Abstract

The scattering and absorption of incident polarized radiation by thin flat circular disks composed of homogeneous isotropic material of complex refractive index is investigated by solving an integral equation for the induced currents. The method is particularly suitable for use in the resonant region where the free space wavelength is neither very small nor very large compared to the radius. Illustrative numerical results for bistatic, total, and absorption cross sections for broadside. and edge-on incidence are given, using refractive indices for ice in the ir.

© 1976 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. D. Reilly, J. Comput. Phys. 11, 463 (1973).
  2. D. E. Livesay, K. M. Chen, IEEE Trans. Microwave Theory Tech. MTT-22, 1273 (1974).
  3. R. F. Harrington, Field Computation by Moment Methods (Macmillan, New York, 1968).
  4. C. M. Chu, H. Weil, “Integral Equation Calculation for the Scattering and Absorption of Electromagnetic Radiation by Thin Discs of Lossy Dielectric,” to be published in J. Comput. Phys.
  5. W. M. Irvine, J. B. Pollack, Icarus 8, 324 (1968).
  6. F. R. Faxvog, Appl. Opt. 13, 1913

1974

D. E. Livesay, K. M. Chen, IEEE Trans. Microwave Theory Tech. MTT-22, 1273 (1974).

1973

E. D. Reilly, J. Comput. Phys. 11, 463 (1973).

1968

W. M. Irvine, J. B. Pollack, Icarus 8, 324 (1968).

1913

F. R. Faxvog, Appl. Opt. 13, 1913

Chen, K. M.

D. E. Livesay, K. M. Chen, IEEE Trans. Microwave Theory Tech. MTT-22, 1273 (1974).

Chu, C. M.

C. M. Chu, H. Weil, “Integral Equation Calculation for the Scattering and Absorption of Electromagnetic Radiation by Thin Discs of Lossy Dielectric,” to be published in J. Comput. Phys.

Faxvog, F. R.

F. R. Faxvog, Appl. Opt. 13, 1913

Harrington, R. F.

R. F. Harrington, Field Computation by Moment Methods (Macmillan, New York, 1968).

Irvine, W. M.

W. M. Irvine, J. B. Pollack, Icarus 8, 324 (1968).

Livesay, D. E.

D. E. Livesay, K. M. Chen, IEEE Trans. Microwave Theory Tech. MTT-22, 1273 (1974).

Pollack, J. B.

W. M. Irvine, J. B. Pollack, Icarus 8, 324 (1968).

Reilly, E. D.

E. D. Reilly, J. Comput. Phys. 11, 463 (1973).

Weil, H.

C. M. Chu, H. Weil, “Integral Equation Calculation for the Scattering and Absorption of Electromagnetic Radiation by Thin Discs of Lossy Dielectric,” to be published in J. Comput. Phys.

Appl. Opt.

F. R. Faxvog, Appl. Opt. 13, 1913

Icarus

W. M. Irvine, J. B. Pollack, Icarus 8, 324 (1968).

IEEE Trans. Microwave Theory Tech.

D. E. Livesay, K. M. Chen, IEEE Trans. Microwave Theory Tech. MTT-22, 1273 (1974).

J. Comput. Phys.

E. D. Reilly, J. Comput. Phys. 11, 463 (1973).

Other

R. F. Harrington, Field Computation by Moment Methods (Macmillan, New York, 1968).

C. M. Chu, H. Weil, “Integral Equation Calculation for the Scattering and Absorption of Electromagnetic Radiation by Thin Discs of Lossy Dielectric,” to be published in J. Comput. Phys.

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 (4)

Fig. 1
Fig. 1

Cross sections in m2 for broadside incidence on a disk vs normalized disk radius ka. Normalized thickness = 0.1. Refractive indices n = 1.13–0.02273j — and n = 1.13–0.2273j - - -: (a) absorption; (b) backscatter; (c) total scattering; (d) extinction.

Fig. 2
Fig. 2

Plots of bistatic cross sections of a disk for broadside incidence for ka = 6.0, ka = 1.07. Normalized thickness = 0.1, refractive index n = 1.13–0.2273j. To the accuracy of these figures the shapes of the curves for the E plane (ϕ = 90°) and H plane (ϕ = 0°) are identical. Similarly the shapes of the corresponding curves for n = 1.13–0.02273j are the same as those shown.

Fig. 3
Fig. 3

Cross sections in m2 for edge-on incidence on a disk with incident electric field parallel to the disk edge plotted vs normalized disk radius ka. Normalized thickness = 0.1. Refractive indices n = 1.13–0.02273j — and n = 1.13–0.2273j - - - - -: (a) total scattering; (b) absorption; (c) backscatter; (d) bistatic into direction ( z ^) of the axis of the disk (labeled ⊥) and forwardscatter (labeled F).

Fig. 4
Fig. 4

Polar plots of bistatic cross sections of a disk for edge-on incidence. Normalized radii ka = 1.07, 6.0. Normalized thickness = 0.1. Refractive indices n = 1.13–0.02273j— and n = 1.13–0.-0273j - - -: (a) H plane ϕ = 0°, 0° ≤ θ ≤ 90° in forward hemisphere; ϕ = 180°, 0° ≤ θ ≤ 90° in back hemisphere. (b) E plane θ = 90°, 0° ≤ ϕ ≤ 90° in forward hemisphere; θ = 90°, 90° ≤ ϕ ≤ 180° in back hemisphere. (c) Transverse plane ϕ = 90°, 0° < θ ≤ 90°. (θ = 0° gives scattering normal to the disk; θ = 90° gives scattering in plane of disk.) In each figure the radial scales for the individual curves differ. Refer to Table I for numerical values at the lobe maxima from which the individual radial scales may be inferred.

Tables (1)

Tables Icon

Table I Maximum Values of σ(θ,ϕ); σ in m2 × 10−16

Equations (18)

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

J = ω 0 ( n 2 - 1 ) E , in D = 0 , outside of D ,
E = E i + Λ ˜ · J .
E ( r ) = - j ω A - ϕ = - j ω μ 0 [ d v J ( r ) ] G ( r , r ) + k - 2 { d v [ · J ( r ) ] G ( r , r ) } ,
E s = Λ · J - j ω μ 0 k 2 Λ ˜ · J = - j ω μ 0 k 2 { D d V J ( R ) G ( R , R ) - S d S [ J ( R ) · n ^ ( R ) ] G ( R ) } .
E i = - 1 j ω 0 [ Λ ˜ · J - J n 2 - 1 ]
J ( R ) = - j ω 0 i α i W i ( R ) .
· W i = 0 in D , W · n ^ 0 on S ,
E i = i α i [ Λ ˜ · W i - 1 n 2 - 1 W i ] .
f , g d v f ( R ) · g ( R )
W j , E i = - i α i [ Z i j - W i j n 2 - 1 ] ,
W i j W i , W j
Z i j W i , Λ ˜ · W j .
Z i j = D d V D d V W i ( R ) · W j ( R ) G ( R , R ) - d S d S n ^ · W i ( R ) n ^ · W j ( R ) G ( R , R ) .
σ B ( θ , ϕ ) = [ d P ( θ , ϕ ) = [ d P ( θ , ϕ ) / d Ω ] / S ,
σ t = 4 π σ B d Ω
σ a = P abs / S ,
n 2 = r - j σ / ( ω 0 ) ,
J c = - j J ( 2 n n ) / ( n 2 - 1 ) .

Metrics