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Applied aspects of the high-frequency Drude—Sommerfeld model…
Engineering Journal: Science and Innovation
# 12·2017 9
Applied aspects of the high-frequency Drude—Sommerfeld
model for describing field scattering on finite targets
in problems of steady-state vibration theory
© V.F. Apeltsin
Bauman Moscow State Technical University, Moscow, 105005, Russia
Inverse problems of diffraction theory and wave propagation are most important for re-
al-world engineering applications. Huygens’ Principle forms the basis for mathematical
models of such problems. This principle, taken as a physical model of scattered field for-
mation in the problems of electromagnetic (or acoustic) wave scattering on finite targets,
assumes that the scattered field is generated by currents that the initial excitation field
induces over the scattered surface or in its bulk, or, in a general case, along each param-
eter discontinuity boundary in a medium. This secondary field coupled with the excitation
one ensures fulfilment of boundary conditions. In this case the scattered field generally
propagates transversally to the surfaces listed above.
In practice, all direct methods of obtaining approximate numerical solutions to this type
of boundary problems employ Huygens’ Principle to construct mathematical models of
wave phenomena. This concerns the integral equation method (surface or volumetric),
methods of auxiliary currents, of non-orthogonal series, and various modifications of fi-
nite element methods. Nevertheless, this approach has its drawbacks: slow convergence
in the high-frequency region, the problem of Raleigh representation of scattered field in
external boundary problems, and considerable difficulties in deriving an acceptably ac-
curate numerical solution for a model containing dielectric layers with thicknesses much
smaller than the wavelength.
We show that the Sommerfeld method, or its generalization for the case of targets differ-
ent from a circle (a sphere), makes it possible to solve the problems outlined above and
ensure explicit solutions for the high-frequency case. In particular, when synthesizing ra-
diation-absorbent aircraft coating, it can yield an equation determining its permittivity,
and it can also describe a new optical effect in an illuminated area that may lead to cre-
ating a device for nondestructive control of thin synthetic film parameters.
Keywords
: Huygens’ principle, electromagnetic waves, diffraction, asymptotics, Sommer-
feld method, Keller's equations, anti-reflection optical coating principle
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