Spatial Kramers-Kronig relations and the reflection of waves

Year: 2015

Authors: Horsley SAR., Artoni M., La Rocca GC.

Autors Affiliation: Univ Exeter, Dept Phys & Astron, Exeter, Devon, England;‎ Univ Brescia, Sensor Lab, Dept Engn & Informat Technol, INO CNR, Brescia, Italy;‎ European Lab Nonlinear Spect, Sesto Fiorentino, Italy; Scuola Normale Super Pisa, Pisa, Italy; CNISM, Pisa, Italy

Abstract: When a planar dielectric medium has a permittivity profile that is an analytic function in the upper or lower half of the complex position plane x = x’ + ix ”. then the real and imaginary parts of its permittivity are related by the spatial Kramers-Kronig relations. We find that such a medium will not reflect radiation incident from one side, whatever the angle of incidence. Using the spatial Kramers-Kronig relations, one can derive a real part of a permittivity profile from some given imaginary part (or vice versa) such that the reflection is guaranteed to be zero. This result is valid for both scalar and vector wave theories and may have relevance for designing materials that efficiently absorb radiation or for the creation of a new type of anti-reflection surface.


Volume: 9 (7)      Pages from: 436  to: 439

DOI: 10.1038/NPHOTON.2015.106

Citations: 171
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