
Decompose the incident field into TE & TM components of the zeroth
order Floquet modes (denoted by coefficients A001 & A002 respectively) 

Expand the transmitted & reflected fields as an infinite series of
Floquet modes with unknown coefficients 

Match the boundary conditions at the filter, assuming an infinitely
thin, perfectly conducting filter 

Substitute the integral representation of the reflection and
transmission coefficients into the resulting equation to form an integral equation 

Provide faster convergence by expanding the tangential field at the
filter into orthonormal functions that span the aperture space (the set of wave guide
modes) 

Use the orthonormality of the wave guide functions to convert the
integral equation into a matrix equation (Galerkin's moment method) 

Decide where to truncate the infinite matrix equation 

Solve numerically by matrix inversion to determine unknown transmission
and reflection coefficients 

Use the coefficients to find the aperture field distribution 