  Floquet topological photonic insulators characterized by periodically-varying
Hamiltonians are known to exhibit much richer topological behaviors than static
systems. In a Floquet insulator, the phase evolution of the Floquet-Bloch modes
plays a crucial role in determining its topological behaviors. Here we show
that by perturbing the driving sequence, it is possible to manipulate the
cyclic phase change of the system over each evolution period to induce quantum
self-interference of a bulk mode, leading to a new topological resonance
phenomenon called Floquet Mode Resonance (FMR). The FMR is fundamentally
different from other types of optical resonances in that it is cavity-less
since it does not require physical boundaries. Its spatial localization pattern
is instead dictated by the driving sequence and can thus be used to probe the
topological characteristics of the system. We demonstrated excitation of FMRs
by edge modes in a Floquet octagon lattice on silicon-on-insulator, achieving
extrinsic quality factors greater than 10^4. Imaging of the scattered light
pattern directly revealed the hopping sequence of the Floquet system and
confirmed the spatial localization of FMR in a bulk-mode loop. The new
topological resonance effect could enable new applications in lasers, optical
filters and switches, nonlinear cavity optics and quantum optics.
