The topological Dirac nodal-line semimetal CaAgAs has received significant research attention due to its unique physical properties. Moreover, CaAgAs offers an ideal platform to study the linear and second-order nonlinear optical properties of nodal-line semimetals owing to the tunable radius of the nodal ring in the $\mathrm{CaAg}{\mathrm{As}}_{1-x}{\mathrm{P}}_x$ alloy and the structural centrosymmetric symmetry breaking. In this work, we study the linear and second-order nonlinear optical properties of CaAgX $(X=\mathrm{As} \text{and} \mathrm{P})$ and their alloys by density functional theory and a low-energy effective Hamiltonian. The peak values of the imaginary part of the dielectric function and the plateaus of optical conductivity in the low-frequency range are tunable by the radius of the nodal ring in the $\mathrm{CaAg}{\mathrm{As}}_{1-x}{\mathrm{P}}_x$ alloy with different concentrations of P doping. The peak value of the second-harmonic generation for both materials is around 400 pm/V, while the peak value of the shift current for both materials is around 20 $\mu \mathrm{A}/{\mathrm{V}}^2$. The linear band of topological node-line semimetal can inhibit second-harmonic generation within a low-frequency range due to the linear band dispersion near the Fermi level. The shift current of $\mathrm{CaAg}X$ $(X=\mathrm{As} \text{and} \mathrm{P})$ remains small in the low-frequency range, which is attributed to the low joint density of states value in this range. Our research results indicate that $\mathrm{CaAg}X$ holds potential for applications in nonlinear optics and tunable linear electro-optic devices.

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• Optical conductivity
• Dirac semimetal
• Nodal-line semimetals
• Topological materials
• Density functional calculations
• Optical second-harmonic generation
• Wannier function methods
• k dot p method