On a numerical minimization problem for a new class of nonlinear partial differential equations arising in nonspherical geometrical optics and beamforming lenticular antennas

摘要

A mixed numerical and analytical procedure for solving the problem of determining the surfaces I and I′ of a three-dimensional, aperture or volume extremized and ellipticized, bifocal, nonsperical, singlet optical, radar or sonar lens antenna defined by a system of four nonlinear partial differential equations with specified symmetry and boundary conditions subject to a minimizing side condition on the antenna focal length, or f-number, is presented. The index of refraction n0, the maximum lens diameter 2b0 and the bifocal off-axis angle ψ0 are assumed given. Applications are noted in radar, sonar and satellite communications.