antenna array with a Luneburg lens for a mobile satellite communications terminal, which provides a continuous and stable signal. This antenna operates in the 10.9 to 14.5 GHz frequency range. Possesses vertical polarization. The overall dimensions of the antenna array are: diameter of the diagram-forming lens 256 mm (thickness 5 mm, material FLAN 2.8 (epsilon 2.8, tangent delta 0.0015)); waveguide length 600 mm (internal section 10.5 mm by 5 mm, filling FLAN 2.8). Slotted waveguide antennas and lens are made of standard FLAN 2.8 material (epsilon 2.8, tangent delta 0.0015) 5mm thick, foiled on both sides. There are 17 coaxial cables to the HF switch (equal lengths are not required), the scanning step in elevation is 5 degrees. When using 54 waveguide-slot antennas and 18 switch inputs, a scanning sector in elevation of 90 degrees is provided. All the nodes were pre-modeled separately a cylindrical Luneburg lens with suitable waveguides, excited by slits; slotted waveguide antennas; coaxial-waveguide transitions.