  We have investigated the transmission and reflection properties of structures
incorporating left-handed materials with graded index of refraction. We present
an exact analytical solution to Helmholtz' equation for a graded index profile
changing according to a hyperbolic tangent function along the propagation
direction. We derive expressions for the field intensity along the graded index
structure, and we show excellent agreement between the analytical solution and
the corresponding results obtained by accurate numerical simulations. Our model
straightforwardly allows for arbitrary spectral dispersion.
