Reverse ray tracing for transformation optics

Abstract

Ray tracing is an important technique for predicting optical system performance. In the field of transformation optics, the Hamiltonian equations of motion for ray tracing are well known. The numerical solutions to the Hamiltonian equations of motion are affected by the complexities of the inhomogeneous and anisotropic indices of the optical device. Based on our knowledge, no previous work has been conducted on ray tracing for transformation optics with extreme inhomogeneity and anisotropicity. In this study, we present the use of 3D reverse ray tracing in transformation optics. The reverse ray tracing is derived from Fermat's principle based on a sweeping method instead of finding the full solution to ordinary differential equations. The sweeping method is employed to obtain the eikonal function. The wave vectors are then obtained from the gradient of that eikonal function map in the transformed space to acquire the illuminance. Because only the rays in the points of interest have to be traced, the reverse ray tracing provides an efficient approach to investigate the illuminance of a system. This approach is useful in any form of transformation optics where the material property tensor is a symmetric positive definite matrix. The performance and analysis of three transformation optics with inhomogeneous and anisotropic indices are explored. The ray trajectories and illuminances in these demonstration cases are successfully solved by the proposed reverse ray tracing method.

Asymptotics of near-cloaking

“…As explained in Ref. [14], the unrealistic values of ρ and λ in ( 12), (7) as r ↓ a need not arise for cloaks such as 'pentamaterials' that have more general anisotropy. In this paper, we will avoid infinite parameter values by regularising the model so that the target is expanded from r = a to r = a (1 + ), where 0 < 1.…”

“…Ray theory has been applied to the numerical solution of cloaking models by several authors (Gao et al [5], Tanaka et al, [21], Crosskey et al [2] and Hu et al [7], for example). Here, we will use the method to obtain explicit asymptotic solutions for large K. 3…”

Transformation Optics: From Classic Theory and Applications to its New Branches

“…In addition to the above aspects, TO has many other applications, such as calculating the optical force, designing gratings, designing spontaneous emissions, reverse ray tracings, designing perfect matched layers in numerical simulations, etc. In recent years, more and more new branches are emerging from TO, such as TO with graphene, TO with photonic crystals, TO with meta‐surfaces, TO with Fourier optics, TO for lossy media by complex coordinate transformations, etc.…”

“…[192][193][194] The same idea has also been applied to other kinds of lenses, such as Maxwell's fisheye lenses. [230] In addition to the above aspects, TO has many other applications, such as calculating the optical force, [231] designing gratings, [232][233][234] designing spontaneous emissions, [235] reverse ray tracings, [236] designing perfect matched layers in numerical simulations, [237] etc. In recent years, more and more new We set a line current with unit amplitude in free space without the rotator.…”