Quantized bulk response functions are hallmark signatures of topological phases, but their manifestation in periodically driven (Floquet) systems is not yet fully established. Here, we show that two-dimensional anomalous Floquet systems exhibit a quantized bulk response encoded in a Chern-Simons axion (CSA) coupling angle ${\theta }_{\mathrm{CS}}^F\in 2\pi \mathbb{Z}$, reflecting a topological magnetoelectric effect analogous to that in three-dimensional insulators. The periodic drive introduces an emergent “photon” dimension, allowing the system to be viewed as a three-dimensional Sambe lattice. Within this framework, quantized cross-correlated responses—namely, photon-space polarization and magnetization density—emerge as physical signatures of the CSA coupling. The CSA angle, constructed from the non-Abelian Berry connection of Floquet states, admits a natural interpretation in terms of the geometry of hybrid Wannier states. These results provide a unified framework linking Floquet band topology to quantized bulk observables, demystifying the topology of gapped 2D anomalous Floquet systems by establishing their connection to static 3D topological systems.

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• Chern-Simons gauge theory
• Magnetoelectric effect
• Topological phases of matter
• Floquet systems
• Wannier function methods