  In this study, a tight-binding model on square octagon lattice with
nearest-neighbour and next-nearest-neighbour hoppings is considered. The system
is topologically trivial although it exhibits quadratic band-touching points in
its band-structure. It is shown that the system drives towards topologically
non-trivial phases as soon as it is exposed to monochromatic circularly
polarized light. Multiple topological phases are found to emerge with the
variation of amplitude of light. An effective time-independent Hamiltonian of
the system is obtained following the Floquet-Bloch formulation. Quasi-energy
band-structures along with definite values of Chern numbers for respective
bands are obtained. Characterization of topological phases are made in terms of
band structure and Chern numbers. In addition, Hall conductance and
topologically protected chiral edge states are obtained to explain the
topological properties. Density of states is obtained in every case. The system
undergoes a series of topological phase transitions among various topological
phases upon variations of both amplitude of light and hopping strengths. It
exhibits Chern insulating and Chern semimetallic phases depending on the values
of lattice filling.
