Vol. 8

Latest Volume
All Volumes
All Issues

A Uapo-Based Solution for the Scattering by a Lossless Double-Negative Metamaterial Slab

By Gianluca Gennarelli and Giovanni Riccio
Progress In Electromagnetics Research M, Vol. 8, 207-220, 2009


A closed form solution is here proposed for evaluating the field diffracted by the edge of a lossless, isotropic and homogeneous double-negative metamaterial slab when illuminated by a plane wave at skew incidence. It is obtained by considering a Physical Optics approximation of the electric and magnetic equivalent surface currents in the radiation integral and by performing a uniform asymptotic evaluation of this last. The final expression is given in terms of the Geometrical Optics response of the structure and the standard transition function of the Uniform Geometrical Theory of Diffraction, so that it results easy to handle and simple to implement in a computer code. As demonstrated by numerical tests, it allows one to compensate the discontinuities of the Geometrical Optics field at the reflection and incidence shadow boundaries. Moreover, the accuracy of the solution is well assessed by means of comparisons with a commercial tool based on Finite Element Method.


Gianluca Gennarelli and Giovanni Riccio, "A Uapo-Based Solution for the Scattering by a Lossless Double-Negative Metamaterial Slab," Progress In Electromagnetics Research M, Vol. 8, 207-220, 2009.


    1. Engheta, N. and R. W. Ziolkowski, "A positive future for double-negative metamaterials," IEEE Trans. Microw. Theory Tech., Vol. 53, No. 4, 1535-1556, 2005.

    2. Engheta, N. and R. W. Ziolkowski, Metamaterials: Physics and Engineering Explorations, Wiley-InterScience, 2006.

    3. Caloz, C. and T. Itoh, Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications, Wiley-InterScience, Hoboken, 2006.

    4. Ziolkowski, R. W. and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E, Vol. 64, 056625:1-15, 2001.

    5. Caloz, C., C. C. Chang, and T. Itoh, "Full-wave verification of the fundamental properties of left-handed materials (LHMs) in waveguide configurations," J. App. Phys., Vol. 90, No. 11, 5483-5486, 2001.

    6. Moss, C. D., T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, "Numerical studies of left handed metamaterials," Progress In Electromagnetics Research, Vol. 35, 315-334, 2002.

    7. Ziolkowski, R. W., "Pulsed and CW Gaussian beam interactions with double negative metamaterial slabs," Optics Express, Vol. 11, No. 7, 662-681, 2003.

    8. So, P. P. M., H. Du, and W. J. R. Hoefer, "Modeling of metamaterials with negative refractive index using 2D-shunt and 3D-SCN TLM networks," IEEE Trans. Microwave Theory Tech., Vol. 53, No. 4, 1496-1505, 2005.

    9. Shi, Y. and C.-H. Liang, "Analysis of the double-negative mateials using multi-domain pseudospectral time-domain algorithm," Progress In Electromagnetics Research, Vol. 51, 153-165, 2005.

    10. Lertwiriyaprapa, T., P. H. Pathak, and J. L. Volakis, "A UTD for predicting fields of sources near or on thin planar positive/negative material discontinuities," Radio Science, Vol. 42, RS6S18, 2007.

    11. Cory, H. and C. Zach, "Wave propagation in metamaterial multi-layered structures," Microwave Opt. Technol. Lett., Vol. 40, No. 6, 460-465, 2004.

    12. Kong, J. A., "Electromagnetic wave interaction with stratified negative isotropic media," Progress In Electromagnetics Research, Vol. 35, 1-52, 2002.

    13. Kouyoumjian, R. G. and P. H. Pathak, "A uniform geometrical heory of diffraction for an edge in a perfectly conducting surface," Proc. IEEE, Vol. 62, No. 11, 1448-1461, 1974.

    14. Gennarelli, C., G. Pelosi, C. Pochini, and G. Riccio, "Uniform asymptotic PO diffraction coefficients for an anisotropic impedance half-plane," Journal of Electromagnetic Waves and Applications,, Vol. 13, No. 7, 963-980, 1999.

    15. Senior, T. B. A. and J. L. Volakis, Approximate Boundary Conditions in Electromagnetic, IEE Electromagnetic Waves Series, Institution of Engineering and Technology, London, 1995.