What algorithm does GSOLVER use?
GSOLVER solves the full vector Maxwell’s equations for each grating layer. The fields are then matched across each boundary giving the fields in the superstrate and substrate. The diffraction efficiency is then determined for each real propagating order. The first order Maxwell’s equations are written down using a fourier decomposition of the permitivity (and impermitivity) in each layer. The curl equations are used to eliminate the H field giving equations in the E fields. The fourier expansion leads to a set of coupled first order equations. There are 2N+1 equations for each vector component of the E field, where N is the number of orders retained. For TE polarization there is one non-zero vector component. For TM polarization there are two, and for arbitrary polarization there are three. GSOLVER takes the number of non-zero component into account. Thus TE mode is solved much faster than the other polarization cases. The set of coupled equations are solved via standard algebraic eige
