Abstract

The theory for finding the internal field within a dielectric helix when the radiation has a wavelength larger than the diameter of the helical wire is presented. Intensities are calculated and compared to an experiment and to the theoretical results of an earlier paper that does not include the self-interaction effect. The internal field is defined in terms of a polarization matrix that is assumed to be constant across any cross section of the helix. It is found that target self-iteractions have a significant effect on the internal field. It is also noted that this effect for the far field intensities, although significant and generally a better fit to the data, is not profoundly different. That is, the effects of a more appropriately constructed internal field are less important than the geometry effect in the far field.

© 1989 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. 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]
  2. K. S. Shifrin, Scattering of Light in a Turbid Medium (Moscow, 1951; NASA TTF 447, Washington, DC, 1968).
  3. C. Acquista, “Light Scattering by Tenuous Particles: A Generalization of the Rayleigh-Gans-Rocard Approach,” Appl. Opt. 15, 2932 (1976).
    [Crossref] [PubMed]
  4. L. D. Cohen, R. D. Haracz, A. Cohen, C. Acquista, “Scattering of Light from Arbitrarily Oriented Finite Cylinders,” Appl. Opt. 22, 742 (1983).
    [Crossref] [PubMed]
  5. R. D. Haracz, L. D. Cohen, A. Cohen, “Perturbation Theory for Scattering from Dielectric Spheroids and Short Cylinders,” Appl. Opt. 23, 436 (1984).
    [Crossref] [PubMed]
  6. R. D. Haracz, L. D. Cohen, C. Acquista, “Light Scattering from Dielectric Targets Composed of a Continuous Assembly of Circular Disks,” Appl. Opt. 25, 4386 (1986).
    [Crossref] [PubMed]
  7. S. Zeitz, A. Belmont, C. Nicolini, “Differential Scattering of Circularly Polarized Light as a Unique Probe of Polynecleonsome Superstructures,” Cell Biophys. 5, 163 (1983).
  8. C. Bustamente, M. F. Maestre, D. Keller, I. Tinoco, “Differential Scattering (CIDS) of Circularly Polarized Light by Dense Particles,” J. Chem. Phys. 80, 4817 (1984).
    [Crossref]
  9. S. B. Singham, C. F. Bohren, “Lights Scattering by an Arbitrary Particle: A Physical Reformation of the Coupled Dipole Method,” Opt. Lett. 12, 10 (1987).
    [Crossref] [PubMed]
  10. G. W. Kattawar, C-R Hu, M. E. Parkin, P. Herb, “Mueller Matrix Calculations for Dielectric Cubes: Comparison with Experiments,” Appl. Opt. 26, 4174 (1987).
    [Crossref] [PubMed]
  11. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1965), see Appendix 5.
  12. A paper has just appeared in Applied Optics that also makes a comparison of theory to the same experiment as used in Ref. 1 for a right-handed helix; see P. Chiappetta and B. Torresani, “Electromagnetic Scattering from a Dielectric Helix,” Appl. Opt. 27, 4856 (1988).

1987 (3)

1986 (1)

1984 (2)

R. D. Haracz, L. D. Cohen, A. Cohen, “Perturbation Theory for Scattering from Dielectric Spheroids and Short Cylinders,” Appl. Opt. 23, 436 (1984).
[Crossref] [PubMed]

C. Bustamente, M. F. Maestre, D. Keller, I. Tinoco, “Differential Scattering (CIDS) of Circularly Polarized Light by Dense Particles,” J. Chem. Phys. 80, 4817 (1984).
[Crossref]

1983 (2)

L. D. Cohen, R. D. Haracz, A. Cohen, C. Acquista, “Scattering of Light from Arbitrarily Oriented Finite Cylinders,” Appl. Opt. 22, 742 (1983).
[Crossref] [PubMed]

S. Zeitz, A. Belmont, C. Nicolini, “Differential Scattering of Circularly Polarized Light as a Unique Probe of Polynecleonsome Superstructures,” Cell Biophys. 5, 163 (1983).

1976 (1)

Acquista, C.

Belmont, A.

S. Zeitz, A. Belmont, C. Nicolini, “Differential Scattering of Circularly Polarized Light as a Unique Probe of Polynecleonsome Superstructures,” Cell Biophys. 5, 163 (1983).

