Is the coupled-wave algorithm approach numerically unstable for deep gratings?
Only if it (like any other algorithm approach) is poorly implemented. This claim has appeared at various times in the literature, but is unfounded as it describes a particular implementation. The Coupled-Wave algorithm is based on firmly established algebraic techniques for solving a set of coupled differential equations. The problem probably arrises from implementers that fail to calculate normalized eigenvalues (since exponential functions of some eigenvalue times layer depth are formed). In GSOLVER, it is a simple matter to look at say a binary grating in metal and run the calculation over depth. Using a 1 micron period, Aluminum substrate, the calculation coverges nicely for both TE and TM for depths greater that 106 microns (a meter deep!) though this type of grating behaves the same as an infinite depth grating for depths as ‘shallow’ as 500 microns.
