Abstract
We introduce a definition of the electromagnetic chirality of an object and show that it has an upper bound. Reciprocal objects attain the upper bound if and only if they are transparent for all the fields of one polarization handedness (helicity). Additionally, electromagnetic duality symmetry, i.e., helicity preservation upon interaction, turns out to be a necessary condition for reciprocal objects to attain the upper bound. We use these results to provide requirements for the design of such extremal objects. The requirements can be formulated as constraints on the polarizability tensors for dipolar objects or on the material constitutive relations for continuous media. We also outline two applications for objects of maximum electromagnetic chirality: a twofold resonantly enhanced and background-free circular dichroism measurement setup, and angle-independent helicity filtering glasses. Finally, we use the theoretically obtained requirements to guide the design of a specific structure, which we then analyze numerically and discuss its performance with respect to maximal electromagnetic chirality.
Highlights
An object is chiral if it cannot be superimposed onto its mirror image
Quantifying how chiral an object is the purpose of scalar measures of chirality, which vanish only for achiral objects and assign the same value to an object and its mirror image [2,3]
There are many different scalar measures of chirality [3], but none of them allows us to sort general objects according to their chirality or to establish what a maximally chiral object is [4] in an unambiguous way
Summary
An object is chiral if it cannot be superimposed onto its mirror image. This simple definition hides significant problems that arise when attempting to measure chirality [1]. The lack of upper bounds and unambiguous ranking for the magnitude of chirality is a handicap for both theoretical and practical developments It is a handicap for the systematic design of chiral structures for interaction with the electromagnetic field. We show that any maximally electromagnetically chiral and reciprocal object must have electromagnetic duality symmetry; i.e., interaction does not change the helicity of the incident fields. We particularize these results to obtain the constraints that reciprocity plus maximum electromagnetic chirality impose on material constitutive relations, and on the polarizability tensor of an isolated scatterer. The analysis and results contained in this article apply to linear interactions with finite cross sections
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