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On Inhomogeneous Metamaterials Media: a New Alternative Method for Analysis of Electromagnetic Fields Propagation

By Consuelo Bellver-Cebreros and Marcelo Rodriguez-Danta
Progress In Electromagnetics Research, Vol. 149, 101-108, 2014


The analysis of waves propagation in homogeneous anisotropic media constitutes a classical topic in every field of science and has been preferentially discussed using locally plane waves. Specific physical quantities and their behaviour laws are really what make the difference. Although the use of Fourier transform enables an approach formally analogous to that of plane waves in linear evolution equations, its application to constitutive equations of inhomogeneous media involves cumbersome convolution products that mask the solution. This paper proposes a polar representation (amplitude and phase) of electromagnetic fields, that appears to be more suitable and provides two sets of equations that can be easily decoupled, reducing the problem to the superposition of two simpler ones. The procedure is based upon the following steps: a) The identification of dispersion equation with Hamilton-Jacobi equation yields the evolution laws of rays and/or wave-fronts. b) From the knowledge of tensor ε(r) at any point r of the wave front (or the ray), the use of the intrinsic character (conjugation relations) of fields, introduced by the authors in a previous work, together with ray velocity or phase gradient (found in the first step) the remaining fields are immediately obtained.


Consuelo Bellver-Cebreros and Marcelo Rodriguez-Danta, "On Inhomogeneous Metamaterials Media: a New Alternative Method for Analysis of Electromagnetic Fields Propagation," Progress In Electromagnetics Research, Vol. 149, 101-108, 2014.


    1. Leonhardt, U. and T. G. Philbin, Geometry and Light: The Science of Invisibility, Dover, Mineola, 2010.

    2. Urzhumov, Y. A., N. B. Kundtz, D. R. Smith, and J. B. Pendry, "Cross-section comparison of cloaks designed by transformation optical and optical conformal mapping approaches," Journal of Optics, Vol. 13, 024002, 2011.

    3. Pendry, J. B., D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science, Vol. 312, No. 5781, 1780-1782, 2006.

    4. Halimeh, J. C. and M. Wegener, "Time-of-flight imaging of invisibility cloaks," Opt. Express, Vol. 20, No. 1, 63-74, 2012.

    5. Halimeh, J. C. and M. Wegener, "Photorealistic rendering of unidirectional free-space invisibility cloaks," Opt. Express, Vol. 21, 9457-9472, 2013.

    6. Bellver-Cebreros, C. and M. Rodriguez-Danta, "An alternative model for wave propagation in anisotropic impedance-matched metamaterials," Progress In Electromagnetics Research, Vol. 141, 149-160, and References Therein, 2013.

    7. Melrose, D. B. and R. C. McPhedran, Electromagnetic Processes in Dispersive Media, Cambridge University Press, Cambridge , 1991.

    8. Schurig, D., J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express, Vol. 14, No. 21, 9794-9804, 2006.

    9. Bellver-Cebreros, C. and M. Rodriguez-Danta, "Eikonal equation from continuum mechanics and analogy between equilibrium of a string and geometrical light rays," Am. J. Phys., Vol. 69, 360-367, 2001.

    10. Jacobi, C. G., Vorlesungen Fiber Dynamik, A. Clebsch, Berlin, 1866, Reprinted by Chelsea, 1969.

    11. Arnold, V. I., Mathematical Methods of Classical Mechanics, 2nd Ed., (Section 47), Springer-Verlag, 1989.

    12. Bellver-Cebreros, C. and M. Rodriguez-Danta, "Conjugacy and reciprocal bases in anisotropic dielectric media," Optica Pura Y Aplicada, Vol. 44, No. 3, 571-580, 2011.

    13. Born, M. and E. Wolf, Principles of Optics, Pergamon Press, New York, 1999.

    14. Chandrasekharaiah, D. L. and L. Debnath, Continuum Mechanics, Page 80, Academic Press, San Diego, 1994.

    15. Jackson, J. D., Classical Electrodynamics, Page 80, John Wiley and Sons, Hoboken, New Jersey, 1994.

    16. Landau, L. D. and E. M. Lifshitz, The Classical theory of Fields, 3rd Ed., Vol. 2, Pergamon Press, Oxford, 1971.

    17. Landau, L. D., E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd Ed., Vol. 8, Butterworth-Heinemann, Oxford, 1984.

    18. Fung, Y. C., Foundations of Solid Mechanics, Prentice Hall, Englewood Cliffs, New Jersey, 1965.

    19. Bellver-Cebreros, C. and M. Rodriguez-Danta, "Analogies between the torque-free motion of a rigid body about a fixed point and light propagation in anisotropic media," Eur. J. Phys., Vol. 30, 285-294, 2009.

    20. Salmon, G., A Treatise on Conic Sections, AMS Chelsea Publishing, Providence, Rhode Island, 1960.

    21. Zwikker, C., The Advanced Geometry of Plane Curves and Their Applications, Dover Publications, Mineola, NY, 2005.

    22. Landau, L. D. and E. M. Lifshitz, Mechanics, Pergamon Press, 1976.

    23. Bellver-Cebreros, C., M. Rodriguez-Danta, and E. Gomez-Gonzalez, "Angle eikonal from reciprocal action and other optical-mechanical analogues," Optik, Vol. 111, No. 6, 261-268, and References Therein, 2000.