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Radio Science

Boundaries of geometrical optics applicability and related problems


  • Yu. A. Kravtsov,

  • Yu. I. Orlov


On the basis of the Huygens-Fresnel principle as well as the concept of a Fresnel volume (the part of space essential for diffraction), the following criteria of the ray method applicability are suggested. (1) Parameters of the medium involved and characteristics of the wave (amplitude and phase gradient) should vary just slightly over the cross section of the Fresnel volume. (2) The phase difference of two rays arriving at the same point of space should exceed π. These criteria may be evaluated from the conditions of applicability of the stationary phase method. The effectiveness of the suggested criteria is demonstrated by considering various problems allowing either rigorous or approximate solutions. Moreover, one can formulate generalized criteria for the case of space-time geometrical optics and for geometrical theory of diffraction as well. And finally, some related problems are considered, the most important one being estimation of the wave field intensity in the vicinity of caustics in terms of the energy conservation law in a ray tube corresponding to the caustical zone width.

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