Photonic apparatus with periodic structures

An optical apparatus for receiving light propagating along a first direction, the optical apparatus comprising:

• a refractive element adjacent to an optical medium for transmitting or receiving incident light, the refractive element comprising:
• a surface with a predetermined radius of curvature,
• a plurality of structures arranged periodically on the surface,
• wherein the plurality of structures are arranged to have a 90 degree rotational symmetry and configured to focus or defocus the incident light propagating along the first direction by a joint phase shift;
• and
• a modulation element comprising interdigitated doped regions that create one or more p-n junctions, wherein each of the one or more p-n junctions creates a respective depletion region with a depletion width extending perpendicular to the first direction, the modulation element being optically coupled to the refractive element,
• wherein, during operation of the optical apparatus, the modulation element changes an effective refractive index of the refractive element by applying an electrical field to the optical apparatus to cause a change in a carrier concentration or a change in a mechanical structure of the refractive element.