Limitations of the wide-angle beam propagation method in nonuniform systems

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Abstract
A new approach is proposed that makes clear the basic assumptions in the beam propagation method (BPM) and that leads to an improved formulation free of difficulties with power conservation wide-angle propagation. The new approach allows one to understand the limitations of the wide-angle BPM. Theoretically, arbitrary accuracy could be achieved for weakly guiding systems, even for angles θ ~ 40° from the z axis, provided that a small enough sampling step is used, together with a BPM solver of sufficient order in nonparaxiality. On the contrary, inevitable errors occur with strongly guiding systems because the local-mode expansion of the physical field rapidly involves evanescent local modes, both forward and backward propagating, that cannot be handled in the BPM propagation algorithms. In this case the new formulation is more accurate than the classical BPM for moderate angles only.