at least $D=100\,$nm ([see also supporting informations (SI), Figs. S1-S2]{}). By setting $\varphi=0$ or $\varphi=\pi$ in equations  we obtain the conditions for zero scattering in forward (FW), respectively backward (BW) direction. For TM polarized illumination we find: $$\label{eq:pure_FW_BW_conditions_TM}
 \begin{aligned}
    T_1\Big|_{\varphi=0} & \approx b_0 + 2 b_1 = 0 \quad\quad \text{for pure BW scat.}\\
    T_1\Big|_{\varphi=\pi} & \approx b_0 - 2 b_1 = 0 \quad\quad \text{for pure FW scat.}
 \end{aligned}$$ The same conditions hold for $T_2$ and $a_{0,1}$ in the TE configuration. Hence if the conditions in Eqs.  are met, it is possible to obtain uni-directional scattering from 1D dielectric nanowires, which is the result of interference between the simultaneously excited first two multipole contributions. In figure \[fig:fig1\](a-b), the FW/BW scattering ratio is shown (dashed green lines) for a SiNW of diameter $D=100\,$nm for (a) TE and (b) TM polarized excitation, revealing zones of strongly directional scattering. For the dispersion of silicon we use tabulated data from Ref.  throughout this paper. In the [SI Figs S3-S4]{} we show the first two order Mie coefficients for SiNWs as function of the wavelength and the nanowire diameter and find that zones where the conditions in Eqs.  are approached do exist at several wavelength / 