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.
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)
- R. H. MacPhie, J. Dalmas, and R. Deleuil, Rotational-translational addition theorems for scalar spheroidal wave functions, Quart. Appl. Math. 44 (1987), no. 4, 737–749. MR 872824, DOI https://doi.org/10.1090/S0033-569X-1987-0872824-8
- Bernard Friedman and Joy Russek, Addition theorems for spherical waves, Quart. Appl. Math. 12 (1954), 13–23. MR 60649, DOI https://doi.org/10.1090/S0033-569X-1954-60649-8
- Seymour Stein, Addition theorems for spherical wave functions, Quart. Appl. Math. 19 (1961), 15–24. MR 120407, DOI https://doi.org/10.1090/S0033-569X-1961-0120407-5
- Orval R. Cruzan, Translational addition theorems for spherical vector wave functions, Quart. Appl. Math. 20 (1962/63), 33–40. MR 132851, DOI https://doi.org/10.1090/S0033-569X-1962-0132851-2
- Carson Flammer, Spheroidal wave functions, Stanford University Press, Stanford, California, 1957. MR 0089520
J. A. Stratton, Electromagnetic Theory, McGraw-Hill Book Company, New York and London, 1941
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)
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)
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)
S. Asano and G. Yamamoto, Light scattering by a spheroidal particle, Appl. Optics 14, 29–49 (1975)
- Bateshwar P. Sinha and Robert H. MacPhie, Electromagnetic scattering by prolate spheroids for plane waves with arbitrary polarization and angle of incidence, Radio Sci. 12 (1977), no. 2, 171–184. MR 459329, DOI https://doi.org/10.1029/RS012i002p00171
- 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 (1980), no. 5, 637–649 (French, with English summary). MR 577735, DOI https://doi.org/10.1080/713820293
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)
J. Dalmas, Indicatrices de diffusion d’un ellipsoïde de révolution allongé de conduction infinie en incidence oblique, Optica Acta 28, 1277–1287 (1981)
J. Dalmas and R. Deleuil, Diffusion multiple des ondes électromagnétiques par des ellipsoïdes de révolution allongés, Optica Acta 29, 1117–1131 (1982)
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)
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)
A. R. Edmonds, Angular Momentum in Quantum Mechanics, Princeton University Press, Princeton, New Jersey, third printing, 1974
- M. Danos and L. C. Maximon, Multipole matrix elements of the translation operator, J. Mathematical Phys. 6 (1965), 766–778. MR 175515, DOI https://doi.org/10.1063/1.1704333
- Jeannine Dalmas and Roger Deleuil, Translational addition theorems for prolate spheroidal vector wave functions ${\bf M}^r$ and ${\bf N}^r$, Quart. Appl. Math. 44 (1986), no. 2, 213–222. MR 856176, DOI https://doi.org/10.1090/S0033-569X-1986-0856176-1
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)
- Bateshwar P. Sinha and Robert H. Macphie, Translational addition theorems for spheroidal scalar and vector wave functions, Quart. Appl. Math. 38 (1980/81), no. 2, 143–158. MR 580875, DOI https://doi.org/10.1090/S0033-569X-1980-0580875-9
J. R. Reitz and F. J. Milford, Foundations of electromagnetic theory, Addison-Wesley Publishing Company, Palo Alto and London, 1960
- Jeannine Dalmas and Roger Deleuil, Electromagnetic scattering and mutual interactions between closely spaced spheroids, Electromagnetic and acoustic scattering: detection and inverse problem (Marseille, 1988) World Sci. Publ., Teaneck, NJ, 1989, pp. 36–44. MR 1118167
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)
R. H. MacPhie, J. Dalmas, and R. Deleuil, Rotational-translational addition theorems for scalar spheroidal wave functions, Quart. Appl. Math. 44, 737–749 (1987)
B. Friedman and J. Russek, Addition theorems for spherical waves, Quart. Appl. Math. 12, 13–23 (1954)
S. Stein, Addition theorems for spherical wave functions, Quart. Appl. Math. 19, 15–24 (1961)
O. Cruzan, Translational addition theorems for spherical vector wave functions, Quart. Appl. Math. 20, 33–40 (1962)
C. Flammer, Spheroidal Wave Functions, Stanford University Press, Palo Alto, Calif., 1957
J. A. Stratton, Electromagnetic Theory, McGraw-Hill Book Company, New York and London, 1941
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)
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)
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)
S. Asano and G. Yamamoto, Light scattering by a spheroidal particle, Appl. Optics 14, 29–49 (1975)
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)
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)
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)
J. Dalmas, Indicatrices de diffusion d’un ellipsoïde de révolution allongé de conduction infinie en incidence oblique, Optica Acta 28, 1277–1287 (1981)
J. Dalmas and R. Deleuil, Diffusion multiple des ondes électromagnétiques par des ellipsoïdes de révolution allongés, Optica Acta 29, 1117–1131 (1982)
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)
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)
A. R. Edmonds, Angular Momentum in Quantum Mechanics, Princeton University Press, Princeton, New Jersey, third printing, 1974
M. Danos and L. C. Maximon, Multipole matrix elements of the translation operator, J. Math. Phys. 6, no. 5, 766–778 (1965)
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)
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)
B. P. Sinha and R. H. MacPhie, Translational addition theorems for spheroidal scalar and vector wave functions. Quart. Appl. Math. 38, 145–158 (1980)
J. R. Reitz and F. J. Milford, Foundations of electromagnetic theory, Addison-Wesley Publishing Company, Palo Alto and London, 1960
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)
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
78A45,
33A55
Retrieve articles in all journals
with MSC:
78A45,
33A55
Additional Information
Article copyright:
© Copyright 1989
American Mathematical Society