The Coupling of Degenerate Modes in Two Parallel Dielectric Waveguides

Optical fibers a p p e a r a t t r a c t i v e as waveguides for the transmission of light. Since m a n y such fibers arc likely to be bunched together to form a cable, the problem of crosstalk between t h e different fibers of t h e cable arises. T h e r e are several sources of crosstalk. Light scattered in one fiber m a y excite a guided mode of an a d j a c e n t fiber. T h i s double scattering mechanism is discussed in the next p a p e r in this issue. 1791 1792 T H E BELL SYSTEM TECHNICAL JOURNAL, J U L Y - A U G U S T 1971 T h e present paper is concerned with the direct coupling of power between two parallel dielectric waveguides. Even though it addresses itself to crosstalk in optical fibers the theory is more general and applies to dielectric waveguides of arbitrary distribution of the refractive index. T h e modes carried by the two guides need not be identical. However, we assume t h a t the phase velocities of the modes in either guide are identical. We call modes with identical phase velocity degenerate modes. We furthermore admit the possibility t h a t the media of the waveguides as well as the surrounding medium in which the guides are embedded m a y be lossy. The restriction to degenerate modes is no serious limitation for cases of practical interest. Provided t h a t the coupling coefficients are constant, appreciable coupling of power from a mode in one guide to a mode in the other guide is possible only if the modes have identical phase velocities. T h e coupling theory is based on finding the change of the propagation constant of t h e mode of one guide caused by the presence of the other guide.