This study reports the observation of Floquet-Bloch bands on the surface of a topological insulator (TI) using time- and angle-resolved photoemission spectroscopy (TrARPES). The research demonstrates that an intense mid-infrared (MIR) pulse with energy below the bulk band gap hybridizes with the surface Dirac fermions of a TI, forming Floquet-Bloch bands. These bands exhibit polarization-dependent band gaps at avoided crossings, and circularly polarized photons induce an additional gap at the Dirac point, indicating broken time-reversal symmetry (TRS) on the surface. These findings establish the existence of Floquet-Bloch bands in solids and open new avenues for optical manipulation of topological quantum states. The surface states of TIs obey the Dirac equation and exhibit spin-momentum locking, protected by TRS. Breaking TRS can lead to exotic states, and coherent light-matter interactions offer a promising route to achieve this. The study uses MIR photons to induce Floquet-Bloch bands, which repeat in both energy and momentum. Circularly polarized light breaks TRS, causing the surface Dirac cone to become gapped. The Floquet theorem explains that a time-periodic Hamiltonian has quasi-static eigenstates spaced by the photon energy. The study confirms that Floquet-Bloch bands form in TIs, with band gaps opening at avoided crossings. The research uses TrARPES to probe the photo-induced band gaps on the TI surface. The MIR pump pulses are tuned to 4-17 μm, with a peak energy of 1 μJ. The study shows that the surface band structure changes with the polarization of light, with circularly polarized light inducing a band gap at the Dirac point. The energy distribution curves (EDCs) confirm that circularly polarized light opens a band gap at the Dirac point, consistent with a two-photon process. The results suggest the existence of a photoinduced anomalous quantum Hall phase without Landau levels, described by axion electrodynamics. The findings demonstrate the general applicability of Floquet theory to Dirac systems and open new possibilities for optical control of topological orders. The study provides evidence for Floquet Majorana modes in these materials. The results are consistent with theoretical predictions and show the potential for future applications in topological quantum computing and spintronics.This study reports the observation of Floquet-Bloch bands on the surface of a topological insulator (TI) using time- and angle-resolved photoemission spectroscopy (TrARPES). The research demonstrates that an intense mid-infrared (MIR) pulse with energy below the bulk band gap hybridizes with the surface Dirac fermions of a TI, forming Floquet-Bloch bands. These bands exhibit polarization-dependent band gaps at avoided crossings, and circularly polarized photons induce an additional gap at the Dirac point, indicating broken time-reversal symmetry (TRS) on the surface. These findings establish the existence of Floquet-Bloch bands in solids and open new avenues for optical manipulation of topological quantum states. The surface states of TIs obey the Dirac equation and exhibit spin-momentum locking, protected by TRS. Breaking TRS can lead to exotic states, and coherent light-matter interactions offer a promising route to achieve this. The study uses MIR photons to induce Floquet-Bloch bands, which repeat in both energy and momentum. Circularly polarized light breaks TRS, causing the surface Dirac cone to become gapped. The Floquet theorem explains that a time-periodic Hamiltonian has quasi-static eigenstates spaced by the photon energy. The study confirms that Floquet-Bloch bands form in TIs, with band gaps opening at avoided crossings. The research uses TrARPES to probe the photo-induced band gaps on the TI surface. The MIR pump pulses are tuned to 4-17 μm, with a peak energy of 1 μJ. The study shows that the surface band structure changes with the polarization of light, with circularly polarized light inducing a band gap at the Dirac point. The energy distribution curves (EDCs) confirm that circularly polarized light opens a band gap at the Dirac point, consistent with a two-photon process. The results suggest the existence of a photoinduced anomalous quantum Hall phase without Landau levels, described by axion electrodynamics. The findings demonstrate the general applicability of Floquet theory to Dirac systems and open new possibilities for optical control of topological orders. The study provides evidence for Floquet Majorana modes in these materials. The results are consistent with theoretical predictions and show the potential for future applications in topological quantum computing and spintronics.