基于光在厚度变化曲面传播有效理论的引力红移光学模拟方法

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【Abstract】This study is based on the system of Maxwel's equations in curved space and uses the thin-shellmethod to derivetheefectivescalaropticalequations withinsurfacesofnon-uniformthickness.Theresearchfindsthattheeffective potentialenergy generated by thickness variations is independent ofcurvature and dominates ight propagation compared tothegeometricpotentialinducedbycurvature.Thisthickness-dependent effectivepotential exhibitsmode-wavenumber sensitivity，enabling even minor thickness variations to significantly alter light propagation characteristics.A paraxial wave equation is furtherdeveloped forlight propagation onrevolution surfaces with non-uniform thickness，facilitating efcientcomputationofaxial intensitydistributions.Basedontheseefectiveequations，weproposeascheme to simulate the gravitationalredshift efect neara black hole using thickness variations on curved waveguides.This scheme simulates the spacetimedimensionsofablackholethrough variationsinthesurfaceandthicknes，achieving spatial broadeningand redshift effects for light.Toobservemacroscopicredshift，wesuggestusing light with similar wavelengths to generate beat frequencies. Computationalresults indicate that this schemecan successullysimulate gravitationalredshift， matching theoretical predictions.The studycan alsoprovidetheoretical guidance for thedesignofcurved waveguides with nonuniform thickness in application fields.

【Key words】 varying thickness; curved surface waveguide; gravitational redshift; blackhole

[中图分类号]043 [文献标识码]A

[文章编号]1674-3229（2025）03-0063-08

0 引言

作为宇宙中最具挑战性的天体物理研究对象之一，黑洞的极端时空特性始终是理论物理学的前沿课题。（剩余11527字）