Scalar approximation of Maxwell equations: derivation and accuracy

Replacing Maxwell equations by a scalar wave equation is often used in computational imaging to simulate the light-sample interaction. It significantly reduces the computational burden but provides field maps that are insensitive to the polarization of the incident field, provided the latter is constant throughout the sample. Here, we develop a scalar approximation that accounts for the polarization of the incident field. Comparisons with rigorous simulations show that this approach is more accurate than the classical scalar approximation with similar computational cost.