| Summary: | 博士 === 國立成功大學 === 光電科學與工程學系 === 105 === Transformation optics have been widely discussed in the area of advanced metamaterials since it allows spatial coordinate transformations of electromagnetic fields. Ray tracing is a method for the simulation of ray propagation in geometrical optics allowing for calculation of the optical system efficiency. The Hamiltonian equations of motion are based on ordinary differential equations (ODEs) and are used for ray tracing. However, the full solution to ordinary differential equations is may not be easily found because of the complexities of the inhomogeneous and anisotropic indices of the optical device. The failure of ray tracing due to singularity and complex wave vectors at the interface between air and transformed spaces is not well studied. To resolve this deficiency, we provide a 3D reverse ray tracing method for these situations which combines the sweeping method for Hamilton–Jacobi equations and ray trajectory. The sweeping method provides the eikonal function (time map) of the interested domain and back-propagation from the location of interest to the source gives the ray trajectory. Wave vectors, which represent illuminance, are obtained from the gradient of the eikonal function map in the transformed space.
This approach is applicable in any form of transformation optics where the material property tensor is a symmetric positive definite matrix. This method is not dependent on finding solutions to the Hamiltonian motion equations and also avoids the problems of a singularity or complex wave vector arising from the evanescent wave for the initial Hamiltonian motion equation conditions. In this thesis, the idea of transformation optics with function of directivity emitting and polarization rotation as secondary optics are explored. The accuracy of ray trajectories and illuminances are demonstratively solved by the proposed reverse ray tracing method for a number of example instances.
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