Modelling of semiconductor rib wave guides by a finite difference method

The method of finite differences is used to solve the scalar wave equation for semiconductor rib wave guides. Boundary conditions derived from continuity relations are applied between regions of different refractive index, allowing more accurate evaluation of the propagation constants for ideal cases of abrupt change in the index. Also appropriate external boundary conditions alleviate the inaccuracy generally introduced by setting the field equal to zero on the external limit of the mesh. Our results agree with various other techniques when applied to typical guiding structures. As an example, we model a multiple-quantum-well structure by using an equivalent layered structure. Mode characteristics and confinement factors obtained by the method are of interest in understanding the behaviour of the lasers and modulators fabricated in our laboratory.