Fast solution of near-field time reversal electromagnetic field of sub-wavelength perfect conducting ball arrays

Abstract

To solve the near-field time reversal electromagnetic fields of sub-wavelength perfect conducting ball arrays rapidly, an analytical formulation is presented based on the equivalent dipole model. As is well known, the efficient use of evanescent information is the key to the realization of sub-wavelength focusing and imaging. However, evanescent components always suffer exponential decays with the increase of propagating distance. Therefore, in order to effectively control the evanescent waves, some measures should be taken in the near field region of the scatters before their amplitudes are reduced to an undetectable level. Since small perfect conducting ball is the basic component of large scatter, the first step should be to study the scattering properties of small perfect conducting ball. The far-field scattering fields of perfect conducting balls have been analyzed for plane waves. However, for spherical waves, the analytical results are not convenient to extend to multi-ball situation since they are all expressed by series. In this paper, the analytical solution to scattering field of the small perfect conducting balls irradiated by spherical radiative waves is analyzed. The result shows that the scattering fields can be approximately equivalent to the superposition of the radiation fields of electrical and magnetic dipoles in some restrictive conditions. The intensity of the equivalent dipole is proportional to the magnitude of the original excitation source dipole. Therefore all the equivalent dipole moments can be calculated easily by setting up the coupling equations between different equivalent dipoles and source dipole. Then, the forward dyadic Green's function can be obtained by combining the vacuum electrical and magnetic Green's function. At the same time, the time reversal dyadic Green's function can be derived through the time reversal cavity theory. Afterwards, the near-field time reversal electromagnetic field of the perfect conductive ball arrays can be calculated directly by the time reversal dyadic Green's function. The results obtained from the proposed method and a numerical software are compared, which shows that a coincidence extent reaches more than 0.95. This confirms the correctness and high efficiency of the proposed method. After that, an imaging experiment is implemented and the result shows that an imaging resolution of 0.3 can be obtained by loading small conducting balls in the near field. All these experiments show that combined with near-field loading of sub-wavelength scatterer arrays, the time reversal technique has the potential to realize super-resolution focusing and imaging.