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The polarization-dependent characteristics of an etched diffraction grating demultiplexer are analyzed using the boundary element method. Comparisons are made between an echelle grating coated with a metal and a dielectric grating with retro-reflecting facets. The results indicate that an echelle grating coated with a metal can be approximated as a grating with a perfectly conducting surface. A retro-reflecting-facet grating based on a high index material has a lower polarization dependent loss (PDL), while the other performances are similar to an echelle grating coated with a metal. It is also shown that by titling the shaded facets appropriately the overall PDL performance can be improved when the total number of used channels is not too large. The influence of the surface roughness of the shaded facets on the PDL of the device is also investigated for all wavelength channels.