Numerical analyses of optically coupled active and passive dielectric slab waveguides for TM modes

Propagation characteristics of optically coupled dielectric waveguides including active and passive waveguides are studied in terms of scalar and vector field finite element methods. First, characteristics of couplings for asymmetric passive waveguides, i.e., modal dispersions and field distributions, are obtained using a vector field finite element method. Second, a scalar field finite element method is applied to active coupled slab waveguides, and modal propagation characteristics, i.e., dispersion relationships, modal gains, phase characteristics, and electromagnetic field distributions, are investigated in detail. Characteristics depending on parameters such as gain, symmetrical conditions of waveguides, and numbers of waveguides are obtained. As a result, weak coupling phenomena due to unequal gains are observed and it is found that a modal gain depends on optical power confinement factors. In this paper only TM modes are treated, but our method can be used to obtain TE modes.