Abstract

Isotropic scattering is considered for infinite cylinders thin in the sense that ka1, although |ka| and cross-sectional shape can be arbitrary within limits (k and k are, respectively, free-space and interior propagation constants, and a is a characteristic dimension of the cylinder). For circular cylinders, scattering width is found to saturate at its perfectly conducting value, and absorption width is found to peak, when skin depth becomes comparable with cylinder diameter. For a variety of cylinders with and without edges, both scattering and absorption widths are then found to be effectively identical to those of the circular cylinder with equal cross-sectional area. A new analytical formula is obtained for high but not infinite conductivity, and the connection with scattering cross sections of corresponding finite cylinders is discussed.

© 2000 Optical Society of America

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References

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  1. P. C. Waterman, “Surface fields and the T matrix,” J. Opt. Soc. Am. A 16, 2968–2977 (1999).
    [CrossRef]
  2. H. C. Van de Hulst, Light Scattering by Small Particles, 2nd ed. (Wiley, New York, 1957), pp. 304 ff.
  3. D. E. Barrick, “Spheres,” in Radar Cross Section Handbook, G. T. Ruck, D. E. Barrick, W. D. Stuart, C. K. Krichbaum, eds. (Plenum, New York, 1970), pp. 302 ff.
  4. P. C. Waterman, J. C. Pedersen, “Scattering by finite wires of arbitrary ϵ, μ, and σ,” J. Opt. Soc. Am. A 15, 174–184 (1998).
    [CrossRef]
  5. E. H. Newman, “A unified theory of thin material wires,” IEEE Trans. Antennas Propag. 39, 1488–1496 (1991).
    [CrossRef]
  6. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Chaps. 7 and 14.
  7. K. W. Whites, “Resistive and conductive tube boundary condition models for material wire-shaped scatterers,” IEEE Trans. Antennas Propag. 46, 1548–1554 (1998).
    [CrossRef]
  8. P. C. Waterman, “New formulation of acoustic scattering,” J. Acoust. Soc. Am. 45, 1417–1429 (1969).
    [CrossRef]
  9. G. T. Ruck, “Planar surfaces,” in Radar Cross Section Handbook, G. T. Ruck, D. E. Barrick, W. D. Stuart, C. K. Krichbaum, eds. (Plenum, New York, 1970), p. 502.

1999 (1)

1998 (2)

P. C. Waterman, J. C. Pedersen, “Scattering by finite wires of arbitrary ϵ, μ, and σ,” J. Opt. Soc. Am. A 15, 174–184 (1998).
[CrossRef]

K. W. Whites, “Resistive and conductive tube boundary condition models for material wire-shaped scatterers,” IEEE Trans. Antennas Propag. 46, 1548–1554 (1998).
[CrossRef]

1991 (1)

E. H. Newman, “A unified theory of thin material wires,” IEEE Trans. Antennas Propag. 39, 1488–1496 (1991).
[CrossRef]

1969 (1)

P. C. Waterman, “New formulation of acoustic scattering,” J. Acoust. Soc. Am. 45, 1417–1429 (1969).
[CrossRef]

Barrick, D. E.

D. E. Barrick, “Spheres,” in Radar Cross Section Handbook, G. T. Ruck, D. E. Barrick, W. D. Stuart, C. K. Krichbaum, eds. (Plenum, New York, 1970), pp. 302 ff.

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Chaps. 7 and 14.

Newman, E. H.

E. H. Newman, “A unified theory of thin material wires,” IEEE Trans. Antennas Propag. 39, 1488–1496 (1991).
[CrossRef]

Pedersen, J. C.

Ruck, G. T.

G. T. Ruck, “Planar surfaces,” in Radar Cross Section Handbook, G. T. Ruck, D. E. Barrick, W. D. Stuart, C. K. Krichbaum, eds. (Plenum, New York, 1970), p. 502.

Van de Hulst, H. C.

H. C. Van de Hulst, Light Scattering by Small Particles, 2nd ed. (Wiley, New York, 1957), pp. 304 ff.

Waterman, P. C.

Whites, K. W.

