Abstract

The solution of the multiple-scattering problem for two parallel infinite dielectric cylinders is considered for plane wave illumination perpendicular to the cylinder axes. Numerical results show the coupling effect with respect to cylinder size, separation, and orientation of the cylinder axes with respect to the incident wave. The coupling effect is illustrated by calculations of the internal and near-field intensity for end-on and broadside incidence. Results for circular cylinders with a size/wavelength ratio corresponding to a particular morphology-dependent resonance (size parameter = 45.329) show that the local effect of the resonance is completely damped when the two cylinders touch.

© 1988 Optical Society of America

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References

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  1. V. Twersky, “Multiple Scattering of Radiation by an Arbitrary Configuration of Parallel Cylinders,” J. Acoust. Soc. Am. 24, 42 (1952).
    [CrossRef]
  2. V. Twersky, “Scattering of Waves by Two Objects,” in Electromagnetic Waves, R. E. Langer, Ed. (U. Wisconsin Press, Madison, 1962), pp. 361–389.
  3. G. O. Olaofe, “Scattering by Two Cylinders,” Radio Sci. 5, 1351 (1970).
    [CrossRef]
  4. J. W. Young, J. C. Bertrand, “Multiple Scattering by Two Cylinders,” J. Acoust. Soc. Am. 58, 1190 (1975).
    [CrossRef]
  5. W. Wasylkiwskyj, “On the Transmission Coeffient of an Infinite Grating of Parallel Perfectly Conducting Circular Cylinders,” IEEE Trans. Antennas Propag. AP-19, 704 (1971).
    [CrossRef]
  6. H. A. Kalhor, A. Armand, “Scattering of Waves by Gratings of Conducting Cylinders,” Proc. IEEE 122, 245 (1975).
    [CrossRef]
  7. H. Sugiyama, S. Kozaki, “Multiple Scattering of a Gaussian Beam by Two Cylinders Having Different Radii,” Trans. Inst. Electron. Commun. Eng. Jpn. E65, 173 (1982).
  8. T. Kojima, A. Ishikura, M. Ieguchi, “Scattering of Hermite-Gaussian Beams by Two Parallel Conducting Cylinders,” Report of the Technical Group on Antennas and Propagation TGAP 83-36 (Institute of Electronics and Communications Engineers of Japan, Tokyo, Aug.1983).
  9. S. Kozaki, “Scattering of a Gaussian Beam by a Homogeneous Dielectric Cylinder,” J. Appl. Phys. 53, 7195 (1982).
    [CrossRef]
  10. M. Yokota, T. Takenaka, O. Fukumitsu, “Scattering of a Hermite-Gaussian Beam Mode by Parallel Dielectric Cylinders,” J. Opt. Soc. Am. A 3, 580 (1986).
    [CrossRef]
  11. B. Schlicht, K. F. Wall, R. K. Chang, P. W. Barber, “Light Scattering by Two Parallel Glass Fibers,” J. Opt. Soc. Am. A 4, 800 (1987).
    [CrossRef]
  12. D. S. Benincasa, P. W. Barber, J. Z. Zhang, W. F. Hsieh, R. K. Chang, “Spatial Distribution of the Internal and Near-Field Intensity of Large Cylindrical and Spherical Scatterers,” Appl. Opt. 26, 1348 (1987).
    [CrossRef] [PubMed]
  13. J. F. Owen, R. K. Chang, P. W. Barber, “Internal Electric Field Distributions of a Dielectric Cylinder at Resonance Wavelengths,” Opt. Lett. 6, 540 (1981).
    [CrossRef] [PubMed]
  14. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

1987 (2)

1986 (1)

1982 (2)

H. Sugiyama, S. Kozaki, “Multiple Scattering of a Gaussian Beam by Two Cylinders Having Different Radii,” Trans. Inst. Electron. Commun. Eng. Jpn. E65, 173 (1982).

