Abstract

We compute the differential scattering cross sections for a dielectric helix whose dimensions are comparable to the incident radiation wavelength, using a discrete model and a multiple scattering development (low energy model). The numerical results are compared to experimental data on microwave scattering by a dielectric right-handed helix.

© 1988 Optical Society of America

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References

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  1. E. M. Purcell, C. R. Pennypacker, “Scattering and Absorption of Light by Nonspherical Dielectric Grains,” Astrophys. J. 186, 705 (1973).
    [CrossRef]
  2. P. Chiappetta, “Multiple Scattering Approach to Light Scattering by Arbitrarily Shaped Particles,” J. Phys. A Gen. Phys. 13, 220 (1980).
  3. P. Chiappetta, J. M. Perrin, B. Torresani, “Low Energy Light Scattering: A Multiple Scattering Description,” Nuovo Cimento 9D, 717 (1987).
    [CrossRef]
  4. R. T. Wang, “Electromagnetic Scattering from a Helix,” Final report TCN-85-597 CRDC, Battelle (1986).
  5. R. D. Haracz, L. D. Cohen, A. Cohen, R. T. Wang, “Scattering of Linearly Polarized Microwave Radiation from a Dielectric Helix,” Appl. Opt. 26, 4632 (1987).
    [CrossRef] [PubMed]
  6. K. S. Shifrin, Scattering of Light in a Turbid Medium (Moscow, 1951; NASA TTF 447, Washington, DC, 1968); C. Aquista, “Light Scattering by Tenuous Particles: A Generalization of the Rayleigh-Gans-Rocard Approach,” Appl. Opt. 15, 2932 (1976).
    [CrossRef]

1987 (2)

P. Chiappetta, J. M. Perrin, B. Torresani, “Low Energy Light Scattering: A Multiple Scattering Description,” Nuovo Cimento 9D, 717 (1987).
[CrossRef]

R. D. Haracz, L. D. Cohen, A. Cohen, R. T. Wang, “Scattering of Linearly Polarized Microwave Radiation from a Dielectric Helix,” Appl. Opt. 26, 4632 (1987).
[CrossRef] [PubMed]

1980 (1)

P. Chiappetta, “Multiple Scattering Approach to Light Scattering by Arbitrarily Shaped Particles,” J. Phys. A Gen. Phys. 13, 220 (1980).

1973 (1)

E. M. Purcell, C. R. Pennypacker, “Scattering and Absorption of Light by Nonspherical Dielectric Grains,” Astrophys. J. 186, 705 (1973).
[CrossRef]

Chiappetta, P.

P. Chiappetta, J. M. Perrin, B. Torresani, “Low Energy Light Scattering: A Multiple Scattering Description,” Nuovo Cimento 9D, 717 (1987).
[CrossRef]

P. Chiappetta, “Multiple Scattering Approach to Light Scattering by Arbitrarily Shaped Particles,” J. Phys. A Gen. Phys. 13, 220 (1980).

Cohen, A.

Cohen, L. D.

Haracz, R. D.

Pennypacker, C. R.

E. M. Purcell, C. R. Pennypacker, “Scattering and Absorption of Light by Nonspherical Dielectric Grains,” Astrophys. J. 186, 705 (1973).
[CrossRef]

Perrin, J. M.

P. Chiappetta, J. M. Perrin, B. Torresani, “Low Energy Light Scattering: A Multiple Scattering Description,” Nuovo Cimento 9D, 717 (1987).
[CrossRef]

Purcell, E. M.

E. M. Purcell, C. R. Pennypacker, “Scattering and Absorption of Light by Nonspherical Dielectric Grains,” Astrophys. J. 186, 705 (1973).
[CrossRef]

Shifrin, K. S.

K. S. Shifrin, Scattering of Light in a Turbid Medium (Moscow, 1951; NASA TTF 447, Washington, DC, 1968); C. Aquista, “Light Scattering by Tenuous Particles: A Generalization of the Rayleigh-Gans-Rocard Approach,” Appl. Opt. 15, 2932 (1976).
[CrossRef]

Torresani, B.

P. Chiappetta, J. M. Perrin, B. Torresani, “Low Energy Light Scattering: A Multiple Scattering Description,” Nuovo Cimento 9D, 717 (1987).
[CrossRef]

Wang, R. T.

