An Extremal Problem Related to Negative Refraction Kristian Seip and Johannes Skaar
نویسنده
چکیده
We solve an extremal problem that arises in the study of the refractive indices of passive metamaterials. The problem concerns Hermitian functions in H of the upper half-plane, i.e., H functions satisfying f(−x) = f(x). An additional requirement is that the imaginary part of f be nonnegative for nonnegative arguments. We parameterize the class of such functions whose real part is constant on an interval, and solve the problem of minimizing the imaginary part on the interval on which the function’s real part takes a given constant value.
منابع مشابه
Bounds for the refractive indices of metamaterials
The set of realizable refractive indices as a function of frequency is considered. For passive media we give bounds for the refractive index variation in a finite bandwidth. Special attention is given to the loss and index variation in the case of left-handed materials.
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