Rigorous analysis of axisymmetric transformation optics lenses embedded in layered media illuminated by obliquely incident plane waves

Abstract

ABSTRACTA body of revolution, finite‐difference time‐domain (BOR‐FDTD) method is developed for rigorous analysis of axisymmetric transformation optics (TO) lens devices. For normal incidence, a one dimensional (1‐D) FDTD method based on the total‐field scattered‐field (TFSF) technique was proposed to model the propagation of a plane wave launched from the top of a layered medium in cylindrical coordinates. The 1‐D FDTD solutions were employed to efficiently inject normally incident plane waves into the BOR‐FDTD method. For oblique incidence, analytical formulations were derived and presented by expanding the plane wave into a series of cylindrical modes via Fourier series expansion of the ϕ‐dependent variables, which were then used to introduce obliquely incident plane waves into the TFSF formulas associated with the BOR‐FDTD method. These procedures allowed for accurate simulations of BOR TO lenses embedded in layered media illuminated by obliquely incident waves. The accuracy and efficiency of the proposed method were verified by comparing numerical results with either analytical solutions or a commercial software (COMSOL) package. Thereafter, the developed BOR‐FDTD code was utilized to study the imaging properties of (a) radial gradient‐index (GRIN) lenses with a parabolic index profile, (b) a flat TO GRIN lens, (c) a spherical Luneburg lens, and (d) a cylindrical TO Luneburg lens both in free space and on top of a substrate. Here the TO GRIN lenses were designed by using the quasi‐conformal transformation optics (QCTO) technique. It was found that the flat TO lens was able to provide identical focusing properties as a cemented doublet in both free space and over a dielectric substrate. Moreover, the numerical results demonstrated that the flattened TO Luneburg lens possessed the desired imaging properties under different illuminations for both polarizations.