Convergence problems in modal methods for TM polarized fields are often attributed to the inaccuracies in computing the modes of a grating. We report that even in the absence of these inaccuracies convergence problems persist. These arise because of the truncation of the infinite set of linear equations resulting from matching the fields at the grating–substrate and grating–superstrate interfaces with a square matrix. We show that dramatic improvement in convergence can be achieved if the infinite set of linear equations is truncated with a rectangular matrix and by seeking a solution with minimum least squared error.
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