Surface scattering antennas

A method, comprising:

• selecting a first antenna radiation pattern;
• and
• for an antenna that includes a waveguide supporting a guided wave mode and a plurality of subwavelength scattering elements coupled to the guided wave mode, the scattering elements being adjustable responsive to one or more control inputs, determining first values of the one or more control inputs corresponding to the first selected antenna radiation pattern;
• wherein the guided wave mode is within the waveguide;
• wherein the waveguide includes an upper conductor, the scattering elements are arranged along the upper conductor, and the guided wave mode is beneath the upper conductor;
• wherein the plurality of scattering elements corresponds to a respective plurality of apertures in the upper conductor;
• and
• wherein the plurality of scattering elements includes a respective plurality of conducting islands that are electrically disconnected from the upper conductor, and the antenna further includes a plurality of bias voltage lines configured to provide respective bias voltages between the upper conductor and the respective plurality of conducting islands.