A Non-paraxial Optical Inverse Problem From A Geometric-optics Point Of View

The inverse problem of geometric optics is an important branch of geometric optics research,which has broad application prospects and background.In this article,we revisit the problem of scattering from a dielectric sphere for light rays and define a form of optical inverse problem in the sense of geometrical optics.Optical inverse problem is complicated in the first place,as it is indirect to pin-down the traversing medium when only the incidence and the exit waves are known to the designer.Transformation optics however provides an elegant way to inversely-design the impedance-matched profile of refraction medium when a curved light trajectory is pre-defined,thanks to the state-of-the-art to manufacture artificial electromagnetic materials.Moreover when the impedance-matching condition is relaxed,the space of possible inhomogeneous media becomes larger to explore by making use of Maxwell’s equations.It is curious to note that the analytic tool set of transformation optics and its derivatives build themselves largely on basis of geometric opticswhich approximates wave optics and reduces the field distribution for electromagnetic waves into the eikonal functions along the trajectories for light rays.We use the same strategy and hope to get some simple conclusions on complex optical inverse problems.In this article,we revisit the problem of scattering from a dielectric sphere for light rays and define a form of optical inverse problem in the sense of geometrical optics.After obtaining the corresponding conclusions,wave optics and ray tracing numerical simulation are applied to verify the correctness of our conclusions,and explain the more complicated caustics obtained during the simulation.