Design and optimisation of axisymmetric millimetre-wave shaped lens antennas with directive, secant-squared and conical beams

The paper investigates the optimisation of rotationally-symmetric shaped dielectric substrate lenses at millimetre wave frequencies. The aim is to determine the best lens profile that complies with an arbitrary desired far-field power template. The design procedure is briefly described in three main steps. First, determination of the starting lens shape using an analytical geometrical optics (GO) formulation; secondly computation of the radiation characteristics of the lens using a hybrid GO-PO (physical optics) technique accounting for diffraction effects and, thirdly, iterative optimisation of trial lens profiles using a local minimisation procedure based on a multidimensional conjugate gradient method (M-CGM). The characteristics of the optimisation algorithm are then studied numerically, in terms of convergence speed and analysis of sensitivity. To this end, the authors design, discuss and compare several shaped lenses radiating directive, secant-squared and conical beams. These various examples demonstrate very good performance and promising potentially of optimised lens antennas for shaped-beam applications