Advances in the spectral index method for optoelectronic design

The spectral index (SI) approach can be applied for 3D problems. The SI approximation that the small field penetration into the air regions can be modelled by using a slightly larger rib geometry can be carried over to the 3D case. Obviously, this presupposes that any discontinuities primarily scatter into the substrate and not the air regions. A 2D variational boundary condition applied in the plane of the base of the rib when used in conjunction with a suitable decomposition of the field amplitudes on this plane, can be used to solve fully 3D rib circuit problems. The principal advantage of this approach is that it ultimately only requires solution of a small set of linear equations to completely determine the fields in the full structure. The SI method is a valuable analysis tool for the optoelectronics designer.