  Floquet higher order topological insulators (FHOTIs) are a novel topological
phase that can occur in periodically driven lattices. An appropriate
experimental platform to realize FHOTIs has not yet been identified. We
introduce a periodically-driven bipartite (two-band) system that hosts FHOTI
phases, and predict that this lattice can be realized in
experimentally-realistic optical waveguide arrays, similar to those previously
used to study anomalous Floquet insulators. The model exhibits interesting
phase transitions from first-order to second-order topological matter by tuning
a coupling strength parameter, without breaking lattice symmetry. In the FHOTI
phase, the lattice hosts corner modes at eigenphase $0$ or $\pi$, which are
robust against disorder in the individual couplings.
