Design considerations of grating couplers in directionally coupled waveguides

The far-field pattern of an optical wave radiating from a grating coupler integrated in a directional coupler is discussed based on the coupled mode theory. It is shown that there are two types of intensity distributions with respect to the radiation angle. One type shows a simple single lobe, while the other has a deformed lobe or two lobes. Far-field patterns are discussed along with near-field patterns. They are determined by directional coupling strength as well as radiation decay strength. A parameter is introduced to indicate the type. The indicator is useful as a key parameter for device design.