Effects of numerical dispersion on the accuracy of FDTD modeling of propagating and evanescent waves in negative index media

Discrete space-time methods, primarily FDTD, have played a major role in illuminating the underlying physics of unconventional phenomena (negative refraction, growing evanescent waves and super-lensing) in negative index media. Yet, a survey of the relevant FDTD literature indicates a number of contradictory results, which stem from inherent limitations of the method. This paper is focused on the impact of numerical dispersion on the FDTD study of the ldquoperfect lensrdquo. It is shown that the calculated resolution of such a lens is primarily related to the FDTD cell size rather than the medium itself, due to the sensitivity of the numerical attenuation constant of evanescent waves. While the introduction of material losses improves the convergence of such simulations, it deteriorates their accuracy. Specific conditions are stated for achieving certain accuracy levels with standard FDTD and high-order finite differences.