Integrated optical branching filter consisting of three-dimensional waveguide and its nonradiative condition

A branching wavelength-selective filter for optical communication systems consisting of a three-dimensional Input waveguide with a grating and an output slab waveguide is analyzed. It is found that insertion loss occurs due to the radiation of the light from the grating into the substrate. Conditions for lossless operation of the filter are given. Optical branching filters with three-dimensional input waveguides were fabricated by using an electron-beam exposure system. Filtering resolution was measured experimentally and found to agree with theory.