Padé approximate solution for wave propagation in graded-index metamaterials

Abstract

A new approximate solution for wave propagation in graded-index media is developed wherebythe exact wave propagation equation is replaced by any one of a sequence of higher-order(m, n) Padé approximant operators. The resulting formulations may be discretized bycommon numerical schemes and solvable by existing numerical techniques. Theaccuracy of this approximate calculation of the wave propagator is demonstratedin comparison with the exact result. We then employ the resulting method toinvestigate wave propagation in metamaterials with graded-index profiles whichchange according to a hyperbolic tangent function along the propagation direction.