Fig. 7: Linear and nonlinear optical responses of TaAs (112).

a Crystal structure and experimental orientation. b The effective complex refractive indices at ω frequency as a function of incident angle (\(\theta ^i\)). c p- and s-polarized second harmonic responses as a function of azimuthal angle (φ) at various incident angles (\(\theta ^i\)). d Comparison of the correct ratios of nonlinear coefficients (pale green background) as against other forced approximations (pale orange background). Uni, Iso, and KS, respectively, represent uniaxial, isotropic symmetry, and Kleinman’s symmetry approximations. \(Iso(\varepsilon _{ii})\) indicates that the component \(\varepsilon _{ii}\) was assumed in all directions under the isotropic approximation, where i is the direction index. Uni(\(\left| {{{{\tilde{\boldsymbol{\varepsilon }}}}}} \right|\)) and Uni(\({{{\tilde{\boldsymbol{\varepsilon }}}}}_R\)), respectively, mean using the magnitudes of complex relative dielectric permittivity and only the real part of the dielectric permittivity as tensor values while retaining the uniaxial dielectric permittivity tensor symmetry. Misoriented case represents analysis using the plane normal as [112] which is discussed in detail in Supplementary Note 2.