Perturbation on the perfect lens: the near-perfect lens

We present the full wave solution for a dipole source above a slab of left-handed medium of refractive index n = - 1, but with epsilon and mu differing from those ideal values that create the perfect lens through taking epsilon = -(1 + delta)(-1) and mu = -(1 + delta), where delta, and hence epsilon and mu, are real. Any modifications in resolution are therefore not due to loss effects within the lens. Finite solutions for the form of the fields throughout all space are obtained using the method of Hertz potentials, thereby regularizing the singular perfect lens solution. This regularization will facilitate subsequent perturbation analyses. Using an appropriately defined criterion, we examine the sensitivity of the lens resolution to the material imperfection delta. It is found that the resolution converges logarithmically with delta upon that of the perfect lens. Comparison of theoretical results with experimental data suggests that even this slow convergence is the best that can be achieved.