Open AccessActive manipulation of exterior electromagnetic fields by using surface sources
Author(s) -
Daniel Onofrei,
Eric Platt,
Neil Jerome A. Egarguin
Publication year - 2020
Publication title -
quarterly of applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.603
H-Index - 41
eISSN - 1552-4485
pISSN - 0033-569X
DOI - 10.1090/qam/1567
Subject(s) - electromagnetic field , scalar (mathematics) , bounded function , surface (topology) , computation , representation (politics) , constructive , integral equation , scalar potential , magnetic field , physics , mathematics , classical mechanics , computer science , mathematical analysis , geometry , algorithm , quantum mechanics , process (computing) , politics , political science , law , operating system
In this paper, we establish a scheme for the active manipulation of electromagnetic fields in prescribed exterior regions using a surface source. We prove the existence of the necessary surface current (electric or magnetic) on a single source to approximate prescribed electromagnetic fields on given regions of space (bounded or possibly the far field). We provide two constructive schemes for the computation of the required surface currents: our first strategy makes use of the Debye representation results for the electromagnetic field and builds up on previous control results for scalar fields discussed in [J. Integral Equations Appl. 26 (2014), pp. 553–579]; the second strategy we propose makes use of integral electromagnetic representation results and follows theoretically from the first. We provide theoretical validation for both computational schemes and present supporting numerical simulations for the first strategy in several applied scenarios.