Two-dimensional and three-dimensional discrete constrained lenses with minimized optical aberrations

A beamforming network, comprising:

• a three-dimensional discrete lens with a front aperture and a back aperture, each comprising a plurality of discrete elements;
• and
• a propagation part in which electromagnetic radiation can propagate and illuminate the back aperture of the discrete lens;
• wherein:
• each discrete element of the back aperture is homologous to a respective discrete element of the front aperture;
• the discrete lens further comprises a plurality of transmission lines connecting respective pairs of homologous discrete elements of the front aperture and the back aperture;
• a ratio of a size of the back aperture and a size of the front aperture defines a zooming factor that determines a relationship between an angle of incidence of electromagnetic radiation incident on the back aperture and an angle of emergence of a beam of electromagnetic radiation emitted by the front aperture in reaction to the electromagnetic radiation incident on the back aperture;
• the value of the zooming factor is different from unity, so that angles of emergence of beams from the front aperture are either tilted towards a center axis of the discrete lens or tilted away from the center axis, compared to angles of incidence of corresponding beams on the back aperture;
• the front aperture is shaped as a flat surface;
• the back aperture is shaped as a portion of a sphere;
• the lengths of the plurality of transmission lines are chosen to be equal;
• for each pair of homologous discrete elements, a ratio between radial excursions of the respective homologous discrete elements of the back aperture and the front aperture in the pair from the center axis of the discrete lens is equal to the zooming factor;
• and
• the discrete lens has one focal point located in the propagation part on a center of the sphere.