Abstract
Discussed are cross-coupling coefficients of two coupled step-index slabs using a ray-optic method. Calculations are made and compared with the so-called the conventional coupled-mode theory (CMT) and the improved CMT proposed by Marcatili. Here both weakly and strongly coupled slabs are illustrated and quantitatively compared. For weakly coupled slabs, excellent agreements among these three methods are found. For strongly coupled slabs, our ray-optic result can be close to that of the improved CMT. From illustrating examples, our ray-optic method demonstrates a better and accurate result in comparison with the improved CMT. Furthermore, the concept, formulation, and calculations of our ray-optic method turn out to be much simpler than those of the sophisticated improved CMT. To examine the cross couplings of the guided modes in each of the coupled slabs in further detail, we investigate the cross coupling of the fundamental mode to the fundamental mode and of the first-excided mode to the first-excited mode. Accordingly, we can easily check the validity of the basic assumption of any a CMT. From our presented examples, it seems that our ray-optic method is a powerful approach in analyzing slab waveguides and related devices. In this work, we also demonstrate the usefulness and importance of an often neglected phenomenon Goos-Hahnchen shift in the analysis of step-index two dimensional slabs.