Optimal Synthesis of Directivity Constrained Pencil Beams by Means of Circularly Symmetric Aperture Fields

The problem of the optimal synthesis of circularly symmetric aperture distributions able to radiate pencil beams fulfilling well-defined requirements on the far-field and/or the directivity is addressed and solved. In particular, constraints concerning both the sidelobe level (SLL) and the directivity within a coverage zone are dealt with while being careful not to incur into the so called super-directive sources or into aperture fields actually difficult to be realized. The case wherein a constraint is enforced on the dynamics of the excitations is also considered. Numerical examples concerning cases of practical relevance are also shown in support to the given theory.