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Approximate Step‐Function Response of a Vertically Polarized Electromagnetic Plane Wave Reflected at an Imperfectly Conducting Surface

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1 Author(s)
Monroe, Richard L. ; U. S. Army Mobility Equipment Research and Development Center, Fort Belvoir, Virginia 22060

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A three‐term expression consisting of a constant plus two exponentials is given for the reflected field of a vertically polarized (E field in the plane of incidence) plane wave in free space with a step‐function time variation incident obliquely on a plane imperfectly conducting surface. Curves computed with this expression are shown to be in good agreement with corresponding curves obtained numerically for a time range 0≤t≤10tr, where tr, the relaxation time, is the ratio of permittivity to conductivity in the reflecting medium. Although the exponential time variation is limited to early times, it is shown that the three‐term approximation can be extended to times greater than 10tr at the expense of introducing modified Bessel functions of zeroth order. The first approximation to the step‐function response is used to investigate the transient reflected field of a rectangular pulse: Explicit expressions are obtained for the reflected field, the energy of the reflected field, and the ratio of reflected to incident energy. The latter indicates that the ratio of reflected to incident energy for incident pulses less than tr in length is approximately equal to α02, where α0 is the Fresnel reflection coefficient for a perfect dielectric.

Published in:

Journal of Applied Physics  (Volume:40 ,  Issue: 9 )

Date of Publication:

Aug 1969

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