Optical coupling apparatus and methods of making same

A system for communication, comprising:

• a photonic die on a substrate;
• an optical fiber attached to the photonic die;
• and
• an array of scattering elements on the photonic die for transmitting light between the photonic die and the optical fiber, wherein:
• the array of scattering elements is arranged in a planar layer at a plurality of intersections of a first set of concentric elliptical curves crossing with a second set of concentric elliptical curves rotated proximately 90 degrees to form a two-dimensional (2D) grating,
• the 2D grating is configured for receiving an incident light from the optical fiber with an incident angle,
• the incident angle is measured in plane of incidence between an axis of the optical fiber and a direction perpendicular to the planar layer,
• each scattering element has a first length along a first direction that is in a top surface of the planar layer and perpendicular to the plane of incidence, and has a second length along a second direction that is in the top surface and perpendicular to the first direction, and
• a ratio of the second length to the first length is determined based on the incident angle.