  For systems that can be modeled as a single-particle lattice extended along a
privileged direction as, e.g., quantum wires, the so-called eigenvalue method
provides full information about the propagating and evanescent modes as a
function of energy. This complex-band structure method can be applied either to
lattices consisting of an infinite succession of interconnected layers
described by the same local Hamiltonian or to superlattices: Systems in which
the spatial periodicity involves more than one layer. Here, for time-dependent
systems subject to a periodic driving, we present an adapted version of the
superlattice scheme capable of obtaining the Floquet states and the Floquet
quasienergy spectrum. Within this scheme the time periodicity is treated as
existing along spatial dimension added to the original system. The solutions at
a single energy for the enlarged artificial system provide the solutions of the
original Floquet problem. The method is suited for arbitrary periodic
excitations including strong and anharmonic drivings. We illustrate the
capabilities of the methods for both time-independent and time-dependent
systems by discussing: (a) topological superconductors in multimode quantum
wires with spin-orbit interaction and (b) microwave driven quantum dot in
contact with a topological superconductor.
