Power distribution and radiation losses in multimode dielectric slab waveguides

Guided modes of multimode waveguides exchange power if the waveguide deviates in any way from its perfect geometry. The power exchange problem is studied for a multimode slab waveguide under the assumption that the power coupling is caused by irregularities of the core-cladding interfaces. The problem is treated by means of coupled power equations. The main result of this study is the realization that the power distribution versus mode number settles down to a steady state distribution if the waveguide is sufficiently long. The shape of the steady state distribution depends on the correlation length of the function describing the core-cladding interface irregularities. For very short correlation length only the lowest-order mode carries an appreciable amount of power while the power carried by all the other modes is orders of magnitude smaller. For very long correlation length, on the other hand, all guided modes carry equal amounts of power. The steady state distribution is achieved regardless of the way in which the power was distributed over all the modes at the beginning of the guide. However, the total power in the steady state mode distribution is dependent on the initial power distribution.