Bohren, C. F.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1965), see Appendix 5.

Bustamente, C.

C. Bustamente, M. F. Maestre, D. Keller, I. Tinoco, “Differential Scattering (CIDS) of Circularly Polarized Light by Dense Particles,” J. Chem. Phys. 80, 4817 (1984).
[Crossref]

Cohen, A.

Cohen, L. D.

Haracz, R. D.

Herb, P.

Hu, C-R

Kattawar, G. W.

Keller, D.

C. Bustamente, M. F. Maestre, D. Keller, I. Tinoco, “Differential Scattering (CIDS) of Circularly Polarized Light by Dense Particles,” J. Chem. Phys. 80, 4817 (1984).
[Crossref]

Maestre, M. F.

C. Bustamente, M. F. Maestre, D. Keller, I. Tinoco, “Differential Scattering (CIDS) of Circularly Polarized Light by Dense Particles,” J. Chem. Phys. 80, 4817 (1984).
[Crossref]

Nicolini, C.

S. Zeitz, A. Belmont, C. Nicolini, “Differential Scattering of Circularly Polarized Light as a Unique Probe of Polynecleonsome Superstructures,” Cell Biophys. 5, 163 (1983).

Parkin, M. E.

Shifrin, K. S.

K. S. Shifrin, Scattering of Light in a Turbid Medium (Moscow, 1951; NASA TTF 447, Washington, DC, 1968).

Singham, S. B.

Tinoco, I.

C. Bustamente, M. F. Maestre, D. Keller, I. Tinoco, “Differential Scattering (CIDS) of Circularly Polarized Light by Dense Particles,” J. Chem. Phys. 80, 4817 (1984).
[Crossref]

Wang, R. T.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1965), see Appendix 5.

Zeitz, S.

S. Zeitz, A. Belmont, C. Nicolini, “Differential Scattering of Circularly Polarized Light as a Unique Probe of Polynecleonsome Superstructures,” Cell Biophys. 5, 163 (1983).

Appl. Opt. (6)

Cell Biophys. (1)

S. Zeitz, A. Belmont, C. Nicolini, “Differential Scattering of Circularly Polarized Light as a Unique Probe of Polynecleonsome Superstructures,” Cell Biophys. 5, 163 (1983).

J. Chem. Phys. (1)

C. Bustamente, M. F. Maestre, D. Keller, I. Tinoco, “Differential Scattering (CIDS) of Circularly Polarized Light by Dense Particles,” J. Chem. Phys. 80, 4817 (1984).
[Crossref]

Opt. Lett. (1)

Other (3)

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1965), see Appendix 5.

A paper has just appeared in Applied Optics that also makes a comparison of theory to the same experiment as used in Ref. 1 for a right-handed helix; see P. Chiappetta and B. Torresani, “Electromagnetic Scattering from a Dielectric Helix,” Appl. Opt. 27, 4856 (1988).

K. S. Shifrin, Scattering of Light in a Turbid Medium (Moscow, 1951; NASA TTF 447, Washington, DC, 1968).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Reference or laboratory frame of reference (x0,y0,z0), where the z0 axis is in the direction of the incident radiation. ko is the wave vector for the incident radiation. The axis of the helix, zt, is located relative to (x0,y0,z0) by the polar and azimuthal angles ϕt and γt, respectively. The vector h(ϕ) traces the axis of the helix, with ϕ ranging from zero to 2π times the number of turns.

Fig. 2
Fig. 2

Target frame (xt,yt,zt) is shown along with two disks (cross sections of the helix). The internal field point is located at the center of the disk located by h(ϕ). This disk is located relative to any other in the helix by the vector d(ϕ, ϕ′).

Fig. 3
Fig. 3

Expanded view of the internal field disk (ϕ) relative to any other disk (ϕ′). The inclusion of self-interaction involves adding the effects of all source points (located by r) at the center of the field disk. The integration discussed in the text in connection with Eq. (8) involves the parameters θ and ρ appearing here.

Fig. 4
Fig. 4

Intensity I11(0,0) refers to both incident and scattered radiation linearly polarized perpendicular to the scattering plane. The experimental points of Ref. 1 are shown as crosses, the theoretical points using a constant A matrix is shown as a solid line, and the theoretical points using A determined from Eq. (8) are shown as a solid line with diamonds. The orientation of the helical axis is ϕt = 0° and γt = 0°.

