Demonstrates LSQR-based dipole optimization to suppress sidelobes in a parabolic dish radiation pattern.

This script simulates the far-field radiation pattern of a parabolic reflector fed by a circular aperture, then uses a ring of dipoles placed beyond the reflector's rim to reduce sidelobes via LSQR optimization. It targets regions outside the 3dB beamwidth for attenuation while preserving the main lobe.

Inputs

• Parabolic dish geometry: focal length f, diameter d, curvature R, resolution parameters
• Feed excitation: frequency freq, amplitude E0, circular aperture radius a
• Dipole ring: number of dipoles N, radius rho_loc, azimuthal placement
• Sidelobe suppression region defined via a rectangular window around main lobe troughs

Outputs

• Radiation pattern before and after dipole field superposition
• 3D visualization of dish surface and dipole placement
• Polar plot of radiation pattern with sidelobe suppression
• Plots comparing dipole coefficients with their antisymmetric counterparts

Notes

• The optimization enforces antisymmetry by plotting dipole weights against their diametrically opposite positions
• Useful for validating ring-based dipole arrangements and phase symmetry strategies
• Target field is zeroed outside the main beam (rectangular window), achieving directional attenuation