IN-PERSON MATHEMATICAL PHYSICS SEMINAR
RUTGERS UNIVERSITY
HILL 705
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Michael Vogelius – Rutgers University
Date/Time/Location
Thursday, January 30th, 2025, 12:10 pm; Hill Center 705
Passive Cloaking and Non-scattering
In this talk I shall discuss some theoretical results concerning invisibility, non-scattering and, time permitting, (lack of) second harmonic generation. The results are in frequency domain and are formulated in the context of the Helmholtz equation. The word passive refers to the fact that the invisibility results from changes in material parameters, not the use of any active sources. In this context a fundamental technique is the so-called cloaking by mapping technique". The results pertaining to non-scattering are based on regularity results for an associated free boundary problem, and a consequence of these is the assertion that singularities almost always scatter". Second harmonic generation refers to a technique, that employs a non-linear material in order to produce a scattered signal, which also contains a component at twice the frequency of that present in the incident monochromatic wave. Time permitting, I will describe some recent work, which potentially indicates that this process may encounter di_culties at low frequencies, due to a non-scattering phenomenon.