Seminar Series: Technology Trends 2005
Electromagnetic Waves: direct and inverse
scattering techniques and applications.
Professor
Paul Smith, Department of Mathematics, Macquarie University
Waves are ubiquitous, involving the transfer of energy and
information without bulk motion; light, sound, and elastic waves as
well as less obvious varieties are important to us in natural and
technological senses. Whilst our perception of the world depends
heavily on interpreting light and sound waves, the last century has
seen the birth of many new technologies exploiting electromagnetic
(EM) waves such as telecommunications, radar (including remote
sensing and imaging radars), and lasers; in the acoustic domain,
ultrasonic imaging finds application in non-destructive testing and
medicine.
Further development and exploitation depends crucially on
mathematical modelling and analysis of wave phenomena -– their
radiation, propagation, interaction with scattering objects and
their detection via sensors. Such models allow us to interpret the
intrinsic information contained in waves that are otherwise
invisible (or inaudible), and infer the presence (or absence) of
certain types of scattering features in the environment.
At a fundamental level Maxwell's equations completely describes
all EM phenomena, when supplemented with appropriate boundary,
radiation and edge conditions. However, these equations encompass a
huge diversity of wave scattering problems, ranging from antenna
design to signature analysis and image reconstruction. Since
analytic closed form solutions exist only for a small number of
scenarios involving simple scatterers, the challenge is to devise
approximate analytical methods and numerical methods, of reasonable
generality, that are robust, reliable and efficient. This talk
surveys current computational methods available for the direct
scattering problem where the interaction of the wave energy with an
object or its environment is to be calculated, and concludes with
some remarks on the inverse scattering problem, where the shape of
the object or material properties of its environment are to be
inferred from measurements of the energy reflected or scattered at
different angles. Some challenging problems for modern
electromagnetics will be outlined.
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