Curved spacetime-induced control of photonic modes via spatially dependent band structure
Conventionally, controlling photonic modes require complex artificial structures made of electromagnetic media such as photonic crystal, metamaterial, and waveguide systems. Here, we report a new mechanism for mode control induced solely by curved spacetime, which give rise to a spatially dependent photonic band structure. In this framework, the photonic mode can naturally undergo conversion in the spatial domain. We select two canonical models from general relativity--the Rindler spacetime and the Einstein-Rosen bridge (ERB)--to demonstrate light propagation effects. In Rindler spacetime, a light beam transitions to a diffusive mode for positive acceleration and to a highly collimated propagating mode for negative acceleration. In the ERB, beam transmission is governed by the Schwarzschild radius, which determines the extend of the spatial bandgap. Furthermore, an intriguing tunneling effect is also illustrated. Finally, we propose several feasible experimental methods to verify our theoretical predictions. Our findings elucidate a distinctive formation mechanism of photonic band structure in curved spacetime, enabling precise spatial control of light and the design of photonic devices within a non-Euclidean geometrical framework.