A Study into the Possibility of Field Focusing Using 'Left-Handed' Materials

摘要

The problem of focusing fluxes of electromagnetic field energy in the presence of structures of "left-handed" matter (LHM) assumed a special importance in the light of recent idea of Prof. J.B. Pendry [1] that a parallel-sided slab of LHM under certain conditions (ε = μ = -1) may serve as a "superlens" with unique focusing properties, whose resolution is not restricted by the well-known diffraction limit. The phenomenon is expected to exist owing to amplification of evanescent modes in an LHM-slab, which exponentially decay in ordinary media. Papers with argumented objections were published (in particular, [2, 3]); however, some researchers did not recognize these objections as being exhaustive and convincing and, for all we know, this scientific discussion is far from being finished. In order to solve the problem of the quality limit of focusing of the image of a point source utilizing the realistic finite-width dissipative LHM-slab, we used numerical methods to investigate the spatial distribution of components of electromagnetic field and its major characteristics (in particular, the Poynting vector) under conditions of excitation of a slab by one and two filamentary sources spaced some small distance apart. The solution was obtained by the method of volume integral equations using the Green's function of free space, with the slab parameters ε = μ ≈ -1 included in the expressions for polarization currents. This solution (as distinct, for example, from eigenfunction expansions or surface integral equations) does not at all involve the concept of the propagation coefficient of an LHM-filled space and is not associated with the use of other multiple valued functions whose arguments would include (possibly negative) permittivity and permeability. Moreover, the polarization currents singled out in the Maxwell equations may be identified with actually existing currents in the inclusions of the composite whose model is provided by LHM. Therefore, the method of volume integral equations offers a good tool for checking assumptions and testing solutions obtained by other methods.