Electromagnetic Time Reversal Algorithms and Source Localization in Lossy Dielectric Media |
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Authors: | Abdul Wahab Amer Rasheed Tasawar Hayat Rab Nawaz |
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Institution: | 1. Department of Mathematics, COMSATS Institute of Information Technology, 47040, Wah Cantt., Pakistan;
2. Department of Mathematics, Quaid-i-Azam University, 45320, Islamabad, Pakistan;
3. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia |
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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. |
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Keywords: | time reversal electromagnetic waves inverse source problem Debye's law attenuation operators |
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