Abstract

An expression is derived for the scattering of electromagnetic radiation by small, nonabsorbing, compound ellipsoids that contain an inner ellipsoidal region and an outer confocal ellipsoidal shell. For certain combinations of dielectric constant, the scattering is zero, thereby rendering the body invisible.

© 1975 Optical Society of America

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Corrections

Milton Kerker, "Erratum: Invisible bodies," J. Opt. Soc. Am. 65, 1085_1-1085 (1975)
https://www.osapublishing.org/josa/abstract.cfm?uri=josa-65-9-1085_1

References

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  1. Milton Kerker, Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), pp. 224–232, 242.
  2. Rayleigh, Philos. Mag. 44, 28 (1897).
  3. J. C. Maxwell, Treatise on Electricity and Magnetism, 3rd ed. (Oxford U. P., Oxford, 1892), Vol. II, pp. 66–70.
  4. J. A. Stratton, Electromagnetic Theory (McGraw–Hill, New York, 1941), pp. 207–213.
  5. E. Weber, Electromagnetic Theory (Dover, New York, 1965), pp. 484–486.
  6. A. L. Aden and M. Kerker, J. Appl. Phys. 22, 1242 (1951). For small-particle limit, see Ref. 1, p. 197.
    [Crossref]
  7. M. Kerker, D. D. Cooke, and W. D. Ross, J. Paint Tech. 47, April (1975).

1975 (1)

M. Kerker, D. D. Cooke, and W. D. Ross, J. Paint Tech. 47, April (1975).

1951 (1)

A. L. Aden and M. Kerker, J. Appl. Phys. 22, 1242 (1951). For small-particle limit, see Ref. 1, p. 197.
[Crossref]

1897 (1)

Rayleigh, Philos. Mag. 44, 28 (1897).

Aden, A. L.

A. L. Aden and M. Kerker, J. Appl. Phys. 22, 1242 (1951). For small-particle limit, see Ref. 1, p. 197.
[Crossref]

Cooke, D. D.

M. Kerker, D. D. Cooke, and W. D. Ross, J. Paint Tech. 47, April (1975).

Kerker, M.

M. Kerker, D. D. Cooke, and W. D. Ross, J. Paint Tech. 47, April (1975).

A. L. Aden and M. Kerker, J. Appl. Phys. 22, 1242 (1951). For small-particle limit, see Ref. 1, p. 197.
[Crossref]

Kerker, Milton

Milton Kerker, Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), pp. 224–232, 242.

Maxwell, J. C.

J. C. Maxwell, Treatise on Electricity and Magnetism, 3rd ed. (Oxford U. P., Oxford, 1892), Vol. II, pp. 66–70.

Rayleigh,

Rayleigh, Philos. Mag. 44, 28 (1897).

Ross, W. D.

M. Kerker, D. D. Cooke, and W. D. Ross, J. Paint Tech. 47, April (1975).

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw–Hill, New York, 1941), pp. 207–213.

Weber, E.

E. Weber, Electromagnetic Theory (Dover, New York, 1965), pp. 484–486.

J. Appl. Phys. (1)

A. L. Aden and M. Kerker, J. Appl. Phys. 22, 1242 (1951). For small-particle limit, see Ref. 1, p. 197.
[Crossref]

J. Paint Tech. (1)

M. Kerker, D. D. Cooke, and W. D. Ross, J. Paint Tech. 47, April (1975).

Philos. Mag. (1)

Rayleigh, Philos. Mag. 44, 28 (1897).

Other (4)

J. C. Maxwell, Treatise on Electricity and Magnetism, 3rd ed. (Oxford U. P., Oxford, 1892), Vol. II, pp. 66–70.

J. A. Stratton, Electromagnetic Theory (McGraw–Hill, New York, 1941), pp. 207–213.

E. Weber, Electromagnetic Theory (Dover, New York, 1965), pp. 484–486.

Milton Kerker, Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), pp. 224–232, 242.

