The Goos-Hänchen shift of a normally incident optical beam to a metagrating consisting of magneto-optical material is studied. The metagrating consists of a compound grating of magneto-optical rods atop a dielectric slab, which features staggered lateral shifts of the rods. The compound grating induces zone-folding quasibound states in the continuum at the $\mathrm{\Gamma }$ point with nonzero group velocity, whose $Q$ factor is inversely proportional to the lateral shift. By applying stationary-phase theory, the Goos-Hänchen shift of a normally incident quasiplane wave are found to be enhanced at the reflection peak. The maximum magnitude of the Goos-Hänchen shift within the reflection peak is proportional to the $Q$ factor of the zone-folding quasibound states in the continuum. Simulations of a normally incident Gaussian beam with a finite beamwidth show that the Goos-Hänchen shift is dependent on the beamwidth.

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• Interference & diffraction of light
• Magneto-optics
• Nanophotonics
• Nanostructures