Electromagnetic Time Reversal Algorithms and Source Localization in Lossy Dielectric Media

Abstract

The problem of reconstructing the spatial support of an extended radiating electric current source density in a lossy dielectric medium from transient boundary measurements of the electric fields is studied. A time reversal algorithm is proposed to localize a source density from loss-less wave-field measurements. Further, in order to recover source densities in a lossy medium, we first build attenuation operators thereby relating loss-less waves with lossy ones. Then based on asymptotic expansions of attenuation operators with respect to attenuation parameter, we propose two time reversal strategies for localization. The losses in electromagnetic wave propagation are incorporated using the Debye's complex permittivity, which is well-adopted for low frequencies (radio and microwave) associated with polarization in dielectrics.

Super-resolution in recovering embedded electromagnetic sources in high contrast media

“…Its principle is to exploit the reciprocity of wave propagation. Intuitively, we retrace the path of the wave observed in the far field backwards in chronology to find the location of its generating source [37,36,19,20]. For a far-field imaging system using the timereversal method, we know from the Helmholtz-Kirchhoff integral that its resolution is limited by the imaginary part of the Green's function of the wave equations associated with the background medium [12,13].…”

Numerical simulation study on bowtie antenna-based time reversal mirror for super-resolution target detection

“…The TR technique was postulated on the reciprocity property of the wave equation and is analogous to phase conjugation in optics. G. Lerosey et al [11,20] proposed an approach of overcoming the diffraction limit with a narrow band TR focusing using some vertical wire array with element spacing of λ/30 for far-field time reversal. This has stimulated lots of interest in subwavelength imaging and target localization applications including this contribution [21,22].…”

“…scatterers on the radiators and substrate for superresolution focusing with far-field time reversal incorporating with wire metamaterials medium is proposed here as TRM. It is found that majority of the reported subwavelength arrays such as [16][17][18][19][20][21][22]27] were all wide-band to ultra-wide-band antenna designs to the best of our knowledge. In this work, a dual-band bowtie antenna [26] referred as the basic structure is first considered.…”

Stability and Resolution Analysis of Topological Derivative Based Localization of Small Electromagnetic Inclusions

“…The potential applications envisioned by the imaging of electromagnetic inclusions of diminishing size can be found in non-destructive testing of small material impurities, medical diagnosis and therapeutic protocols, especially for detecting and curing cancers of vanishing size and for brain imaging. It is worthwhile precising that the problem of detecting small electromagnetic inclusions has been previously studied by using MUSIC-type algorithms [6], time reversal and phase conjugation techniques [36][37][38], reverse time migration [19], topological derivative based imaging [30], and asymptotic expansion techniques [8,9]. For the imaging of thin electromagnetic inclusions and cracks in a two dimensional setting, we refer the reader to [33,34] for instance.…”