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Chapter 4:
Fresnel Diffraction by a Semi-Infinite Plane
In this chapter, the function U1 derived in Chapter 3 is applied to the diffraction of a monochromatic spherical wave by a semi-infinite plane; the analysis is first applied to a scalar wave, showing that the use of the multiple-valued function U1 as part of a Huygens’ construction permits a simple (though approximate) way of accounting for the diffraction induced by a boundary condition on a semi-infinite plane. The scalar U1 is then applied to Fresnel diffraction by a semi-infinite, perfectly conducting plane in a manner similar to Sommerfeld’s analysis of Fraunhofer diffraction, and also valid for all wavelengths of the incident radiation. The chapter concludes with an alternate method of analysis dependent on a suitable choice of a generator vector, valid for all wavelengths of the incident radiation.
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