S. Kozaki, “Scattering of a Gaussian Beam by a Homogeneous Dielectric Cylinder,” J. Appl. Phys. 53, 7195 (1982).
[CrossRef]

1981 (1)

1975 (2)

H. A. Kalhor, A. Armand, “Scattering of Waves by Gratings of Conducting Cylinders,” Proc. IEEE 122, 245 (1975).
[CrossRef]

J. W. Young, J. C. Bertrand, “Multiple Scattering by Two Cylinders,” J. Acoust. Soc. Am. 58, 1190 (1975).
[CrossRef]

1971 (1)

W. Wasylkiwskyj, “On the Transmission Coeffient of an Infinite Grating of Parallel Perfectly Conducting Circular Cylinders,” IEEE Trans. Antennas Propag. AP-19, 704 (1971).
[CrossRef]

1970 (1)

G. O. Olaofe, “Scattering by Two Cylinders,” Radio Sci. 5, 1351 (1970).
[CrossRef]

1952 (1)

V. Twersky, “Multiple Scattering of Radiation by an Arbitrary Configuration of Parallel Cylinders,” J. Acoust. Soc. Am. 24, 42 (1952).
[CrossRef]

Armand, A.

H. A. Kalhor, A. Armand, “Scattering of Waves by Gratings of Conducting Cylinders,” Proc. IEEE 122, 245 (1975).
[CrossRef]

Barber, P. W.

Benincasa, D. S.

Bertrand, J. C.

J. W. Young, J. C. Bertrand, “Multiple Scattering by Two Cylinders,” J. Acoust. Soc. Am. 58, 1190 (1975).
[CrossRef]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Chang, R. K.

Fukumitsu, O.

Hsieh, W. F.

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Ieguchi, M.

T. Kojima, A. Ishikura, M. Ieguchi, “Scattering of Hermite-Gaussian Beams by Two Parallel Conducting Cylinders,” Report of the Technical Group on Antennas and Propagation TGAP 83-36 (Institute of Electronics and Communications Engineers of Japan, Tokyo, Aug.1983).

Ishikura, A.

T. Kojima, A. Ishikura, M. Ieguchi, “Scattering of Hermite-Gaussian Beams by Two Parallel Conducting Cylinders,” Report of the Technical Group on Antennas and Propagation TGAP 83-36 (Institute of Electronics and Communications Engineers of Japan, Tokyo, Aug.1983).

Kalhor, H. A.

H. A. Kalhor, A. Armand, “Scattering of Waves by Gratings of Conducting Cylinders,” Proc. IEEE 122, 245 (1975).
[CrossRef]

Kojima, T.

T. Kojima, A. Ishikura, M. Ieguchi, “Scattering of Hermite-Gaussian Beams by Two Parallel Conducting Cylinders,” Report of the Technical Group on Antennas and Propagation TGAP 83-36 (Institute of Electronics and Communications Engineers of Japan, Tokyo, Aug.1983).

Kozaki, S.

S. Kozaki, “Scattering of a Gaussian Beam by a Homogeneous Dielectric Cylinder,” J. Appl. Phys. 53, 7195 (1982).
[CrossRef]

H. Sugiyama, S. Kozaki, “Multiple Scattering of a Gaussian Beam by Two Cylinders Having Different Radii,” Trans. Inst. Electron. Commun. Eng. Jpn. E65, 173 (1982).

Olaofe, G. O.

G. O. Olaofe, “Scattering by Two Cylinders,” Radio Sci. 5, 1351 (1970).
[CrossRef]

Owen, J. F.

Schlicht, B.

Sugiyama, H.

H. Sugiyama, S. Kozaki, “Multiple Scattering of a Gaussian Beam by Two Cylinders Having Different Radii,” Trans. Inst. Electron. Commun. Eng. Jpn. E65, 173 (1982).

Takenaka, T.

Twersky, V.

V. Twersky, “Multiple Scattering of Radiation by an Arbitrary Configuration of Parallel Cylinders,” J. Acoust. Soc. Am. 24, 42 (1952).
[CrossRef]

V. Twersky, “Scattering of Waves by Two Objects,” in Electromagnetic Waves, R. E. Langer, Ed. (U. Wisconsin Press, Madison, 1962), pp. 361–389.

