  The study of high-index dielectric nanoparticles currently attracts a lot of
attention. They do not suffer from absorption but promise to provide control on
the properties of light comparable to plasmonic nanoparticles. To further
advance the field, it is important to identify versatile dielectric
nanoparticles with unconventional properties. Here, we show that breaking the
symmetry of an all-dielectric nanoparticle leads to a geometrically tunable
magneto-electric coupling, i.e. an omega-type bianisotropy. The suggested
nanoparticle exhibits different backscatterings and, as an interesting
consequence, different optical scattering forces for opposite illumination
directions. An array of such nanoparticles provides different reflection phases
when illuminated from opposite directions. With a proper geometrical tuning,
this bianisotropic nanoparticle is capable of providing a $2\pi$ phase change
in the reflection spectrum while possessing a rather large and constant
amplitude. This allows creating reflectarrays with near-perfect transmission
out of the resonance band due to the absence of an usually employed metallic
screen.
