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.
Radiation of horizontal electric dipole on large dielectric sphere
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
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.
Electromagnetic fields in air of traveling-wave currents above the earth
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
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
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
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
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
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
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
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).