Abstract

The electromagnetic scattering from finite-length dielectric fibers with a diameter much smaller than the wavelength and for a perpendicular incidence case is considered. The induced fields are assumed to be uniform on the cross section of the fiber. This yields a one-dimensional integral equation for the inner field which is solved by employing Galerkin’s method. Numerical results for the scattering amplitude are obtained for specific cases. In addition, it is shown that the energy finiteness criterion is satisfied.

© 1978 Optical Society of America

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References

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  1. N. K. Uzunoglu, “Theoretical Calculations of Scattering of Electromagnetic Waves from Precipitation Particles,” Ph.D. Thesis, Colchester, England (unpublished).
  2. N. K. Uzunoglu and A. R. Holt, “The scattering of electromagnetic radiation from dielectric scatterers,” J. Phys. A: Math, Nucl. Gen. 10, 413 (1977).
    [Crossref]
  3. T. Oguchi, “Scattering properties of oblate raindrops and cross polarization of radio waves due to rain: Calculations at 19.3 and 34.8 GHz,” J. Radio Res. Lab. 20, 79 (1973).
  4. J. A. Morrison and M. J. Cross, “Scattering of a plane electromagnetic wave by axisymmetric raindrops,” Bell Syst. Tech. J. 53, 955 (1974).
    [Crossref]
  5. P. C. Waterman, “Matrix Formulation of Electromagnetic Scattering,” Proc. IEEE,  53, 805 (1965).
    [Crossref]
  6. R. H. Duncan and F. A. Hinchey, “Cylindrical Antenna Theory,” J. Res. Nat. Bur. Stand. D: Radio Prop. 64D, 569 (1960).
    [Crossref]
  7. D. S. Jones, The Theory of ElectromagnetismPergamon, London, 1964) Chap. 9.
  8. R. F. Harrington, Field Computation by Moment Methods, (Macmillan, New York, 1968).
  9. P. M. Morse and H. Feschbach, Methods of Theoretical Physics, (McGraw-Hill, New York, 1953).
  10. R. G. Newton, Scattering of Waves and Particles, (McGraw-Hill, New York, 1964), Chap. 1.

1977 (1)

N. K. Uzunoglu and A. R. Holt, “The scattering of electromagnetic radiation from dielectric scatterers,” J. Phys. A: Math, Nucl. Gen. 10, 413 (1977).
[Crossref]

1974 (1)

J. A. Morrison and M. J. Cross, “Scattering of a plane electromagnetic wave by axisymmetric raindrops,” Bell Syst. Tech. J. 53, 955 (1974).
[Crossref]

1973 (1)

T. Oguchi, “Scattering properties of oblate raindrops and cross polarization of radio waves due to rain: Calculations at 19.3 and 34.8 GHz,” J. Radio Res. Lab. 20, 79 (1973).

1965 (1)

P. C. Waterman, “Matrix Formulation of Electromagnetic Scattering,” Proc. IEEE,  53, 805 (1965).
[Crossref]

1960 (1)

R. H. Duncan and F. A. Hinchey, “Cylindrical Antenna Theory,” J. Res. Nat. Bur. Stand. D: Radio Prop. 64D, 569 (1960).
[Crossref]

Cross, M. J.

J. A. Morrison and M. J. Cross, “Scattering of a plane electromagnetic wave by axisymmetric raindrops,” Bell Syst. Tech. J. 53, 955 (1974).
[Crossref]

Duncan, R. H.

R. H. Duncan and F. A. Hinchey, “Cylindrical Antenna Theory,” J. Res. Nat. Bur. Stand. D: Radio Prop. 64D, 569 (1960).
[Crossref]

Feschbach, H.

P. M. Morse and H. Feschbach, Methods of Theoretical Physics, (McGraw-Hill, New York, 1953).

Harrington, R. F.

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

Hinchey, F. A.

R. H. Duncan and F. A. Hinchey, “Cylindrical Antenna Theory,” J. Res. Nat. Bur. Stand. D: Radio Prop. 64D, 569 (1960).
[Crossref]

Holt, A. R.

