A universal 2D transformation formula for embedded transformation optics is suggested. Linear and nonlinear transformation results using the suggested formula under different conditions reveal several interesting phenomena and potential applications, and designs for various polarization controllers can be achieved based on this idea. For example, an incident Gaussian beam can be transformed into a typical spherical wave, and a “cloak” based on a polarization splitter is proposed for the first time.
Localization of an electromagnetic field can be achieved by transformation optics using metamaterials. A coordinate transformation structure different from traditional resonator is proposed. Wherein, arbitrary frequency of the whole band of electromagnetic wave can be localized without energy loss, i.e., the modes in this structure are continuous. Theoretical analysis and numerical simulation show that the material parameter variations at the outer boundary of the structure have little influence on the localization property. When realizable physical structure is considered, multi-layer approximation should be applied. The calculated results show that the estimated localization time is about 100 ns for an 8-layer inhomogeneous approximation, and it could reach several seconds for a 30-layer homogeneous approximation. The present work may present a new application of transformation optics.