Abstract
Transformation optics is a mathematical method that is based on the geometric interpretation of Maxwell’s equations. This technique enables a direct link between a desired electromagnetic (EM) phenomenon and the material response required for its occurrence, providing a powerful and intuitive design tool for the control of EM fields on all length scales. With the unprecedented design flexibility offered by transformation optics (TO), researchers have demonstrated a host of interesting devices, such as invisibility cloaks, field concentrators, and optical illusion devices. Recently, the applications of TO have been extended to the subwavelength scale to study surface plasmon-assisted phenomena, where a general strategy has been suggested to design and study analytically various plasmonic devices and investigate the associated phenomena, such as nonlocal effects, Casimir interactions, and compact dimensions. We review the basic concept of TO and its advances from macroscopic to the nanoscale regimes.
Highlights
Transformation optics (TO) is an emerging technique for the design of advanced electromagnetic (EM) media
The theory of TO shows that the surface plasmon modes supported by the transformed geometry are characterized by three wave vectors despite the 2-D nature of the metasurface.[113,114]
The modes propagating along the vertical direction have two characteristic wave vectors [see Fig. 14(c)], i.e., the Bloch wave vector kBloch, which characterizes the energy flow between neighboring unit cells, and the hidden wave vector kHidden, which characterizes how the surface plasmons propagate toward the singular points
Summary
Transformation optics (TO) is an emerging technique for the design of advanced electromagnetic (EM) media. It is based on the concept that Maxwell’s equations can be written in a form-invariant manner under coordinate transformations, such that only the permittivity and permeability tensors are modified.[1,2,3] With the coordinate transformation applied to the constitutive parameters, EM waves in one coordinate system can be described as if propagating in a different one. The geometric interpretation of Maxwell’s equations utilized in the TO approach provides a powerful and intuitive design tool for the manipulation of EM fields on all length scales. The form invariance of Maxwell’s equations has been exploited as a computational tool to simplify numerical electrodynamic simulations. In 1996, a transformation from Cartesian to cylindrical coordinates was applied to solve for the modes of an optical fiber with circular cross section.[1] This transformation allowed for efficiently solving a cylindrical geometry using a finite-difference computer code implemented
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