diameter combinations for normally illuminated cylindrical silicon nanowires.

![image](fig4_1) ![image](fig4_2)

It is possible to expand the electromagnetic fields inside the cylinder in the same way as the scattered fields of Eq. . For details, we refer to the textbook of Bohren and Huffmann (chapters 4 and 8.4).[@bohren_absorption_1998] In figure \[fig:fig1\] the average internal field intensity enhancement is shown for a SiNW with diameter $D=100\,$nm with a TE (a) and TM (b) polarized incident plane wave, respectively. Interestingly, at the resonant wavelengths we observe not only high electric field intensities (red lines) but also a very strong enhancement of the magnetic field (blue lines), regardless of the incident polarization orientation. For both polarizations, the magnetic field increases even significantly stronger compared to the electric field intensity. We remark that this observation is in agreement with recent results from dielectric cylinders in the GHz regime.[@kapitanova_giant_2017] We conclude that a simultaneous excitation of strong electric and magnetic fields occurs in dielectric, non-magnetic (*i.e.* $\mu_r = 1$) nanowires, even under pure TE or TM polarized illumination and normal incidence. Hence, in analogy to the findings of Kerker *et al.* for the case of spherical dielectric nanoparticles, the observed directionality (dashed green lines in Fig. 