Fields and Poynting vector in and near the focal plane of a slab with index of refraction close to -1 for a line source

The paper presents numerical integral calculations of the exact 2D fields, transmitted through a planar slab due to a magnetic current line source on the opposite side. This source gives a delta function in the electric field component in the plane of the source. We consider cases where relative permittivity, ε_τ, and relative permeability, μ_r, are both close to -1, but further where the real part of the index of refraction, n, is very close or equal to -1. Results for a (real) electric current line source may be obtained by interchanging ε_r and μ_r. We show that focusing in the transverse direction is very different from the focusing in the propagation direction. The transverse width of the focal spot depends on ε_τ, μ_r and slab thickness and is subwavelength in size for these cases. However, the width in the propagation direction is most strongly dependent on the slab thickness and is not subwavelength. Quiver plots of the Poynting vector illustrate an energy flow that generally looks like what would be expected for a real focus when slab thickness is greater than a few wavelengths. For thin slabs, the transmitted intensity falls off monotonically with distance from the slab in the axis plane.