Wall, K. F.

Wasylkiwskyj, W.

W. Wasylkiwskyj, “On the Transmission Coeffient of an Infinite Grating of Parallel Perfectly Conducting Circular Cylinders,” IEEE Trans. Antennas Propag. AP-19, 704 (1971).
[CrossRef]

Yokota, M.

Young, J. W.

J. W. Young, J. C. Bertrand, “Multiple Scattering by Two Cylinders,” J. Acoust. Soc. Am. 58, 1190 (1975).
[CrossRef]

Zhang, J. Z.

Appl. Opt. (1)

IEEE Trans. Antennas Propag. (1)

W. Wasylkiwskyj, “On the Transmission Coeffient of an Infinite Grating of Parallel Perfectly Conducting Circular Cylinders,” IEEE Trans. Antennas Propag. AP-19, 704 (1971).
[CrossRef]

J. Acoust. Soc. Am. (2)

V. Twersky, “Multiple Scattering of Radiation by an Arbitrary Configuration of Parallel Cylinders,” J. Acoust. Soc. Am. 24, 42 (1952).
[CrossRef]

J. W. Young, J. C. Bertrand, “Multiple Scattering by Two Cylinders,” J. Acoust. Soc. Am. 58, 1190 (1975).
[CrossRef]

J. Appl. Phys. (1)

S. Kozaki, “Scattering of a Gaussian Beam by a Homogeneous Dielectric Cylinder,” J. Appl. Phys. 53, 7195 (1982).
[CrossRef]

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

Opt. Lett. (1)

Proc. IEEE (1)

H. A. Kalhor, A. Armand, “Scattering of Waves by Gratings of Conducting Cylinders,” Proc. IEEE 122, 245 (1975).
[CrossRef]

Radio Sci. (1)

G. O. Olaofe, “Scattering by Two Cylinders,” Radio Sci. 5, 1351 (1970).
[CrossRef]

Trans. Inst. Electron. Commun. Eng. Jpn. (1)

H. Sugiyama, S. Kozaki, “Multiple Scattering of a Gaussian Beam by Two Cylinders Having Different Radii,” Trans. Inst. Electron. Commun. Eng. Jpn. E65, 173 (1982).

Other (3)

T. Kojima, A. Ishikura, M. Ieguchi, “Scattering of Hermite-Gaussian Beams by Two Parallel Conducting Cylinders,” Report of the Technical Group on Antennas and Propagation TGAP 83-36 (Institute of Electronics and Communications Engineers of Japan, Tokyo, Aug.1983).

V. Twersky, “Scattering of Waves by Two Objects,” in Electromagnetic Waves, R. E. Langer, Ed. (U. Wisconsin Press, Madison, 1962), pp. 361–389.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

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Figures (13)

Fig. 1
Fig. 1

Geometry of the problem.

Fig. 2
Fig. 2

Extinction efficiency Qext vs the size of the cylinder ka for TM polarization (the index of refraction m = 1.33) as the two cylinders are touching (δ = 2ka). The 2Qext (dashed line) is twice the extinction efficiency of a single cylinder.

Fig. 3
Fig. 3

Same as Fig. 2 except the separation δ = 20ka.

Fig. 4
Fig. 4

Extinction efficiency Qext vs the angle of incidence β for TM polarization, ka = 5, m = 1.33, and five values of cylinder separation. 2Qext is the uncoupled scattering efficiency.

Fig. 5
Fig. 5

Extinction efficiency Qext vs the separation of the two cylinders for TM polarization, ka = 5, m = 1.33, and four values of the incident angle. 2Qext is the uncoupled scattering efficiency.

Fig. 6
Fig. 6

Calculated intensity along the bisector of the two infinite cylinders for end-on illumination and TM polarization when two cylinders are touching (ka = 50, m = 1.33, and δ = 100).

Fig. 7
Fig. 7

Same as Fig. 6 except δ = 200.

Fig. 8
Fig. 8

Same as Fig. 6 except δ = 1000.