N. K. Uzunoglu and A. R. Holt, “The scattering of electromagnetic radiation from dielectric scatterers,” J. Phys. A: Math, Nucl. Gen. 10, 413 (1977).
[Crossref]

Jones, D. S.

D. S. Jones, The Theory of ElectromagnetismPergamon, London, 1964) Chap. 9.

Morrison, J. A.

J. A. Morrison and M. J. Cross, “Scattering of a plane electromagnetic wave by axisymmetric raindrops,” Bell Syst. Tech. J. 53, 955 (1974).
[Crossref]

Morse, P. M.

P. M. Morse and H. Feschbach, Methods of Theoretical Physics, (McGraw-Hill, New York, 1953).

Newton, R. G.

R. G. Newton, Scattering of Waves and Particles, (McGraw-Hill, New York, 1964), Chap. 1.

Oguchi, T.

T. Oguchi, “Scattering properties of oblate raindrops and cross polarization of radio waves due to rain: Calculations at 19.3 and 34.8 GHz,” J. Radio Res. Lab. 20, 79 (1973).

Uzunoglu, N. K.

N. K. Uzunoglu and A. R. Holt, “The scattering of electromagnetic radiation from dielectric scatterers,” J. Phys. A: Math, Nucl. Gen. 10, 413 (1977).
[Crossref]

N. K. Uzunoglu, “Theoretical Calculations of Scattering of Electromagnetic Waves from Precipitation Particles,” Ph.D. Thesis, Colchester, England (unpublished).

Waterman, P. C.

P. C. Waterman, “Matrix Formulation of Electromagnetic Scattering,” Proc. IEEE,  53, 805 (1965).
[Crossref]

Bell Syst. Tech. J. (1)

J. A. Morrison and M. J. Cross, “Scattering of a plane electromagnetic wave by axisymmetric raindrops,” Bell Syst. Tech. J. 53, 955 (1974).
[Crossref]

J. Phys. A: Math, Nucl. Gen. (1)

N. K. Uzunoglu and A. R. Holt, “The scattering of electromagnetic radiation from dielectric scatterers,” J. Phys. A: Math, Nucl. Gen. 10, 413 (1977).
[Crossref]

J. Radio Res. Lab. (1)

T. Oguchi, “Scattering properties of oblate raindrops and cross polarization of radio waves due to rain: Calculations at 19.3 and 34.8 GHz,” J. Radio Res. Lab. 20, 79 (1973).

J. Res. Nat. Bur. Stand. D: Radio Prop. (1)

R. H. Duncan and F. A. Hinchey, “Cylindrical Antenna Theory,” J. Res. Nat. Bur. Stand. D: Radio Prop. 64D, 569 (1960).
[Crossref]

Proc. IEEE (1)

P. C. Waterman, “Matrix Formulation of Electromagnetic Scattering,” Proc. IEEE,  53, 805 (1965).
[Crossref]

Other (5)

D. S. Jones, The Theory of ElectromagnetismPergamon, London, 1964) Chap. 9.

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

P. M. Morse and H. Feschbach, Methods of Theoretical Physics, (McGraw-Hill, New York, 1953).

R. G. Newton, Scattering of Waves and Particles, (McGraw-Hill, New York, 1964), Chap. 1.

N. K. Uzunoglu, “Theoretical Calculations of Scattering of Electromagnetic Waves from Precipitation Particles,” Ph.D. Thesis, Colchester, England (unpublished).

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Figures (4)

FIG. 1
FIG. 1

Geometry of thin and finite scatterer.

FIG. 2
FIG. 2

Backscattering intensity IB vs (kob) for koa = 0.02.

FIG. 3
FIG. 3

Total (extinction) cross section vs (kob) for koa = 0.02.

FIG. 4
FIG. 4

Differential cross section vs (Θs) for kob = 2, koa = 0.02 and n = 10. + i0.0.

