Method and devices for efficient manipulation of light using waveguide scatterer arrays

A grating element comprising:

• a substrate having a bottom surface and a top surface opposite the bottom surface;
• and
• a vertically-oriented light propagating element comprising at least one three-dimensional dielectric member extending vertically away from the top surface of the substrate, along a direction normal to the top surface, by a height equal to half of a beat length of the grating element, the at least one dielectric member configured to;
• guide therethrough, along the direction normal to the top surface, an electromagnetic wave incident on the substrate from one of the bottom surface and the top surface thereof, and
• provide directional scattering of the electromagnetic wave in a radiation pattern caused by one of interference between at least two guided components and interference between at least one guided component and at least one radiative component, the guided and radiative components excited by the electromagnetic wave and propagating vertically through the at least one dielectric member along the direction normal to the top surface of the substrate,
• wherein the grating element is configured to be arranged in an array with a plurality of other grating elements to form an optical grating device having a diffractive period, the at least one dielectric element of each of the grating elements in the array being within the diffractive period.