Abstract

A new coupled-mode formulation for parallel dielectric waveguides is described. The derivation includes radiation modes in addition to the individual guided modes and the coupling equations are obtained by requiring that the additional field be orthogonal to the guided modes. The results apply to any guided modes (TE, TM, or hybrid) in waveguides of arbitrary cross section, dissimilar index, and nonidentical shape. Additional index perturbations not included within the waveguides are encompassed by the theory. Propagation constants and mode patterns for the coupled modes computed according to this theory are shown to agree very well with numerical solutions for the system modes when the latter can be determined. Moreover, the new results are more accurate than those obtained from prior coupled-mode formulations. It is shown that even for lossless guides the coupling coefficient from waveguide b to a and from a to b, described by κ_ab and κ_bg, respectively, are not related by their complex conjugates if the guides are not identical. This fact does not violate energy conservation or reciprocity when the full expressions for the power flow are used.

© 1985 Optical Society of America