Fig. 4: Linear and nonlinear optical responses of GaAs (111).

a Crystal structure and experimental orientation. The \(\left( {L_1,L_2,L_3} \right)\) and \(\left( {a,b,c} \right)\) are the lab coordinate system and crystallographic coordinate system respectively. The dashed dark yellow line represents the projection of the plane of incidence to the \(L_1 - L_2\) plane. b The effective complex refractive indices at ω frequency as a function of incident angle (\(\theta ^i\)), subscript R and I represent real and imaginary respectively. c and d p- and s-polarized second harmonic responses as a function of azimuthal angle (φ) at various incident angles (\(\theta ^i\)). The open circles are experimental results, and the solid lines are theoretical fits. e Comparison of the SHG coefficients with no approximations (labeled as ♯SHAARP, pale green background) as against those extracted with various approximations (pale orange background). \({{{\tilde{\boldsymbol{\varepsilon }}}}}_R\), and \(\left| {{{{\tilde{\boldsymbol{\varepsilon }}}}}} \right|\) represent the real component of \({{{\tilde{\boldsymbol{\varepsilon }}}}}\), and the magnitude of the complex \({{{\tilde{\boldsymbol{\varepsilon}}}}}\), respectively.