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

Padé approximate solution for wave propagation in graded-index metamaterials