because a recent theoretical study [@submitted], using an effective Hamiltonian ($H_{\rm{eff}}$) scheme, revealed that its ground state possesses a spontaneous polarization along the $z$-direction inside the whole composite system, as well as electric vortices in the ($x$,$y$) planes inside each BaTiO$_3$ nanowire, with the same sense of vortex rotation in every wire. Such a phase-locking, ferrotoroidic and polar state is shown in Fig. 1a. It exhibits an electrical toroidal moment being parallel to the polarization. Figure 1a also reveals the presence of antivortices located in the [*medium*]{}, half-way between the centers of adjacent vortices.

In the present study, we use the same $H_{\rm{eff}}$ as in Ref. [@submitted], combined with molecular dynamics techniques, to determine the response of this peculiar state to an $ac$ electric field applied along the main, $z$-direction of the wires. In our simulations, the amplitude of the field was fixed at 10$^9$ V/m and its frequency ranged between 1GHz and 100GHz. The sinusoidal frequency-driven variation of the electric field with time makes therefore this field ranging in time between 10$^9$ V/m (field along \[001\]) and -10$^9$ V/m (field along \[00-1\]). The idea here is to check if the electrical toroidal moment has a [*linear*]{} variation with this 