Geodesic
Paraxial ray theory for Maxwell's equations
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 34, Tome 324 (2005), pp. 190-212 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Paraxial ray theory for Maxwell's equations in the case of an inhomogeneous isotropic medium with finite conductivity and smooth interfaces is developed. We show that the ray centered coordinates are suitable for describing amplitudes and polarization of waves in their propagation and reflection/refraction on a smooth interface. Expressions for the geometrical spreading and second order derivatives of the eikonal are obtained in terms of certain solutions of the equations in variations, i.e., equations which describe rays close to the central ray in linear approximation. 
@article{ZNSL_2005_324_a11,
     author = {J. de Freitas and M. M. Popov},
     title = {Paraxial ray theory for {Maxwell's} equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {190--212},
     year = {2005},
     volume = {324},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_324_a11/}
}
TY  - JOUR
AU  - J. de Freitas
AU  - M. M. Popov
TI  - Paraxial ray theory for Maxwell's equations
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2005
SP  - 190
EP  - 212
VL  - 324
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2005_324_a11/
LA  - en
ID  - ZNSL_2005_324_a11
ER  - 
%0 Journal Article
%A J. de Freitas
%A M. M. Popov
%T Paraxial ray theory for Maxwell's equations
%J Zapiski Nauchnykh Seminarov POMI
%D 2005
%P 190-212
%V 324
%U http://geodesic.mathdoc.fr/item/ZNSL_2005_324_a11/
%G en
%F ZNSL_2005_324_a11
J. de Freitas; M. M. Popov. Paraxial ray theory for Maxwell's equations. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 34, Tome 324 (2005), pp. 190-212. http://geodesic.mathdoc.fr/item/ZNSL_2005_324_a11/

[1] V. M. Babich, V. S. Buldyrev, I. A. Molotkov, Space-Time Ray Method. Linear and Nonlinear Waves, Leningrad Univ. Press, Leningrad, 1985 | MR

[2] V. M. Babich, M. M. Popov, “Gaussian summation method (Review)”, Radiophysics and Quantum Electronics, 32 (1989), 1063–1081 | DOI | MR

[3] M. Born, E. Wolf, Principles of Optics, 7th Edition, Cambridge Press, Cambridge, 1999 | Zbl

[4] V. C̆ervený, Seismic Ray Theory, Cambridge Univ. Press, New York, 2001 | MR | Zbl

[5] V. C̆ervený, F. Hron, “The ray series method and dynamic ray tracing for 3-D inhomogeneous media”, Bull. Seism. Soc. Am., 70 (1980), 47–77

[6] L. B. Felsen, N. Marcuvitz, Radiation and Scattering of waves, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1973 | MR

[7] A. P. Kiselev, “New structures in paraxial Gaussian beams”, Optics and Spectroscopy, 4:4 (2004), 533–535

[8] Yu. A. Kravtsov, Yu. I. Orlov, Geometrical Optics of Inhomogeneous Media, Springer-Verlag, New York, 1990 | MR | Zbl

[9] R. M. Lewis, “Asymptotic theory of transients”, Electromagnetic Wave Theory, Part 2, Pergamon Press, New York, 1967, 845–869

[10] R. K. Luneburg, Mathematical Theory of Optics, University of California Press, Berkeley, 1966 | MR

[11] M. M. Popov, “Geometrical Optics and self-frequencies of resonators”, Vestn. Leningrad. Univ., 4 (1967), 42–51

[12] M. M. Popov, “Self-oscillations of multi-mirror resonators”, Vestn. Leningrad. Univ., 4:22 (1969), 42–54 | MR

[13] M. M. Popov, “On a method of computation of geometrical spreading in an inhomogeneous medium with interfaces”, DAN SSSR, 237:5 (1977), 533–535

[14] M. M. Popov, Ray theory and Gaussian Beam method for geophysicists, EDUFBA, Salvador-Bahia, 2002

[15] M. M. Popov, I. Ps̆enc̆ik, “Ray amplitudes in inhomogeneous media with curved interfaces”, Geofiz. Sb., 24 (1978a), 111–129, Prague

[16] M. M. Popov, I. Ps̆enc̆ik, “Computation of ray amplitudes in inhomogeneous media with curved interfaces”, Studia Geophys. Geodet., 22 (1978b), 248–258 | DOI

[17] S. M. Rytov, “On transition from wave to geometrical optics”, Dokl. Akad. Nauk SSSR, 18:4–5 (1938), 263–266

[18] J. A. Stratton, Electromagnetic Theory, McGRAW-HILL BOOK COMPANY, Inc., New York–London, 1941 | Zbl