Fig. 5
Fig. 5

Intensity I22(0,0) refers to both incident and scattered radiation linearly polarized in the scattering plane. The experimental points of Ref. 1 are shown as crosses, the theoretical points of Ref. 1 are shown as crosses, the theoretical points using a constant A matrix is shown as a solid line, and the theoretical points using A determined from Eq. (8) are shown as a solid line with diamonds. The orientation of the helical axis is ϕt = 0° and γt = 0°.

Fig. 6
Fig. 6

Same as Fig. 4, but the helical axis is oriented by ϕt = 90° and γt = 0°.

Fig. 7
Fig. 7

Same as Fig. 5, but the helical axis is oriented by ϕt = 90° and γt = 0°.

Fig. 8
Fig. 8

Same as Fig. 4, but the helical axis is oriented by ϕt = 90° and γt = 90°; in this case the two curves coincide.

Fig. 9
Fig. 9

Same as Fig. 5, but the helical axis is oriented by ϕt = 90° and γt = 90°.

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

E ( r ) = E o exp ( i kr ) + × × d V ( m 2 1 ) / ( 4 π ) × exp ( i k | r r | ) / | r r | E ( r ) + ( 1 m 2 ) E ( r ) .
E eff ( r ) = ( m 2 + 2 ) / 3 E ( r ) ,
E eff ( r ) = E o exp ( i kr  ) + α × × d V × exp ( i k | r r | ) / | r r | E eff ( r ) 8 π / 3 α U ( r ) E eff ( r ) ,
E eff ( r ) = E o exp ( i kr ) + α lim σ 0 σ d V ( + k 2 ) × exp ( i k | r r | ) / | r r | E eff ( r )  ,
[ E eff ( r ) ] i = A i j [ E inc ( r ) ] j
A i j ( r ) = δ i j + α σ d V exp ( i k R ) / R × [ r 1 δ i k + ( h i + x i ) ( h k + x k ) r 2 ] × A k j ( r ) exp [ i k ( r h ) ] .
r 1 = [ k 2 ( 1 / R ) 2 + i k / R ]  , r 2 = ( k / R ) 2 + 3 / R 4 3 i k / R 3 .
h ( ϕ ) = a  cos ( ϕ ) i t + a sin ( ϕ ) j t + P / ( 2 π ) ϕ k t
A i j ( ϕ ) = δ i j + α 0 2 π    turns ( a 2 + ( P / ( 4 π ) ) 2 d ϕ × ( ϕ ) r w ρ d ρ  exp [ i kd ( ϕ , ϕ ) ] × 0 2 π d θ ×  exp ( i k R / R )  exp [ i ρ τ ( ϕ )  cos ( θ ) ] × T ( ϕ t ) i l [ r 1 δ l m A ( ϕ ) m n + [ d ( ϕ , ϕ ) l ρ l ] × [ d ( ϕ , ϕ ) m ρ m ] A ( ϕ ) m n r 2 ] ϕ  , T ( t ϕ ) i l .
ε ( ϕ ) = [ ε 2 [ a 2 + ( P / ( 2 π ) ] 2 | ϕ ϕ | 2 ) ] 1 / 2 ,
R 2 = 2 a 2 [ 1 cos ( ϕ ϕ ) ] + [ P / ( 2 π ) ] 2 ( ϕ ϕ ) 2 + ρ 2 2 d ( ϕ ϕ ) ρ ( θ ) .
A i j ( ϕ ) = c 0 i j + c 1 i j z + c 2 i j z 2 + + c n i j Z n ,
c 0 11 = c 0 22 = c 0 33 = 1.0 ,
