([see also SI, Figs. S5-S7]{} for more simulations on cylindrical NWs).

![image](fig6)

Asymmetric, Rectangular Silicon Nanowires
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In a second step we analyze what happens if the cylindrical symmetry of the nanowire cross section is broken. We therefore fabricate SiNWs of rectangular section by electron beam lithography (EBL) and subsequent dry-etching on a silicon-on-quartz (SOQ) substrate. For details on the fabrication process, see Methods. We want to point out a great advantage of our top-down approach on SOQ: The possibility to create silicon nanostructures of arbitrary shape by EBL on a transparent substrate This gives us the opportunity for a systematic analysis of the scattering from rectangular SiNWs of variable width. The height of the structures however remains constant, defined by the thickness of the silicon layer on the SOQ substrate ($H=90\,$nm in our case). We choose SiNWs with length long compared to the focal spot of the illuminating optics (all data acquired on NWs with $L=7\,$m) in order to obtain a purely Mie-like response.[@traviss_antenna_2015] SEM images of selected rectangular SiNWs are shown in figure \[fig:fig2\]e. The images are obtained from a second sample, fabricated with the exact same process parameters but on a non-insulating silicon-on-insulator (SOI) substrate. For the 