Electromagnetic-wave propagation near boundaries; scattering

In many situations of practical interest, electromagnetic waves are generated and propagate in the presence of dielectric or conducting boundaries. Part of my research efforts have focused on describing analytically corresponding solutions of Maxwell's equations in various geometries. Examples of such geometries include electrically large dielectric spheres, and arbitrarily-shaped cells immersed in saline fluid. A common theme in my treatments is to identify a small physical parameter and apply perturbation theory or asymptotic analysis for the electric or magnetic field of interest. This approach has led to apparently new, relatively simple asymptotic formulae for the fields. Applications include radiowave propagation on the curved Earth, induction of low-frequency currents in the human body, and pulse propagation in sea water.
Most recently, I have been interested in electromagnetic cloaking. In this case, objects of arbitrary shape may be coated with non-homogeneous and anisotropic materials with exotic properties (``metamaterials'') so that the object and the cloak itself become invisible, or almost invisible, to electromagnetic radiation. I have focused on the case where properties of the object are frequency-dependent and the incident wave is a narrowband electromagnetic pulse.

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Topics and papers:

  • Surface plasmon-polaritons on 2D materials, e.g., Graphene.

    Margetis, D., and M. Luskin, On solutions of Maxwell's equations with dipole sources over a thin conducting film, Journal of Mathematical Physics, accepted for publication (48pp).

  • Radiowave propagation on the surface of large dielectric sphere.

    D. Margetis, Radiation of horizontal electric dipole on large dielectric sphere (PDF), J. Math. Phys., Vol. 43 (6), pp. 3162-3201 (2002).

  • Radiowave propagation on a planar boundary; closed-form formulae for the fields.

    D. Margetis and T. T. Wu, Exactly calculable field components of electric dipoles in planar boundary (PDF), J. Math. Phys., Vol. 42 (2), pp. 713-745 (2001).

  • Low-frequency electromagnetic fields generated by transmission lines near a planar earth; closed-form analytical formulae for all field components.

    D. Margetis, Electromagnetic fields in air of traveling-wave currents above the earth (PDF), J. Math. Phys., Vol. 39 (11), pp. 5870-5893 (1998).

  • Low-frequency pulse propagation in conducting media, specifically sea water.

    1. D. Margetis, Pulse propagation in sea water: The modulated pulse (PDF), in Progress in Electromagnetic Research (PIER), J. A. Kong (Editor), EMW Publishing, Cambridge, MA, Vol. 26, pp. 89-110 (2000).

    2. D. Margetis, Pulse propagation in sea water (PDF), J. Appl. Physics, Vol. 77 (7), pp. 2884-2888 (1995).

    3. D. Margetis and R. W. P. King, Comments on `Propagation of EM pulses excited by an electric dipole in a conducting medium' (PDF), IEEE Transactions Antennas Propagat., Vol. 43 (1), pp. 119-120 (1995).

  • Currents induced inside cells exposed to low-frequency electric fields.

    1. D. Margetis and N. Savva, Low-frequency currents induced in adjacent spherical cells (PDF), Journal of Mathematical Physics, Vol. 47, art. 042902, pp. 1-18 (2006).
    Also selected to appear in the Virtual Journal of Biological Physics Research, May 1, 2006 ( http://www.vjbio.org/bio/ ).

    2. R. W. P. King and D. Margetis, The low-frequency fields induced in a spherical cell including its nucleus (PDF), in Progress in Electromagnetic Research, J. A. Kong (Editor), EMW Publishing, Cambridge, MA, Vol. 36, pp. 61-79 (2002).

    Constrained maximization of directivity in radiation problems:

    In many experimental situations, it is of interest to determine distributions of electric currents on antennas so that the directivity is maximized under constraints, e.g., fixed ohmic losses. The mathematical formulation of a somewhat idealized version of this problem yields a second-kind Fredholm integral equation for the desirable current distribution. This equation can be solved exactly in cases with circular symmetry. I have developed the general formulation, and have derived simple analytical formulae for currents flowing in large circular loops in 2D.

    1. D. Margetis and G. Fikioris, Two-dimensional, highly directive currents on large circular loops (PDF), J. Math. Phys., Vol. 41 (9), pp. 6130-6172 (2000).

    2. D. Margetis, G. Fikioris, J. M. Myers, and T. T. Wu, Highly directive current distributions: General theory (PDF), Phys. Rev. E, Vol. 58 (2), pp. 2531-2547 (1998).

    Probabilistic methods for telecommunication systems:

    1. J. D. Kanellopoulos and D. Margetis, A predictive analysis of differential attenuation on adjacent satellite paths including rain height effects (PDF), European Trans. Telecommunications, Vol. 8 (2), pp. 141-148 (1997).