This paper presents a detailed theoretical investigation of the energy spectrum, band gaps, topological and collective properties, and linear response in $d$-wave altermagnets in the presence of an off-resonance optical dressing field. We consider the altermagnets with both $d_{x^2-y^2}$ and $d_{xy}$ symmetries and focus on anisotropic optical driving fields applied to the initially anisotropic and nonlinear electron Hamiltonian. We have uncovered several crucial properties of the resulting electron-dressed states; specifically, we found that a finite band gap is opened by linearly polarized irradiation, a phenomenon not observed in Dirac materials. Some of the crucial properties of the electron-dressed states in the presence of linearly polarized light can be uncovered only in the second-order perturbation expansion, which is often omitted. We found that introducing an anisotropic driving field leads to several subtle yet important changes in the Edelstein susceptibilities of altermagnets, enabling the fine-tuning of their spin polarizations. We calculate the Berry curvature and Chern numbers for various types of altermagnets and obtain closed-form analytical expressions for circularly polarized irradiation. We demonstrate that the optical driving field can generate finite Berry curvature and Chern numbers in the absence of altermagnetic order. All these results are expected to make a crucial contribution to the rapidly developing fields of spintronics and device physics.

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• Spin-orbit coupling
• Altermagnets
• Floquet systems
• Symmetries in condensed matter