  Reversed structures of artificial spin-ice systems, where elongated holes
with elliptical shape (antidots) are arranged into a square array with two
orthogonal sublattices, are referred to as anti-squared spin-ice. Using
Brillouin light scattering spectroscopy and plane wave method calculations, we
investigate the spin wave propagation perpendicular to the applied field
direction for two 20 nm thick Permalloy nanostructures which differ by the
presence of single and double elliptical antidots. For the spin waves
propagation along the principal antidot lattice axis, the spectrum consists of
flat bands separated by several frequency gaps which are the effect of spin
wave amplitude confinement in the regions between antidots. Contrarily, for
propagation direction at 45 degrees with respect to the antidot symmetry axis,
straight and narrow channels of propagation are formed, leading to broadening
of bands and closing of the magnonics gaps. Interestingly, in this case, extra
magnonic band gaps occur due to the additional periodicity along this
direction. The width and the position of these gaps depend on the presence of
single or double antidots. In this context, we discuss possibilities for the
tuning of spin wave spectra in anti-squared spin ice structures.
