Maxwell equations and the k function

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volumn 17, Issue 8, 2000, Pages 1469-1474

  Stavroudis, Orestes N ^a   Hurtado Ramos, Juan Bautista ^a  

^a CENTRO DE INVESTIGACIONES EN ÓPTICA   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRIC FIELD EFFECTS; ELECTROMAGNETIC FIELD EFFECTS; MAXWELL EQUATIONS; VECTORS;

WAVE-FRONT TRAIN;

ELECTROMAGNETIC WAVES;

EID: 0038103858     PISSN: 10847529     EISSN: 15208532     Source Type: Journal    
DOI: 10.1364/JOSAA.17.001469     Document Type: Article

References (10)

1. G. Joos, Theoretical Physics, translated by I. M. Freeman (Blackie, London, 1941), pp. 322ff.
2. Most modern references start with the dipole oscillator and deduce the spherical wave fronts, such as J. B. Marion and M. A. Heald, Classical Electromagnetic Radiation, 2nd ed. (Academic, New York, 1980), pp. 232-245.
3. O. N. Stavroudis, The Optics of Rays, Wavefronts and Caustics (Academic, New York, 1972), Chaps. VIII and IX.
4. The method of Lagrange and Charpit is used to obtain a general solution; a detailed account can be found in A. R. Forsyth, A Treatise on Differential Equations (Dover, Mineola, N.Y., 1996), Chap. IX.
5. See also O. N. Stavroudis, “The k function in geometrical optics and its relationship to the archetypal wave front and the caustic surface,” J. Opt. Soc. Am. A 12, 1010-1016 (1995).
6. O. N. Stavroudis, R. C. Fronczek, and R.-S. Chang, “Geometry of the half-symmetric image,” J. Opt. Soc. Am. 68, 739-742 (1978).
7. O. N. Stavroudis, “The k function in geometrical optics and its relationship to the archetypal wave front and the caustic,” J. Opt. Soc. Am. 12, 1012-1016 (1995).
8. M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1970), Chap. I.
9. The element of area D, defined in Eq. (5), vanished on the caustic surface so that the wave fronts form a cusp. Turning this around, one can regard the caustic as the cusp locus of the wave-front train.
10. See, for example, G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers, 2nd ed. (McGraw-Hill, New York, 1961), Chap. 1.