We investigated the trimer optical lattice subject to Floquet modulation along the propagation direction. Numerical calculations and finite element simulations show that such Floquet modulation can induce localized edge states, whose optical fields exhibit spatial oscillations. Quasienergy band analysis further indicates that this oscillatory behavior originates from Floquet topological modes (FTMs). More importantly, it is demonstrated that these FTMs can continuously evolve into the Bloch topological modes induced by periodic static structural modulation, all while maintaining an open quasienergy gap. These findings elucidate the intricate mechanisms for controlling topological modes in systems with both Bloch and Floquet periodicity and provide physical insights into topological phase transitions in trimer lattices driven by unconventional gap-closing mechanisms.

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• Topological phase transition
• Topological phases of matter