i=up,down] are based on the Fast Modal Transform (FMT) [12-14] and on the modal scattering operator ([[?
In this analytical case (diffraction of one guided mode on a perfect sheet), the spectra of both scattering operators are successfully compared.
The real domain scattering operator is given by (4):
The modal domain scattering operator is determined from:
The modal domain scattering operator is expressed as the sum of the reflection coefficient of the modes and is given by:
One of the main advantages of the WIP is that it avoids the undesired phenomenon of unbounded operators; relations between currents and fields, obtained using unbounded impedance operators, are transposed to relations between waves, supplied by bounded scattering operators, having a less than unity modulus, the method's convergence being therefore always guaranteed.