Diffraction by a Smooth Transparent Object

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Abstract
In previous investigations the so‐called geometrical theory of diffraction was established. Its application has been limited to problems of diffraction of waves by smooth opaque objects. In the present paper, the geometrical theory of diffraction is extended and applied to problems of diffraction by a smooth transparent object of any shape. For simplicity only scalar fields and two‐dimensional problems are considered. However, this method can be modified easily to apply to vector fields and three‐dimensional problems. In Part I, the fields associated with the geometric rays and the diffracted rays are constructed in detail for the case of a circular cylinder. Afterwards a general method for treating diffraction by a smooth transparent cylinder of arbitrary shape is given. In order to determine the coefficients, the exact solution for the case of a circular cylinder is found and evaluated asymptotically for large ka in Part II. Then it is compared with the solution obtained from geometrical theory in Part I.

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