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Boundaries of geometrical optics applicability and related problems
Author(s) -
Kravtsov Yu. A.,
Orlov Yu. I.
Publication year - 1981
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/rs016i006p00975
Subject(s) - fresnel diffraction , fresnel integral , fresnel number , geometrical optics , diffraction , huygens–fresnel principle , basis (linear algebra) , fresnel zone , point (geometry) , mathematics , physical optics , optics , field (mathematics) , space (punctuation) , phase (matter) , phase space , mathematical analysis , physics , geometry , computer science , quantum mechanics , pure mathematics , operating system
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.