Optical coupling apparatus and methods of making same

An apparatus for optical coupling, comprising:

• a semiconductor layer;
• an array of scattering elements in the semiconductor layer at a plurality of intersections of a first set of concentric elliptical curves crossing with a second set of concentric elliptical curves rotated relative to the first set of concentric elliptical curves to form a two-dimensional (2D) grating, wherein each scattering element of the array of scattering elements is a concave polygon having more than 4 corners, and each scattering element has a reflection symmetry about a first line;
• a first tapered structure optically connecting the 2D grating to a first waveguide;
• and
• a second tapered structure optically connecting the 2D grating to a second waveguide.

An apparatus for optical coupling, comprising:

• a support;
• an electric die on the support;
• a photonic die on the support, wherein the photonic die is connected to the electric die, and the photonic die comprises:
• a semiconductor layer;
• an array of scattering elements in the semiconductor layer at a plurality of intersections of a first set of concentric elliptical curves crossing with a second set of concentric elliptical curves rotated relative to the first set of concentric elliptical curves to form a two-dimensional (2D) grating, wherein each scattering element of the array of scattering elements is a concave polygon having more than 4 corners;
• a first tapered structure optically connecting the 2D grating to a first waveguide;
• and
• a second tapered structure optically connecting the 2D grating to a second waveguide;
• and
• an optical fiber in optical communication with the photonic die.