Motivated by recent experimental demonstrations of Floquet topological insulators, there have been several theoretical proposals for using structured light, either spatial or spectral, to create other properties such as flat band and vortex states. In particular, the generation of vortex states in a massive Dirac fermion insulator irradiated by light carrying nonzero orbital angular momentum (OAM) has been proposed [Kim et al. Phys. Rev. B 105, L081301(2022)].

Here, we evaluate the orbital magnetization and optical conductivity as physical observables for such a system. We show that the OAM of light induces nonzero orbital magnetization and current density. The orbital magnetization density increases linearly as a function of OAM degree, and non-linearly as a function of the frequency of the light field. In certain regimes, we find that orbital magnetization density is independent of the system size, width, and Rabi frequency of light. Furthermore, we study the optical conductivity for various types of electron transitions between different states such as vortex, edge, and bulk that are present in the system. Based on conductance frequency peaks, a scheme for the detection of vortex states is proposed.