Theoretical study on the coupling of two-dimensional gaussian beam to a dielectric slab waveguide

Mode coupling and reflection of a two‐dimensional Gaussian beam incident on an arbitrarily shaped end‐surface of a slab waveguide are studied theoretically. the relation between the shape of the end‐surface and the coupling efficiency is studied in detail by means of numerous numerical examples. It is found that: (1) the vertical planar end‐surface exhibits the highest coupling efficiency if the incident beam has neither axial shift nor angular shift and if the beam waist position coincides with the end‐surface; (2) an optimum shape for the end‐surface exists that provides the best coupling if the beam waist position is separated from the end surface; and (3) extremely high coupling efficiency is attained if the TM beam wave is incident with a Brewster angle. Although the analysis is based mainly on the integral equation method, a simple method is also presented for computing coupled power from the fields approximately obtained from the Fresnel formula.