Kerker Transform: Expanding Fields in a Discrete Basis of Directional Harmonics

Kavli Affiliate: Harry A. Atwater

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| Summary:

We present a linear coordinate transform to expand the solution of scattering
and emission problems into a basis of forward and backward directional vector
harmonics. The transform provides intuitive algebraic and geometric
interpretations of systems with directional scattering/emission across a broad
range of wavelength-to-size ratios. The Kerker, generalized Kerker, and
transverse Kerker effect as well as other forms of highly directional
scattering/emission are easily understood through open and closed loop contours
in the complex plane. Furthermore, the theoretical maximum directivity of any
scattering/emissive system is easily defined. The transformed far field
harmonics have coordinates that are polar-angle invariant, interference between
forward and backward harmonics weakly interact, and interference of same type
harmonics alters directivity. Examples of highly directional scattering are
presented including a Kerker scattering magnetic sphere, a directional
scattering photonic nanojet, both under plane wave illumination, as well as
generalized backward Kerker and transverse Kerker emission from sub-wavelength
spheres that are near-field coupled to emitters. Solutions of
scattering/emission under the Kerker transform are contrasted to the
traditional Mie expansion for comparison.

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