Floquet engineering via external periodic fields has emerged as a powerful dynamic regulation strategy for topological semimetals, yet most existing studies rely on high-frequency approximations with limited applicability across the full frequency domain. In this paper, we investigate the modulation of a Dirac semimetal system driven by an optical comb and, more importantly, derive an exact analytical solution to the corresponding Floquet Hamiltonian, which enables unapproximated exploration of the system across the entire frequency domain. We show that the exact solution captures characteristic features beyond the low-order approximation in the high-frequency regime. With decreasing driving frequency, the system exhibits distinct higher-order hinge states. In the low-frequency regime, nodal lines emerge as a result of the periodic field. Our findings demonstrate that the proposed periodic electric pulses, together with the exact analytical method, provide a rigorous theoretical framework for full-frequency Floquet engineering of topological semimetal systems.

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• Edge states
• Dirac semimetal
• Floquet systems
• Nodal-line semimetals
• Semimetals