Tables (2)

Tables Icon

TABLE I Convergence pattern for the forward scattering amplitude [ z ˆf(π/2) = f(π/2)] computed by using Φ m ( i ) ( z ) ; i = 1 , 2 , 3;i = 1,2,3 representations. The scatterer is defined by koa = 0.02, kob = 2, and n = 10.

Tables Icon

TABLE II Comparison with Rayleigh-Gans approximation for koa = 0.02, kob = 0.5, and n = 1.4.

Equations (24)

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E ( r ) = ê i exp ( i k i · r ) + [ k o 2 ( n 2 - 1 ) ] / 4 π V d r ( 1 + k o - 2 grad grad ) G ( r , r ) · E ( r ) ,
G ( r , r ) = exp ( i k o r - r ) / r - r
E ( z ) = 2 J 1 ( k o a ) k o a + k o 2 ( n 2 - 1 ) 4 π × V d r 0 a ρ d ρ 0 2 π d ϕ ( 1 + k o - 2 d 2 d z 2 ) G ( r , r ) E ( z ) ,
G ( r , r ) = i m = - + exp [ i m ( ϕ - ϕ ) × h = 0 + d h J m ( h ρ ) J m ( h ρ ) h exp ( i s z - z ) / s ,
n 2 E ( z ) = 1 + i ( n 2 - 1 ) × - b / 2 b / 2 d z h = 0 + h d h J 1 2 ( h a ) exp ( i s z - z ) s E ( z ) ,
f ( k s ) = k o 2 ( n 2 - 1 ) 4 π ( l ¯ - k ˆ s k ˆ s ) × V exp ( - i k s · r ) E ( r ) d r ,
f ( Θ s ) = ( k o a ) 2 ( n 2 - 1 ) 4 ( z ˆ - k ˆ s cos Θ s ) × - b / 2 b / 2 d z exp ( - i k o z cos Θ s ) E ( z ) ,
e i s z - z s = - m = - + 1 - ( - 1 ) m exp ( i s b ) b i ( s 2 - k m 2 ) exp [ i k m ( z - z ) ] ,
E ( z ) = i = - N + N c i Φ i ( z ) ,
Φ m ( 1 ) = exp ( i 2 π m z / b ) ,             m = - N , , N ,
Φ m ( 2 ) = exp ( i π m z / b ) ,             m = - N , , N ,
Φ m ( 3 ) = exp ( i k o n z m Z ) ,
m - N + N K ( m , n ) c n = B ( m ) ,
K ( m , n ) = n 2 - b / 2 b / 2 Φ m ( z ) Φ n ( z ) d z + ( n 2 - 1 ) b × - b / 2 b / 2 d z - b / 2 b / 2 d z r = - + Φ * m ( z ) exp [ i k r ( z - z ) ] × Φ n ( z ) a r ,
a r = h = 0 + h d h J 1 2 ( h a ) 1 - ( - 1 ) r exp ( i s b ) s 2 - k r 2
B ( m ) = - b / 2 b / 2 d z Φ * m z ) .
f ( Θ s ) = [ ( k o a ) 2 ( n 2 - 1 ) / 4 ] ( z ˆ - k ˆ s cos Θ s ) i = - N + N c i A ( i ) ,
A ( i ) = - b / 2 b / 2 Φ i ( z ) exp ( - i k o z cos Θ s ) d z .
2 E z ( r ) + k o 2 n 2 E z ( r ) = 0.
E z ( r ) = m p = - 1 + 1 a m ( p ) J m [ k o n ρ ( 1 - p 2 ) 1 / 2 ] × e i k o n p z e i m Φ d p ,
E z ( r ) p = - 1 + 1 a o ( p ) e i k o n p z d p .
f ( π / 2 ) = k o 2 ( n 2 - 1 ) a 2 b / 4
W = - b / 2 b / 2 E * ( z ) E ( z ) d z = b 2 m , m C m * C m × sin [ k o n ( z m - z m ) b / 2 ] ( z m - z m ) k o n b / 2 .
W ( b / 2 ) m , m c m c m .