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The Floquet spectrum in an anisotropic tilted Dirac semimetal modulated bylinearly polarized light is addressed through the solution of thetime-dependent Schr\"odinger equation for the two-dimensional Dirac Hamiltonianvia the Floquet theorem. The time-dependent wave functions and the quasienergyspectrum of the two-dimensional Dirac Hamiltonian under the normal incidence oflinearly polarized waves are obtained for an arbitrarily intenseelectromagnetic radiation. We applied a set of unitary transformations toreduce the Schr\"odinger equation to an ordinary second-order differential Hillequation with complex coefficients. Through the stability analysis of thisdifferential equation, the weak and strong field regimes are clearlydistinguished in the quasi-spectrum. In the weak electric field regime, above acertain threshold given by the field parameters, the spectrum mostly resemblesthat of free electrons in graphene. Below this threshold, in the strongelectric field regime, the spectrum abruptly becomes highly anisotropic and agap opens up. As an example, we apply the results to the particular case ofborophene.

Floquet spectrum for anisotropic and tilted Dirac materials under linearly polarized light at all field intensities