Open AccessEquivalent configurations of optical transformation media
Author(s) -
Tungyang Chen,
Shen Cheng,
Chung Ning Weng
Publication year - 2009
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.17.021326
Subject(s) - transformation (genetics) , bessel function , fourier transform , equivalence (formal languages) , linear map , transformation optics , mathematical analysis , optics , domain (mathematical analysis) , coordinate system , function (biology) , mathematics , physics , metamaterial , geometry , pure mathematics , biochemistry , chemistry , evolutionary biology , biology , gene
We demonstrate that a medium consisting of two adjoining distinct layers of transformation materials, corresponding respectively to two linear coordinate transformations, can behave effectively as that of the same region transformed by another linear transformation. The equivalence means that, irrespective of the direction of incident wave, the fields of the medium exterior to the transformed regions of the two configurations are exactly the same. This property can also apply to a domain that is transformed by a piecewise linear transformation function, and to a medium that is mapped by a general curved function. This proof is shown analytically based on a rigorous Fourier-Bessel analysis. The equivalence suggests that, for a given transformed domain, one can find an infinite number of complementary media that altogether can give a desired effective response of certain transformation path.