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Caustics, Catastrophes and Wave Fields by Yu.A. Kravtsov

By Yu.A. Kravtsov

Caustics, Catastrophes and Wave Fields in a feeling keeps the therapy of the sooner quantity 6 "Geometrical Optics of Inhomogeneous Media" via analysing caustics and their fields at the foundation of contemporary disaster idea. the current quantity covers neighborhood and uniform caustic asymptotic expansions: The Lewis-Kravtsov approach to typical features, Maslov's approach to canonical operators , Orlov's approach to interference integrals, in addition to their variations for penumbra, space-time, random and different different types of caustics. the entire equipment are amply illustrated through labored difficulties touching on proper wave-field purposes.

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Example text

4. Plot of the Airy function 22 2 Rays and Caustics An insignificant modification of the above consideration allows the distance to the first interference zero and to the first interference maximum to be given with amazing accuracy. 13) for the purely geometric phase difference S2 - SI. 3. 34A. 3. 15b) klt/l2 - t/ld = nl2 . 02A. 34A). It may be diminished if we refine the purpose of the estimate. , the distance to the first zero of the Airy function because the zero level of the field provides a clear-cut separation of the branches, whereas for ray estimation of the fields at caustics we take LIve ~ A because this meets the condition of constructive interference LlStot = 0 of the two ray fields.

Let be the coordinate of the emanation point on the x axis, and O(e) the angle, measured from the y axis, at which the ray is launched in the x, y plane, as shown in Fig. 1. 2) In the extended 3-D space {x, y, 0 this equation describes a two-dimensional ray surface SR: = e(x, y). 2 shows schematically such a surface for ray slope varying by the law tan 0 = f3el(e 2 + a 2 ). I Fig. 1. Ray path in the (x. y) plane of a homogeneous medium bJ Fig. 2. (8) Ray surface F in the extended space (x. y. ~).

8. 4 Complex Rays 29 In the considered example of a simple caustic where any point in the lit region is hit by two rays, one may expect that through an arbitrary point in the shadow region there will pass at least two complex rays. From physical considerations it is clear that the field must fall off inward toward the shadow region. Therefore, of the two rays under consideration we should exclude one for which the imaginary part of the eikonal, "''', is negative and increases in magnitude inward toward the caustic shadow.

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