E ( r ) i = E o i  exp ( i kr ) + α 0 2 π turns d ϕ { a 2 + [ P / ( 2 π ) ] 2 } 1 / 2 × J 1 ( q per a ) / ( q per ) ×  exp [ qh ( ϕ ) ] { T ( ϕ ref ) } m n × { A n o ( ϕ ) x n x o A o p ( ϕ ) } ϕ E o p .
A 11 = A 22 = 2 ( m 2 + 2 ) / [ 3 ( m 2 + 1 ) ] = ( 0.850 , i 0.002 ) , A 33 = ( m 2 + 2 ) / 3 = ( 1.548 , i 0.013 ) .
A = [ ( 0.988 , i 0.125 ) 0 ( 0.005 , i 0.001 ) 0 ( 1.002 , i 0.128 ) 0 ( 0.005 , i 0.002 ) 0 ( 1.684 , i 0.253 ) ] .
A = [ ( 0.711 , i 0.232 ) 0 0 0 ( 0.745 , i 0.189 ) ( 0.095 , i 0.030 ) 0 ( 0.270 , i 0.001 ) ( 1.605 , i 0.646 ) ] .
c 0 11 = 1.088 i 0.045 c 1 11   =   2.91 e 2 i 2.52 e 3 ,      c 2 11 = 3.62 e 4 + i 3.13 e 5 , c 0 12 = 6.90 e 3 + i 8.97 e 2 ,      c 1 12 = 1.71 e 4 i 2.22 e 3 ,      c 2 12 = 0.0 , c 0 13 = 2.59 e 2 i 5.17 e 3 ,      c 1 13 = 6.45 e 4 + i 1.28 e 4 ,      c 2 13 = 0.0 , c 0 21 = 5.13 e 2 + i 6.27 e 2 ,      c 1 21 = 1.27 e 3 i 1.55 e 3 ,      c 2 21 = 0.0 , c 0 22 = 1.319 + i 0.033 ,      c 1 22 = 3.81 e 2 + i 1.84 e 2 ,      c 2 22 = 4.73 e 4 i 2.28 e 4 , c 0 23 = 0.172 0.94 ,       c 1 23 = 1.35 e 2 + 8.09 e 3 ,      c 2 23 = 1.68 e 4 1.01 e 4 , c 0 31 = 4.71 e 2 i 9.07 e 3 ,      c 1 31 = 1.17 e 3 + i 2.26 e 4 ,      c 2 31 = 0.0 , c 0 32 = 0.203 i 0.290 ,      c 1 23 = 1.40 e 2 + i 2.08 e 2 ,      c 2 23 = 1.73 e 4 i 2.58 e 4 , c 0 33 = 1.466 + i 0.131 ,      c 1 33 = 4.42 e 2 + i 1.63 e 2 ,      c 2 33 = 5.48 e 4 i 2.02 e 4.
c 0 11 = 0.852 + i 0.444 ,      c 1 11 = 6.45 e 3 i 6.61 e 3 ,      c 2 11 = 1.76 e 5 i 6.14 e 5 , c 0 12 = 2.78 e 2 + i 3.01 e 2 ,      c 1 12 = 5.94 e 3 i 2.69 e 3 ,      c 2 12 = 7.15 e 6 + i 2.14 e 5 , c 0 13 = 6.64 e 3 i 0.262 ,      c 1 13 = 8.57 e 3 + i 9.53 e 3 ,      c 2 13 = 1.71 e 4 i 7.88 e 5 , c 0 21 = 1.85 e 3 i 1.92 e 3 ,      c 1 21 = 1.00 e 3 i 1.91 e 3 ,      c 2 21 = 3.47 e 5 + i 2.69 e 5 , c 0 22 = 0.872 i 2.63 e 2 ,      c 1 22 = 1.40 e 3 + i 8.00 e 3 ,      c 2 22 = 6.74 e 5 i 1.71 e 5 , c 0 23 = 2.84 e 3 i 3.19 e 2 ,       c 1 23 = 1.11 e 3 + i 1.21 e 3 ,     c 2 23 = 9.37 e 6 i 4.63 e 6 , c 0 31 = 0.138 i 0.239 ,      c 1 31 = 1.33 e 2 + i 5.22 e 3 ,      c 2 31 = 1.85 e 4 9.02 e 6 , c 0 32 = 2.49 e 2 i 8.93 e 2 ,      c 1 32 = 4.46 e 3 + i 1.58 e 3 ,      c 2 32 = 4.05 e 5 + i 2.29 e 5 , c 0 33 = 1.211 + 0.002 ,      c 1 33 = 3.48 e 2 + i 3.70 e 2 ,      c 2 33 = 3.45 e 4 i 7.75 e 5.

Metrics