Radiation loss of grating-assisted directional coupler

The coupling between the guided modes and between guided and radiation modes of two parallel slab waveguides forming a directional coupler in order is computed to determine the radiation losses introduced by the coupling grating. The problem is solved in two stages. First, the guided modes for each waveguide are computed separately and the radiation modes are only determined for the more complicated of the two waveguides, the one that is nearer to the grating. Modifications caused by the presence of the opposite waveguide are then taken into account by computing first-order correction terms. For a practical example of slab waveguides defined in GaInAsP, the authors find that the radiation losses per power exchange length remain below 0.02 dB for a rectangular grating depth of 0.01 μm