6.4 Vertical Discretization of the Maxwell Equations

In the preceding two sections we have transformed the PDEs of the Maxwell equations into a complex-valued, linear, first-order ODE system for the lateral Fourier coefficients of the EM field and have established BCs at the starting and ending points of the simulation interval. In this section we will describe how this two-point BVP is solved numerically. We will first briefly recapitulate the main results whereby the multiple BCs resulting from the source discretization procedure will be emphasized. Then a survey of available numerical techniques for the solution of two-point BVPs is given. However, the main content of this section is a detailed description of the implemented numerical algorithm.