We report analytical calculations for the propagation of electromagnetic radiation through an inhomogeneous layer whose refractive index varies in one dimension situated between bulk right-and left-handed media. Significant field localization is generated in the layer that is caused by the coherent superposition of evanescent waves. The strength of the field localization and the transmission properties of the layer are investigated as a function of the layer width, losses and defects in the refractive index; the former two being modelled by continuous changes, and the latter by discontinuous changes, in the index profile.

In manufacturing left-handed media the interfaces will never be perfect; defects and other disturbances to interfaces and material parameters are unavoidable. We report an analytical calculation of electromagnetic wave propagation through a perfect lens with diffuse boundaries. Field localizations are generated in the boundary layers, and the lens' ability to recover evanescent modes in the presence of these boundaries is analyzed and quantified. It is shown that such a diffuse layer produces an effect that is qualitatively similar to a lens with increased losses.

A relationship is established between the autocorrelation function of continuous Gaussian and non-Gaussian stochastic processes and the discrete process that describes their zero or level crossings. Random fractals occur when the distribution for the number of crossings is described by a class of Markov processes whose singlefold statistics are the discrete analog of the Lévy-stable continuous probability densities.

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A slab of left-handed material (LHM) with refractive index -1 forms a perfect lens that retains subwavelength information about a source or object. Such lenses are highly susceptible to perturbations affecting their performance. It is shown that illuminating a roughened interface between air and an LHM produces a regime for enhanced focusing of light close to the boundary. This generates caustics that are brighter, fluctuate more, and cause Gaussian speckle at distances closer to the interface than in right-handed matter. These effects present fresh challenges for perfecting the perfect lens.