Based on rigorous scattering theory we establish a systematic methodology for research of metamaterial-modified current-carrying conductors, from which we mathematically demonstrate the explanation of transformation optics could be extended in metamaterial-modified wireless power transfer system, and based on that we could establish a equivalent model. More important, our demonstration reveals that the equivalent model will still be applicable even when TO could not give a direct explanation, as the requirements of complementary media is not satisfied. And numerical results from our methodology as well as COMSOL verified our findings. The demonstration is not under specific frequency, the conclusion could be extended to a broad range of wavelength, and expected to be applicable for active cloak etc.
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