A possible approach on optical analogues of gravitational attractors

In this paper we report on the feasibility of light confinement in orbital geodesics on stationary, planar, and centro-symmetric refractive index mappings. Constrained to fabrication and [meta]material limitations, the refractive index, n, has been bounded to the range: 0.8 ≤ n(r⃗) ≤ 3.5. Mappings are obtained through the inverse problem to the light geodesics equations, considering trappings by generalized orbit conditions defined a priori. Our simulation results show that the above mentioned refractive index distributions trap light in an open orbit manifold, both perennial and temporal, in regards to initial conditions. Moreover, due to their characteristics, these mappings could be advantageous to optical computing and telecommunications, for example, providing an on-demand time delay or optical memories. Furthermore, beyond their practical applications to photonics, these mappings set forth an attractive realm to construct a panoply of celestial mechanics analogies and experiments in the laboratory.本文研究了稳态、平面且中心对称的折射率映射（refractive index mappings）中，光被束缚于光测地线（light geodesics）轨道的可行性。受限于制造工艺与[超]材料的性能限制，折射率n的取值范围被限定为0.8 ≤ n(⃗r) ≤ 3.5。我们通过求解光测地线方程的逆问题，并结合先验定义的广义轨道束缚条件，得到了此类折射率映射构型。仿真结果表明，针对初始条件而言，上述折射率分布可将光束缚于开放轨道流形中，且同时存在永久型与暂态型束缚模式。此外，凭借其独特的性能优势，此类折射率映射可应用于光计算与电信领域，例如可实现按需可调的光延时或光学存储器。除此之外，除了在光子学领域的实际应用价值外，此类折射率映射还为在实验室中构建一系列天体力学类比系统与相关实验提供了极具吸引力的研究场景。