Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Rotational-translational addition theorems for spheroidal vector wave functions


Authors: Jeannine Dalmas, Roger Deleuil and R. H. MacPhie
Journal: Quart. Appl. Math. 47 (1989), 351-364
MSC: Primary 78A45; Secondary 33A55
DOI: https://doi.org/10.1090/qam/998107
MathSciNet review: 998107
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Rotational-translational addition theorems for spherical and spheroidal vector wave functions are established. These theorems concern the vector wave functions $ {M^a}$ and $ {N^a}$ (with $ a = r, x, y, z$) which can be obtained and used to treat various electromagnetic problems such as multiple scattering of a plane wave from prolate spheroids (with arbitrary spacings and orientations of their axes of symmetry) or radiation from thin-wire antennas. For sake of completeness, rotational-translational addition theorems for the vector wave function L are also established. This work is a natural extension of previous studies concerning simpler transformations of coordinate systems, such as rotation or translation. The two cases $ r \ge d$ and $ r \le d$ are distinguished, where $ d$ is the distance between the centers of the spheroids.


References [Enhancements On Off] (What's this?)

  • [1] R. H. MacPhie, J. Dalmas, and R. Deleuil, Rotational-translational addition theorems for spheroidal wave functions, International I.E.E.E./AP-S, Symposium, University of British Columbia, Vancouver, Canada, June 17-21 (1985)
  • [2] R. H. MacPhie, J. Dalmas, and R. Deleuil, Rotational-translational addition theorems for scalar spheroidal wave functions, Quart. Appl. Math. 44, 737-749 (1987) MR 872824
  • [3] B. Friedman and J. Russek, Addition theorems for spherical waves, Quart. Appl. Math. 12, 13-23 (1954) MR 0060649
  • [4] S. Stein, Addition theorems for spherical wave functions, Quart. Appl. Math. 19, 15-24 (1961) MR 0120407
  • [5] O. Cruzan, Translational addition theorems for spherical vector wave functions, Quart. Appl. Math. 20, 33-40 (1962) MR 0132851
  • [6] C. Flammer, Spheroidal Wave Functions, Stanford University Press, Palo Alto, Calif., 1957 MR 0089520
  • [7] J. A. Stratton, Electromagnetic Theory, McGraw-Hill Book Company, New York and London, 1941
  • [8] J. Bruning and Y. Lo, Multiple scattering of EM waves by spheres, Part I and Part II, I.E.E.E. Trans. Antennas Prop. 19, 378-400 (1971)
  • [9] K. S. Siegel, F. V. Schultz, B. M. Gere, and F. B. Sleator, The theoretical and numerical determination of the radar cross-section of a prolate spheroid, I.R.E. Trans. Antennas Prop. 4, 266-275 (1956)
  • [10] B. P. Sinha and R. H. MacPhie, Electromagnetic scattering from prolate spheroids for axial incidence, I.E.E.E. Trans. Antennas Prop. 23, 676-679 (1975)
  • [11] S. Asano and G. Yamamoto, Light scattering by a spheroidal particle, Appl. Optics 14, 29-49 (1975)
  • [12] B. P. Sinha and R. H. MacPhie, Electromagnetic scattering by prolate spheroids for plane waves with arbitrary polarization and angle of incidence, Radio Science 12, 171-184 (1977) MR 0459329
  • [13] J. Dalmas and R. Deleuil, Diffusion d'une onde électromagnétique par un ellipsoïde de révolution allongé et par un demi-ellipsoïde posé sur un plan en incidence axiale, Optica Acta 27, 637-649 (1980) MR 577735
  • [14] J. Dalmas, Diffusion d'une onde électromagnétique par un ellipsoïde de révolution allongé de conduction infinie en incidence non axiale, Optica Acta 28, 933-948 (1981)
  • [15] J. Dalmas, Indicatrices de diffusion d'un ellipsoïde de révolution allongé de conduction infinie en incidence oblique, Optica Acta 28, 1277-1287 (1981)
  • [16] J. Dalmas and R. Deleuil, Diffusion multiple des ondes électromagnétiques par des ellipsoïdes de révolution allongés, Optica Acta 29, 1117-1131 (1982)
  • [17] B. P. Sinha and R. H. MacPhie, Electromagnetic plane wave scattering by a system of two parallel conducting prolate spheroids, I.E.E.E. Trans. Antennas Prop. 31, 294-304 (1983)
  • [18] J. Dalmas and R. Deleuil, Multiple scattering of electromagnetic waves from two infinitely conducting prolate spheroids which are centered in a plane perpendicular to their axes of revolution, Radio Science 20, 575-581 (1985)
  • [19] A. R. Edmonds, Angular Momentum in Quantum Mechanics, Princeton University Press, Princeton, New Jersey, third printing, 1974
  • [20] M. Danos and L. C. Maximon, Multipole matrix elements of the translation operator, J. Math. Phys. 6, no. 5, 766-778 (1965) MR 0175515
  • [21] J. Dalmas and R. Deleuil, Translational addition theorems for prolate spheroidal vector wave functions M$ ^{r}$ and N$ ^{r}$, Quart. Appl. Math. 44, 213-222 (1986) MR 856176
  • [22] R. J. A. Tough, The transformation properties of vector multipole fields under a translation of coordinate origin, J. Phys. A: Math. Gen. 10, no. 7, 1079-1087 (1977)
  • [23] B. P. Sinha and R. H. MacPhie, Translational addition theorems for spheroidal scalar and vector wave functions. Quart. Appl. Math. 38, 145-158 (1980) MR 580875
  • [24] J. R. Reitz and F. J. Milford, Foundations of electromagnetic theory, Addison-Wesley Publishing Company, Palo Alto and London, 1960
  • [25] J. Dalmas and R. Deleuil, Electromagnetic scattering and mutual interactions between closely spaced spheroids, Colloque sur la diffusion électromagnétique et acoustique: détection et problème inverse, Centre de Physique Théorique, Marseille, France, 31 Mai-3 Juin (1988) MR 1118167

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 78A45, 33A55

Retrieve articles in all journals with MSC: 78A45, 33A55


Additional Information

DOI: https://doi.org/10.1090/qam/998107
Article copyright: © Copyright 1989 American Mathematical Society

American Mathematical Society