Electromagnetic scattering from thin tubular objects and an application in electromagnetic chirality

Asymptotic perturbation formulas characterize the effective behavior of waves as the volume of the scattering object tends to zero.
In this work, wave propagation is described by time-harmonic Maxwell's equations in free space and the corresponding scattering objects are thin tubular objects that feature a different electric permittivity and a different magnetic permeability than their surrounding medium.
For this setting, we derive an asymptotic representation of the scattered electric field away from the thin tubular object and use the corresponding leading order term in a shape identification problem and for designing highly electromagnetically chiral objects.
In inverse problems, the leading order term may be used to find the center curve of a thin wire that is supposed to emit a scattered field, which is reasonably close to a given measured field.
For the optimal design of electromagnetically chiral structures,
the representation formula provides an explicit formula for the leading order term of an asymptotic far field operator expansion.
A chirality measure, usually requiring the far field operator, will now map aforementioned leading order term to a value between $0$ and $1$ dependent on the level of electromagnetic chirality of the thin tubular scatterer.
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This approximation greatly simplifies the challenge to maximize the chirality measure with respect to thin tubular objects.
The fact that neither the evaluation of the leading order term nor the calculation of corresponding derivatives require a Maxwell system to be solved implies that the shape optimization scheme is highly efficient compared to shape optimization algorithms that use e.g. domain derivatives.
In the visible range, the metallic nanowires obtained by our optimization scheme
attain high values of electromagnetic chirality and even exceed those attained by traditional metallic helices.