Layer Matrix [S-Matrix]

The layer matrix solver works in the spatial frequency domain (k domain). It consists of

• an eigenmode solver for each homogeneous layer and
• an S-matrix for matching the boundary conditions at all the interfaces.

The eigenmode solver computes the field solution in the k domain for the homogeneous medium in each layer. The S-matrix algorithm calculates the response of the whole layer system by matching the boundary conditions in a recursive manner. It is well-known for its unconditional numerical stability since, unlike the traditional transfer matrix, it avoids the exponentially growing functions in the calculation steps.