Active manipulation of exterior electromagnetic fields by using surface sources
Authors:
Daniel Onofrei, Eric Platt and Neil Jerome A. Egarguin
Journal:
Quart. Appl. Math. 78 (2020), 641-670
MSC (2010):
Primary 35Q60, 45Q05
DOI:
https://doi.org/10.1090/qam/1567
Published electronically:
January 22, 2020
MathSciNet review:
4148822
Full-text PDF
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Additional Information
Abstract: 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.
References
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References
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- Neil Jerome A. Egarguin, Daniel Onofrei, and Eric Platt, Sensitivity analysis for the active manipulation of helmholtz fields in 3d, Inverse Problems in Science and Engineering (2018).
- Eng Swee Siah, M. Sasena, J. L. Volakis, P. Y. Papalambros, and R. W. Wiese, Fast parameter optimization of large-scale electromagnetic objects using direct with kriging metamodeling, IEEE Transactions on Microwave Theory and Techniques 52 (2004), no. 1, 276–285.
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- Edwin A. Marengo, Anthony J. Devaney, and Fred K. Gruber, Inverse source problem with reactive power constraint, IEEE Trans. Antennas and Propagation 52 (2004), no. 6, 1586–1595. MR 2071404, DOI https://doi.org/10.1109/TAP.2004.829408
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- Andrew N. Norris, Feruza A. Amirkulova, and William J. Parnell, Source amplitudes for active exterior cloaking, Inverse Problems 28 (2012), no. 10, 105002, 20. MR 2974016, DOI https://doi.org/10.1088/0266-5611/28/10/105002
- Michael O’Neil, A generalized Debye source approach to electromagnetic scattering in layered media, J. Math. Phys. 55 (2014), no. 1, 012901, 16. MR 3390430, DOI https://doi.org/10.1063/1.4862747
- Daniel Onofrei, Active manipulation of fields modeled by the Helmholtz equation, J. Integral Equations Appl. 26 (2014), no. 4, 553–579. MR 3299831, DOI https://doi.org/10.1216/JIE-2014-26-4-553
- D. Onofrei and E. Platt, On the synthesis of acoustic sources with controllable near fields, Wave Motion 77 (2018), 12–27. MR 3754438, DOI https://doi.org/10.1016/j.wavemoti.2017.10.004
- J. B. Pendry, D. Schurig, and D. R. Smith, Controlling electromagnetic fields, Science 312 (2006), no. 5781, 1780–1782. MR 2237570, DOI https://doi.org/10.1126/science.1125907
- Vicente Romero-Garcia and Anne-Christine Hladky-Hennion, Fundamentals and applications of acoustic metamaterials: From seismic to radio frequency, Wiley-Interscience, 2019.
- E. G. Peter Rowe, Decomposition of vector fields by scalar potentials, J. Phys. A 12 (1979), no. 1, 145–150. MR 518538
- S. S. Krigman, Exact boundary controllability of Maxwell’s equations with weak conductivity in the heterogeneous medium inside a general domain, Discrete Contin. Dyn. Syst. Dynamical systems and differential equations. Proceedings of the 6th AIMS International Conference, suppl. (2007), 590–601. MR 2409895
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Additional Information
Daniel Onofrei
Affiliation:
Department of Mathematics, University of Houston, Houston, Texas 77004
MR Author ID:
753389
Email:
onofrei@math.uh.edu
Eric Platt
Affiliation:
Department of Mathematics, University of Houston, Houston, Texas 77004
Email:
eplatt314@gmail.com
Neil Jerome A. Egarguin
Affiliation:
Institute of Mathematical Sciences and Physics, University of the Philippines Los Baños, College, Laguna, Philippines; and Department of Mathematics, University of Houston, Houston, Texas 77004
Email:
naegarguin1@up.edu.ph
Keywords:
Control of EM waves,
Maxwell’s equations,
Debye potentials,
integral equations in inverse problems,
near and far field synthesis,
Tikhonov regularization
Received by editor(s):
October 22, 2019
Received by editor(s) in revised form:
November 25, 2019
Published electronically:
January 22, 2020
Additional Notes:
The authors would like to acknowledge the Army Research Office for funding this work under the award W911NF- 17-1-0478.
Article copyright:
© Copyright 2020
Brown University