Multimodal unidirectional pulse propagation equation

In this paper, after a brief recall of the derivation of the unidirectional pulse propagation equation generalized to structured media, a fast modal transform linking the spatiotemporal representation of the field and its modal distribution is presented. This transform is used for solving the propagation equation by using a split-step algorithm in an efficient way. As an example, we present, to the best of our knowledge, the first numerical evidence of the generation of conical waves in highly multimodes waveguides.