  Using Brillouin light scattering spectroscopy and dynamical matrix method
calculations, we study collective spin waves in dense arrays of periodically
double-side width-modulated Permalloy nanowires. Width modulation is achieved
by creating a sequence of triangular notches on the two parallel nanowire
sides, with a periodicity of p=1000 nm, and tunable relative displacement (D)
of the notches sequence on the two lateral sides. Both symmetric (D=0) and
asymmetric (D= 250 and 500 nm) width-modulated nanowires were investigated. We
have found that the detected modes have Bloch-type character and belong to a
doublet deriving from the splitting of the modes characteristics of the
nanowire with homogeneous width. Interestingly, the amplitude of the magnonic
band, the frequency difference of the doublet, as well as their relative
scattering intensity, can be efficiently controlled by increasing D rather than
having single- or symmetric (D=0) double-side width-modulation.
