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 without static counterparts, 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.

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• Exotic phases of matter
• Topological effects in photonic systems
• Topological phase transition
• Topological phases of matter
• Floquet systems
• Bloch-Floquet theorem