Spatial Kramers–Kronig relations and the reflection of waves
نویسندگان
چکیده
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 won’t 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 either efficiently absorb radiation, or for the creation of a new type of anti-reflection surface. PACS numbers: 03.50.De ∗Electronic address: [email protected]
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