Floquet engineering, the concept of tailoring a system by a periodic drive, is increasingly exploited to design and manipulate topological phases of matter. In this work we study periodically driven higher-order topological Dirac semimetals associated with a $k$-dependent quantized quadrupole moment by applying circularly polarized light. The undriven Dirac semimetals feature gapless higher-order hinge Fermi arc states which are the consequence of the higher-order topology of the Dirac nodes. Floquet Weyl semimetal phases with hybrid-order topology, characterized by both a $k$-dependent quantized quadrupole moment and a $k$-dependent Chern number, emerge when illumining circularly polarized light. Such Floquet Weyl semimetals support both hinge Fermi arc states and topological surface Fermi arc states. In addition, Floquet Weyl semimetals with tilted Weyl cones in higher-order topological Dirac semimetals are also discussed. Considering numerous higher-order topological Dirac semimetal materials were recently proposed, our findings can be testable soon.

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• Symmetry protected topological states
• Topological phase transition
• Dirac semimetal
• Floquet systems
• Weyl semimetal
• Bloch-Floquet theorem