  Recent theoretical work on time-periodically kicked Hofstadter model found
robust counter-propagating edge modes. It remains unclear how ubiquitously such
anomalous modes can appear, and what dictates their robustness against
disorder. Here we shed further light on the nature of these modes by analyzing
a simple type of periodic driving where the hopping along one spatial direction
is modulated sinusoidally with time while the hopping along the other spatial
direction is kept constant. We obtain the phase diagram for the quasienergy
spectrum at flux 1/3 as the driving frequency $\omega$ and the hopping
anisotropy are varied. A series of topologically distinct phases with
counter-propagating edge modes appear due to the harmonic driving, similar to
the case of a periodically kicked system studied earlier. We analyze the time
dependence of the pair of Floquet edge states localized at the same edge, and
compare their Fourier components in the frequency domain. In the limit of small
modulation, one of the Floquet edge mode within the pair can be viewed as the
edge mode originally living in the other energy gap shifted in quasienergy by
$\hbar \omega$, i.e., by absorption or emission of a "photon" of frequency
$\omega$. Our result suggests that counter-propagating Floquet edge modes are
generic features of periodically driven integer quantum Hall systems, and not
tied to any particular driving protocol. It also suggests that the Floquet edge
modes would remain robust to any static perturbations that do not destroy the
chiral edge modes of static quantum Hall states.
