Numerical Methods in Photonics

7.5.2  CALCULATING THE FIELD AND NORMAL DERIVATIVE AT THE BOUNDARY

In order to obtain the field and its normal derivative at the boundaries, the approach is to consider the integral equations (7.50) in the limit when the position r approaches the surface of the scatterer from one and the other side. Thereby we end up with two integral equations that are only concerned with fields at positions on the inner and outer surface of the scatterer, that is at c₁ and c₂. While there are two equations, there are four unknowns at the two boundaries of the scatterer, namely the magnetic field and its normal derivative, on each side of the boundary. However, here, we can exploit that the electromagnetics boundary conditions across an interface give that the ...