Analytical solution for wave propagation through a graded index interface between a right-handed and a left-handed material
Journal article, 2009

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.


graded index


continuous media

analytical solution


Mariana Dalarsson

Philippe Tassin

Chalmers, Applied Physics, Condensed Matter Theory

Optics Express

1094-4087 (ISSN)

Vol. 17 8 6747-6752

Areas of Advance

Nanoscience and Nanotechnology (2010-2017)

Subject Categories

Atom and Molecular Physics and Optics

Other Electrical Engineering, Electronic Engineering, Information Engineering

Condensed Matter Physics



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