Surface scattering antennas with lumped elements

An electromagnetic apparatus, comprising:

• a wave-propagating structure;
• a plurality of electromagnetic resonators distributed with subwavelength spacing along a conducting surface of the wave-propagating structure;
• and
• for each electromagnetic resonator in the plurality of electromagnetic resonators, one or more lumped elements arranged symmetrically with respect to the electromagnetic resonator;
• wherein the wave-propagating structure includes a bounding surface, and the plurality of electromagnetic resonators includes a plurality of unit cells each containing a conducting patch above the bounding surface and an iris in the bounding surface;
• and
• wherein the one or more lumped elements are directly connected between the conducting patch and the bounding surface.

A method of controlling an antenna having a plurality of unit cells each containing a subwavelength radiator coupled to a waveguide and one or more lumped elements, the method comprising, for each unit cell:

• applying a first voltage difference between first and second terminals of a lumped
• element selected from the one or more lumped elements;
• and applying a second voltage difference between the first and second terminals of the lumped element selected from the one or more lumped elements;
• wherein:
• the waveguide includes a bounding surface;
• the unit cells each contain a conducting patch above the bounding surface and an iris in the bounding surface;
• and
• for each unit cell, the one or more lumped elements are directly connected between the conducting patch and the bounding surface.