Earlier　researchers　have　designed　nanostructures　such　as　stripe　gratings　(SG)　or　photonic　crystals　array　(PhCA)　to　improve　the　light　extraction　efficiency　(LEE)　of　light-emitting　diodes　(LEDs)　by　the　diffraction　mechanism.　However,　through　k-domain　method　and　simulation　analysis,　this　paper　finds　that　although　SG　perform　well　in　2D　simulation,　their　effect　drops　sharply　in　3D　space,　a　phenomenon　being　overlooked　in　the　community.　This　paper　explains　the　diffraction　mechanism　of　LEDs　with　nanostructure　in　2D　and　3D　space　through　K-domain　analysis,　and　reveals　the　inaccuracy　of　simulating　LED　with　SG　in　2D　space.　Unlike　SG,　PhCA　offers　diffraction　in　two　directions　and　may　be　more　suitable　for　LEDs.　IEEE