axis. For normal incidence, $\mathbf{k}_y=0$. The integral in Eq.  runs over the surface of the 2D particle cross section. This self-consistent equation is solved (*e.g.* using standard LU decomposition) and the field can be computed in the nanowire. Knowing the field inside the nanostructure, application of Eq.  permits to compute the field everywhere, both in the near-field and far-field zone. For details we refer the interested reader to Refs.  and .

All simulations are carried out for SiNWs in vacuum ($n_{\text{env.}}=1$) to allow direct comparison with Mie theory for the cylindrical wires ([see SI, Figs. S5-S10]{}). Given the large index contrast with silicon ($n_{\text{Si}}\approx 4$ in the visible), this is a good approximation, which is supported also by the excellent agreement between simulations and measurements.

This work was supported by Programme Investissements d’Avenir under the program ANR-11-IDEX-0002-02, reference ANR-10-LABX-0037-NEXT, by LAAS-CNRS micro and nanotechnologies platform member of the French RENATECH network, by the Région Midi-Pyrénées and by the computing facility center CALMIP of the University of Toulouse under grant P12167.

Supporting Informations {#supporting-informations .unnumbered}
=======================

In the supporting informations we show further details on FW/BW scattering from nanowires by Mie theory as well as additional simulations.

Notes {#notes .unnumbered}
=====

