Comparison of rigorous scattering models to accurately replicate the behaviour of scattered electromagnetic waves in optical surface metrology

Rigorous scattering models are based on Maxwell's equations and can provide high-accuracy solutions to model electromagnetic wave scattering from objects. Being able to calculate the scattered field from any surface geometry and considering the effect of the polarisation of the incident light, make rigorous models the most promising tools for complex light-matter interaction problems. The total intensity of the electric near-field scattering from a silicon cylinder illuminated by the transverse electric and transverse magnetic polarisation of the incident light is obtained using various rigorous models including, the local field Fourier modal method, boundary element method and finite element method. The intensity of the total electric near-field obtained by these rigorous models is compared using the Mie solution as a reference for both polarisation modes of the incident light. Additionally, the intensity of the total electric near-field scattered from a silicon sinusoid profile using the same rigorous models is analysed. The results are discussed in detail, and for the cylinder, the deviations in the intensity of the total electric field from the exact Mie solution are investigated.