Optimization of non-ideal multimode interference devices

Multimode interference devices are examined outside of the step-index, paraxial regime. To determine the optimum length of these devices, we maximize the projection of the propagated field in the multimode section onto the desired field profile. By consideration of the orthogonality among the guided modes, this reduces to a criterion of minimum weighted phase errors at the imaging plane, with no dependence on the actual mode field profiles. The results are confirmed by comparison with mode propagation analysis simulations. This analysis is immediately applicable to the design of multimode interference devices in weakly-guiding geometries such as shallow ridge waveguides, weakly-guiding materials systems such as photosensitive glasses and polymers, and waveguides with graded claddings and/or weak index gradients in the core, such as those formed through diffusive processes. The procedure is also used to explain the presence of the recently observed pseudo-self-image, which is not predicted by the standard theory of multimode interference.