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Figures (1)

FIG. 1
FIG. 1

Contour diagram of scattering function S over the range of dimensionless size parameter ν = 0.2 to 2.0 and volume fraction of the central region. Refractive indices are m 1 = 1 1 / 2 = 2.97 , m 2 = 2 1 / 2 = 1.00 , m 3 = 3 1 / 2 = 1.51 . Values of S on the contour lines are given in units μm−1 by the values in the parentheses 1 (0.000015), 2 (0.00015), 3 (0.0015), 4 (0.015), 5 (0.15), 6 (0.6), 7 (1.5), 8 (3.8), 9 (7.5), 10 (11.3), 11 (15).

Tables (1)

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TABLE I Conditions that (3R2S) vanishes.a

Equations (33)

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2 ϕ = 0
ϕ 0 = E 0 x x = E 0 x [ ( ξ + a 2 ) ( η + a 2 ) ( ζ + a 2 ) ( b 2 a 2 ) ( c 2 a 2 ) ] 1 / 2 ,
= C 1 F 1 ( ξ ) F 2 ( η ) F 3 ( ζ ) ,
l = ( a 2 δ ) , m = ( b 2 δ ) , n = ( c 2 δ ) .
G 1 ( ξ ) = F 1 ( ξ ) d ξ [ F 1 ( ξ ) ] 2 R ξ
R ξ = [ ( ξ + a 2 ) ( ξ + b 2 ) ( ξ + c 2 ) ] 1 / 2 .
ϕ 1 = C 5 F 1 ( ξ ) F 2 ( η ) F 3 ( ζ ) ,
ϕ 2 = [ C 3 + C 4 ξ d ξ ( ξ + a 2 ) R ξ ] F 1 ( ξ ) F 2 ( η ) F 3 ( ζ ) ,
ϕ 0 + ϕ 3 = [ C 1 + C 2 ξ d ξ ( ξ + a 2 ) R ξ ] F 1 ( ξ ) F 2 ( η ) F 3 ( ζ ) .
ϕ 1 = ϕ 2 ,
1 ϕ 1 ξ = 2 ϕ 2 ξ ;
ϕ 2 = ϕ 0 + ϕ 3 ,
2 ϕ 2 ξ = 3 ( ϕ 0 + ϕ 3 ) ξ .
C 2 = ( 3 R 2 S ) C 1 2 S B 3 R B + 2 3 R / a b c ,
R = B A ( 2 1 2 ) ( 2 l m n ) ,
S = B A ( 2 1 2 ) ( 2 l m n ) 2 a b c ,
A = δ d ξ ( ξ + a 2 ) R ξ ; B = 0 d ξ ( ξ + a 2 ) R ξ .
ϕ 0 + ϕ 3 = E 0 x r cos θ 2 C 2 3 C 1 E 0 x cos θ r 2 .
p = 4 π 3 ( 2 C 2 3 C 1 ) E 0 x .
a = [ 2 C 2 3 C 1 / 1 3 1 + 2 3 ] 1 / 3 .
I = π 2 p 2 r 2 λ 0 4 sin 2 ψ .
C sca = 8 π 3 p 2 3 λ 0 4 .
R = B A ,
S = B A 2 / a b c .
A = 2 3 l 3 ; B = 2 3 a 3 ,
R = 2 3 a 3 2 3 l 3 ( 1 + 2 2 1 2 ) ,
S = 4 3 a 3 2 3 l 3 ( 1 + 2 2 1 2 ) ,
C 2 = 3 a 3 2 ( 1 2 ) ( 2 2 + 3 ) q 3 + ( 2 + 3 ) ( 2 2 + 1 ) ( 1 2 ) ( 2 2 + 2 3 ) q 3 ( 2 + 2 3 ) ( 2 2 + 1 ) ,
3 R 2 S = 0 .
2 = B A + 2 / l m n B A + 2 / l m n 2 / a b c
2 = B A B A 2 / a b c ,
2 = 2 + q 3 2 2 q 3
2 = 1 q 3 1 + 2 q 3 .