K. W. Whites, “Resistive and conductive tube boundary condition models for material wire-shaped scatterers,” IEEE Trans. Antennas Propag. 46, 1548–1554 (1998).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

E. H. Newman, “A unified theory of thin material wires,” IEEE Trans. Antennas Propag. 39, 1488–1496 (1991).
[CrossRef]

K. W. Whites, “Resistive and conductive tube boundary condition models for material wire-shaped scatterers,” IEEE Trans. Antennas Propag. 46, 1548–1554 (1998).
[CrossRef]

J. Acoust. Soc. Am. (1)

P. C. Waterman, “New formulation of acoustic scattering,” J. Acoust. Soc. Am. 45, 1417–1429 (1969).
[CrossRef]

J. Opt. Soc. Am. A (2)

Other (4)

H. C. Van de Hulst, Light Scattering by Small Particles, 2nd ed. (Wiley, New York, 1957), pp. 304 ff.

D. E. Barrick, “Spheres,” in Radar Cross Section Handbook, G. T. Ruck, D. E. Barrick, W. D. Stuart, C. K. Krichbaum, eds. (Plenum, New York, 1970), pp. 302 ff.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Chaps. 7 and 14.

G. T. Ruck, “Planar surfaces,” in Radar Cross Section Handbook, G. T. Ruck, D. E. Barrick, W. D. Stuart, C. K. Krichbaum, eds. (Plenum, New York, 1970), p. 502.

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Figures (6)

Fig. 1
Fig. 1

Cross-section geometry for an infinite cylinder.

Fig. 2
Fig. 2

Scattering widths in decibels versus conductivity x=log[18 σ(ohm m)-1/f(GHz)] for a circular cylinder, ka=0.02π. Dashed line, asymptotic result for absorption from Eq. (11).

Fig. 3
Fig. 3

Cross-sectional shapes: circular, 2:1 and 4:1 elliptical, 2:1 inverted elliptical, square, triangular, semicircular, and conducting strip.

Fig. 4
Fig. 4

Scattering widths in decibels versus conductivity for several cross-sectional shapes, scaled to have equal area (ka=0.02π for the circular cylinder).

Fig. 5
Fig. 5

Scattering widths in decibels as in Fig. 4, for ka=0.001π.

Fig. 6
Fig. 6

Scattering width in decibels versus dielectric constant x=log(ϵrel-1) for several dielectric cylinders, again scaled to equal area (ka=0.02π for the circular cylinder).

Tables (1)

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Table 1 Approximate Values of T00 from Eq. (10) for Perfect Conductorsa

Equations (24)

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kr(θ)=kaρ(θ),
T00=-Reg(Q0)/Q0,
Q0=02πdθ(kr)2×[H0(kr)-(1/2)η0(kr)kr H1(kr)],
η0(kr)=2µrelJ0(kr)/krJ1(kr).
Q0=2π(ka)2[H0(ka)-(1/2)η0(ka)kaH1(ka)],
Ezscat(kr)=T00H0(kr)
T00(2/πkr)0.5 exp i(kr-π/4)forkr1.
σewidth=-(4/k)Re T00,
σswidth=(4/k)|T00|2,
σawidth=-(4/k)(Re T00+|T00|2),
σbwidth=(4/k)|T00|2.
q=k/k=(1+18 iσ/f )0.5,
kδ=k(2/ωμ0σ)0.5=(f/9σ)0.5.
f(Θ)=(4/π)kL2 cos2 Θσswidth[sin(kL cos Θ)/kL cos Θ]2,
σe=Lσewidth
σs=Lσswidth
σa=Lσawidth
σb=(2L2/λ)σbwidth.
T00i(q2/μrel-1)k2Area/4,|ka|1.
T00=-{1+(i/πk2Area)×02πdθ(kr)2[γ+ln(kr/2)-i/qkr]}-1,
T00=-{1+(2i/π)[γ+ln(ka/2)-i/qka]}-1.
ln(kr/2)ln(ka/2)+d(θ).
1/qkr(1/qka)[1-d(θ)].
T00=-{1+(2i/π)[γ+ln(ka/4)]}-1,

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