We present a detailed electromagnetic analysis for the radiation of an electric source located inside grating structures. Our analysis is based on the differential method and uses the scattering-matrix algorithm. We show that gratings that exhibit periodic modulations along two spatial directions (crossed gratings) enable one to couple out the totality of the light emitted by the source into the guided modes of the structure. This property is investigated through the computation of the far-field radiation patterns for crossed gratings with various etching depths. One key result is the possibility to confine the emitted light in a direction about the sample normal, a property that is of interest in the context of spontaneous emission control by microcavity structures.
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