Appl. Opt. (1)

Astrophys. J. (1)

E. M. Purcell, C. R. Pennypacker, “Scattering and Absorption of Light by Nonspherical Dielectric Grains,” Astrophys. J. 186, 705 (1973).
[CrossRef]

J. Phys. A Gen. Phys. (1)

P. Chiappetta, “Multiple Scattering Approach to Light Scattering by Arbitrarily Shaped Particles,” J. Phys. A Gen. Phys. 13, 220 (1980).

Nuovo Cimento (1)

P. Chiappetta, J. M. Perrin, B. Torresani, “Low Energy Light Scattering: A Multiple Scattering Description,” Nuovo Cimento 9D, 717 (1987).
[CrossRef]

Other (2)

R. T. Wang, “Electromagnetic Scattering from a Helix,” Final report TCN-85-597 CRDC, Battelle (1986).

K. S. Shifrin, Scattering of Light in a Turbid Medium (Moscow, 1951; NASA TTF 447, Washington, DC, 1968); C. Aquista, “Light Scattering by Tenuous Particles: A Generalization of the Rayleigh-Gans-Rocard Approach,” Appl. Opt. 15, 2932 (1976).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Geometry of the problem (the scattering plane is the xOz plane).

Fig. 2
Fig. 2

Intensity function i11 vs the scattering angle θ for the helix orientation φt = γt = θ° (helical axis parallel to k). Comparison to experimental data.

Fig. 3
Fig. 3

Intensity function i22 vs the scattering angle θ for the helix orientation φt = γt = 0° (helical axis parallel to k). Comparison to experimental data.

Fig. 4
Fig. 4

Same legend as for Fig. 2 for the helix orientation φt = 90° and γt = 0° (helical axis perpendicular to k but parallel to the scattering plane).

Fig. 5
Fig. 5

Same legend as for Fig. 3 for the helix orientation φt = 90° and γt = 0° (helical axis perpendicular to k but parallel to the scattering plane).

Fig. 6
Fig. 6

Same legend as for Fig. 2 for the helix orientation φt = γt = 90° (helical axis perpendicular to k and to the scattering plane).

Fig. 7
Fig. 7

Same legend as for Fig. 3 for the helix orientation φt = γt = 90° (helical axis perpendicular to k and to the scattering plane).

Fig. 8
Fig. 8

Cross polarized intensity i12 vs the scattering angle θ for the helix orientation φt = γt = 90° (helical axis perpendicular to k and to the scattering plane).

Fig. 9
Fig. 9

Cross polarized intensity i21 vs the scattering angle θ for the helix orientation φt = γt = 90° (helical axis perpendicular to k and to the scattering plane).

Fig. 10
Fig. 10

Intensity functions i11 (full curve) and i22 (dashed curve) vs the scattering angle θ for a left-handed helix in the orientation φt = γt = 90° (helical axis perpendicular to k and to the scattering plane).

Equations (11)

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α = 3 4 π ρ m 2 - 1 m 2 + 2 ,
E inc ( r , t ) = e inc E 0 exp { i ( k · r - ω t ) } .
k = 2 π λ e z .
d i ( t ) = α · E ( r i , t ) .
E ( r i , t ) = E inc ( r i , t ) + j = 1 j 1 N T ( r i j ) · d j ( t ) .
T ( r ) = exp ( i k · r ) r 3 { k 2 r 2 ( 1 - r r r 2 ) + ( 1 - i k r ) ( 3 r r r 2 - 1 ) }
d i ( t ) = α E inc ( r i , t ) + α 2 j = 1 j 1 N T ( r i j ) · E inc ( r j , t ) + α 2 p = 1 p j N j = 1 j i N T ( r i j ) · T ( r j p ) · E inc ( r p , t ) + .
E sca ( r , t ) r k 2 exp ( i k · r ) r i = 1 N exp ( - i k r i · n ) ( 1 - n n ) · d i ( t ) .
d σ d Ω = I sca · n I inc r 2 ,
I = 1 2 R e ( E H * ) ,
i ɛ i ɛ s ( θ , φ ) = lim r 2 k 6 | i = 1 N exp { - i k r i · n } d i ( t ) · e ɛ s | 2 ,

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