This paper reports a new procedure for specifying monochromatic nonradiating (NR) current distributions (NR sources) and the electric and magnetic fields they produce (NR fields). Vector spherical harmonics and a Fourier–Bessel series are used to derive a new vector spherical-wave expansion for continuous NR fields confined within a spherical volume. The analysis yields complete orthogonal sets in terms of which all such NR fields can be expanded. By making use of a Maxwell operator representation for NR current distributions, we obtain a new series expansion for NR current distributions confined within a spherical volume. The analysis also yields complete sets for such NR current distributions. The developed theory is illustrated with special cases.

1.
B. J. Hoenders, “The uniqueness of inverse problems,” in Inverse Source Problems in Optics, edited by H. P. Baltes (Springer, Berlin, 1978), pp. 41–82.
2.
A. D. Yaghjian, Relativistic Dynamics of a Charged Sphere, Lecture Notes in Physics Series, Monograph m11 (Springer, Berlin, 1992).
3.
G. A.
Schott
, “
The electromagnetic field of a moving uniformly and rigidly electrified sphere and its radiationless orbits
,”
Philos. Mag.
15
,
752
761
(
1933
).
4.
G. A.
Schott
, “
The uniform circular motion with invariable normal spin of a rigidly and uniformly electrified sphere, IV
,”
Proc. R. Soc. London, Ser. A
159
,
570
591
(
1937
).
5.
D.
Bohm
and
M.
Weinstein
, “
The self-oscillations of a charged particle
,”
Phys. Rev.
74
,
1789
1798
(
1948
).
6.
G. H.
Goedecke
, “
Classically radiationless motions and possible implications for quantum theory
,”
Phys. Rev.
135
,
B281
288
(
1964
).
7.
A. J.
Devaney
, “
Nonuniqueness in the inverse scattering problem
,”
J. Math. Phys.
19
,
1526
1531
(
1978
).
8.
A. J.
Devaney
and
G. C.
Sherman
, “
Nonuniqueness in inverse source and scattering problems
,”
IEEE Trans. Antennas Propag.
30
,
1034
1037
(
1982
).
9.
K. J. Langenberg, “Applied inverse problems for acoustic, electromagnetic and elastic wave scattering,” in Basic Methods of Tomography and Inverse Problems, edited by P. C. Sabatier (IOP, Bristol, 1987), pp. 127–453.
10.
R. P.
Porter
and
A. J.
Devaney
, “
Holography and the inverse source problem
,”
J. Opt. Soc. Am.
72
,
327
330
(
1981
).
11.
A. J.
Devaney
and
R. P.
Porter
, “
Holography and the inverse source problem. II. Inhomogeneous media
,”
J. Opt. Soc. Am. A
2
,
2006
2011
(
1985
).
12.
K.
Kim
and
E.
Wolf
, “
Non-radiating monochromatic sources and their fields
,”
Opt. Commun.
59
,
1
6
(
1986
).
13.
A.
Gamliel
,
K.
Kim
,
A. I.
Nachman
, and
E.
Wolf
, “
A new method for specifying nonradiating monochromatic, scalar sources and their fields
,”
J. Opt. Soc. Am. A
6
,
1388
1393
(
1989
).
14.
B. J.
Hoenders
and
H. A.
Ferwerda
, “
The non-radiating component of the field generated by a finite monochromatic scalar source distribution
,”
Pure Appl. Opt.
7
,
1201
1211
(
1998
).
15.
A. J.
Devaney
and
E.
Wolf
, “
Radiating and nonradiating classical current distributions and the fields they generate
,”
Phys. Rev. D
8
,
1044
1047
(
1973
).
16.
N.
Bleistein
and
J. K.
Cohen
, “
Nonuniqueness in the inverse source problem in acoustics and electromagnetics
,”
J. Math. Phys.
18
,
194
201
(
1977
).
17.
N.
Meyer-Vernet
, “
Nonradiating sources: The subtle art of changing light into black
,”
Am. J. Phys.
57
,
1084
1089
(
1989
).
18.
B. J.
Hoenders
and
H. P.
Baltes
, “
The scalar theory of nonradiating partially coherent sources
,”
Lett. Nuovo Cimento Soc. Ital. Fis.
25
,
206
208
(
1979
).
19.
A. J.
Devaney
, “
The inverse problem for random sources
,”
J. Math. Phys.
20
,
1687
1691
(
1979
).
20.
B. J.
Hoenders
and
H. P.
Baltes
, “
On the existence of non-radiating frequencies in the radiation from a stochastic current distribution
,”
J. Phys. A: Math. Gen.
13
,
995
1006
(
1980
).
21.
T. M.
Habashy
,
E. Y.
Chow
, and
D. G.
Dudley
, “
Profile inversion using the renormalized source-type integral equation approach
,”
IEEE Trans. Antennas Propag.
38
,
668
682
(
1990
).
22.
J. J.
Xia
,
T. M.
Habashy
, and
J. A.
Kong
, “
Profile inversion in a cylindrically stratified lossy medium
,”
Radi. Sci.
29
,
1131
1141
(
1994
).
23.
T. M.
Habashy
,
M. L.
Oristaglio
, and
A. T.
de Hoop
, “
Simultaneous nonlinear reconstruction of two-dimensional permittivity and conductivity
,”
Radi. Sci.
29
,
1101
1118
(
1994
).
24.
A. J.
Devaney
and
E. A.
Marengo
, “
A method for specifying non-radiating, monochromatic, scalar sources and their fields
,”
Pure Appl. Opt.
7
,
1213
1220
(
1998
).
25.
J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975).
26.
F. G.
Friedlander
, “
An inverse problem for radiation fields
,”
Proc. London Math. Soc.
3
,
551
576
(
1973
).
27.
P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).
28.
G. Arfken, Mathematical Methods for Physicists, 3rd ed. (Academic, San Diego, 1985).
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