Floquet systems with periodically varying in time parameters enable
realization of unconventional topological phases that do not exist in static
systems with constant parameters and that are frequently accompanied by
appearance of novel types of the topological states. Among such Floquet systems
are the Su-Schrieffer-Heeger lattices with periodically-modulated couplings
that can support at their edges anomalous π modes of topological origin
despite the fact that the lattice spends only half of the evolution period in
topologically nontrivial phase, while during other half-period it is
topologically trivial. Here, using Su-Schrieffer-Heeger arrays composed from
periodically oscillating waveguides inscribed in transparent nonlinear optical
medium, we report experimental observation of photonic anomalous π modes
residing at the edge or in the corner of the one- or two-dimensional arrays,
respectively, and demonstrate a new class of topological π solitons
bifurcating from such modes in the topological gap of the Floquet spectrum at
high powers. π solitons reported here are strongly oscillating nonlinear
Floquet states exactly reproducing their profiles after each longitudinal
period of the structure. They can be dynamically stable in both one- and
two-dimensional oscillating waveguide arrays, the latter ones representing the
first realization of the Floquet photonic higher-order topological insulator,
while localization properties of such π solitons are determined by their
power.Comment: 10 pages, 6 figures, to appear in Science Bulleti