On Diffraction by a Strip
 Creators
 Erdélyi, A.
 Papas, C. H.
Abstract
The problem of diffraction by an infinite strip or slit has been the subject of several investigations. There are at least two "exact" methods for attacking this problem. One of these is the integral equation method, the other the FourierLame method. The integral equation obtained for this problem cannot be solved in closed form: expansion of the solution in powers of the ratio (strip width/wavelength) leads to useful formulas for low frequencies. In the FourierLame method the wave equation is separated in coordinates of the elliptic cylinder, the solution appears as an infinite series of Mathieu functions, and the usefulness of the result is limited by the convergence of these infinite series, and by the available tabulation of Mathieu functions. The variational technique developed by Levine and Schwinger avoids some of the difficulties of the abovementioned methods and, at least in principle, is capable of furnishing good approximations for all frequencyranges. The scattered field may be represented as the effect of the current induced in the strip, and it has been proved by Levine and Schwinger that it is possible to represent the amplitude of the farzone scattered field in terms of the induced current in a form which is stationary with respect to small variations of the current about the true current. Substitution, in this representation, of a rough approximation for the current may give a remarkably good approximation of the farzone scattered field amplitude. In this note we assume a normally incident field polarized parallel to the generators of the strip. As a rough approximation, we take a uniform density of the current induced in the strip. Since the incident magnetic field is constant over the strip, Fock's theory may be cited in support of the uniformity of the current distribution, except near the edges where the behaviour of the field indicates an infinite current density. A more detailed analysis of the current, by Moullin and Phillips, is available but was not used here. Once the (approximate) amplitude of the farzone field has been obtained, the scattering crosssection may be found by the application of the scattering theorem which relates this crosssection to the imaginary part of the amplitude of the farzone scattered field along the central line of the umbral region. In spite of the crude approximation adopted for the induced current, the scattering crosssection shows a fair agreement with other available results.
Additional Information
© 1954 National Academy of Sciences. Communicated by P. S. Epstein, December 14, 1953. Most of the work discussed in this note was supported by the Office of Naval Research.
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 Eprint ID
 98496
 DOI
 10.1073/pnas.40.2.128
 Resolver ID
 CaltechAUTHORS:20190906141039522
 PMCID
 PMC527954
 URL
 http://resolver.caltech.edu/CaltechAUTHORS:20190906135712159
 Nonr 220(14) NR 071262
 Office of Naval Research (ONR)
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