Set of modes for the description of wave propagation through slabs with a transverse variation of the refractive index.

The scattering of electromagnetic waves by a slab whose refractive index is changing along its boundary planes is exactly calculated in a closed analytical form. The key feature of the calculation is the introduction of a new set of modes. As a specific example, we calculate the reflected and transmitted fields generated by the interaction of an incoming plane wave with an N-layered medium, the layers of which are perpendicular to the boundary planes of a slab.