Application of gradient cell structures with controlled dielectric permittivity for luneburg lens fabrication of 3D-printing

Among the lens antennas made from dielectric materials, spherical lenses are of particular interest because they allow the required directivity pattern to be formed in any direction. Spherical lenses made of inhomogeneous dielectrics have the best properties. Among these, Luneburg lenses (LL) are considered the most promising for application. According to Luneburg's law, when the dielectric constant of a spherical body changes from 2 at the center to 1 at the surface, the body refracts the rays falling on it so that they leave the sphere parallel to its diameter. It is therefore possible to scan space over a wide angular sector by moving the source around the surface of the LL. However, the exact realization of this law has not yet been achieved. At present, the main method of making LLs is to assemble hemispheres of different dielectric permittivity, which gives a step change in permittivity. This paper investigates the potential of using structures with triple periodic minimum surface (TPMS) geometry in the fabrication of a Luneburg lens. Using TPMSs, it is possible to create gradient structures by varying the filling density, which would allow a smooth change in permittivity as close as possible to the ideal law. In this work, the material for 3D printing the lens is developed, the electret and physical and mechanical properties of the cellular materials are investigated, and the possibility of controlling their dielectric permittivity for use in the creation of LL is explored. It is shown that with the help of structures based on TPMS it is possible to obtain the necessary extreme values of dielectric permittivity by changing the degree of space filling, geometries of TPMS are selected, the formula of dependence of dielectric permittivity on the degree of space filling of the structure is obtained, due to which it is possible to create intermediate layers of Luneburg lens with the predicted value of dielectric permittivity. It is shown that the dependence of the permittivity on the degree of space filling becomes more pronounced as the amount of titanium dioxide filling increases. The use of cellular structures makes it possible to obtain a smooth changing of the dielectric permittivity along the radius in a spherical Luneburg lens.