Tunable Goos–Hänchen Shift in Symmetric Graphene-Integrated Bragg Gratings

We theoretically analyze the spatial Goos-Hänchen (GH) shifts in symmetric Graphene-Integrated Bragg Gratings (GIBGs), where monolayer graphene arrays act as tunable input/output couplers, and a periodically inserted dielectric layer forms a resonant cavity. By optimizing the cavity design, we achieve a GH shift of 1766λ, surpassing the conventional limit of hundreds of wavelengths under single-parameter tuning. The direction and magnitude can be actively controlled by the graphene's chemical potential, grating geometry, or dielectric thickness. This mechanism may enable high-sensitivity refractive index sensors or adaptive optical devices.