Fig. 9
Fig. 9

Calculated intensity along the bisector of the two cylinders for end-on illumination and TM polarization when the cylinder size-to-wavelength ratio corresponds to a morphology-dependent resonance (two cylinders are touching with ka = 45.329, m = 1.530, and δ = 2ka = 90.658).

Fig. 10
Fig. 10

Same as Fig. 9 except δ = 101.99.

Fig. 11
Fig. 11

Same as Fig. 9 except δ = 150.

Fig. 12
Fig. 12

Backscattering efficiency Qbsca vs the size parameter for end-on illumination and different values of separation.

Fig. 13
Fig. 13

Same as Fig. 12 except for broadside incidence.

Equations (22)

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u 1 inc = - exp ( - i w t ) k n = - i n + 1 J n ( ρ 1 ) exp ( - i n γ 1 ) ,
u 2 inc = - exp ( - i w t ) k exp ( i δ cos β ) n = - i n + 1 J n ( ρ 2 ) exp ( - i n γ 2 ) .
u 1 s = exp ( - i w t ) k n = - i n + 1 b 1 n H n ( ρ 1 ) exp ( - i n γ 1 ) ;
u 2 s = exp ( - i w t ) k n = - i n + 1 b 2 n H n ( ρ 2 ) exp ( - i n γ 2 ) .
u 1 trans = exp ( - i w t ) k n = - i n + 1 d 1 n J n ( m ρ 1 ) exp ( - i n γ 1 ) ,
u 2 trans = exp ( - i w t ) k n = - i n + 1 d 2 n J n ( m ρ 2 ) exp ( - i n γ 2 ) ,
exp ( - i n θ 2 ) H n ( ρ 2 ) = ( - 1 ) n l = - H n + l ( δ ) J l ( ρ 1 ) exp ( i l θ 1 ) ,
u 2 s = exp ( - i w t ) k n = - i n + 1 b 2 n H n ( ρ 2 ) exp ( - i n γ 2 ) = exp ( - i w t ) k n = - J n ( ρ 1 ) exp ( i n θ 1 ) B 21 n ,
b 1 n = b n [ 1 + i n + 1 exp ( i n β ) B 21 - n ] ,
b 2 n = b n [ exp ( i δ cos β ) + i n + 1 exp ( i n β ) B 12 - n ] .
B 21 n = l = - ( - 1 ) l i l + 1 b 2 l exp ( - i l β ) H n + l ( δ ) ,
B 12 n = ( - 1 ) n l = - i l + 1 b 1 l exp ( - i l β ) H n + l ( δ ) .
L = F + C L ,
L = b 1 - N b 1 0 b 1 N b 2 - N b 2 0 b 2 N ,
F = b N b 0 b N b N b 0 b N ,
C = [ 0 C 1 C 2 0 ] .
b 1 - n = b n + l = 1 N [ b n i - n + 2 exp ( - i n β ) ( - 1 ) l i - l H n - l ( δ ) exp ( i l β ) ] 2 b - l + [ b n i - n + 2 exp ( - i n β ) H n ] 2 b 0 + l = 1 N [ b n i - n + 2 exp ( - i n β ) ( - 1 ) l i l H n + l ( δ ) exp ( - i l β ) ] 2 b l , b 1 n = b n + l = 1 N [ b n i n + 2 exp ( i n β ) ( - 1 ) l i - l H - n - l ( δ ) exp ( i l β ) ] 2 b - l + [ b n i n + 2 exp ( i n β ) H - n ] 2 b 0 + l = 1 N [ b n i n + 2 exp ( i n β ) ( - 1 ) l i l H - n + l ( δ ) exp ( - i l β ) ] 2 b l ,
b 2 - n = b n exp ( i δ cos β ) + l = 1 N [ ( - 1 ) n b n i - n + 2 × exp ( - i n β ) i - l H n - l ( δ ) exp ( i l β ) ] 1 b - l + [ ( - 1 ) n b n i - n + 2 exp ( - i n β ) H n ] 1 b 0 + l = 1 N [ ( - 1 ) n b n i - n + 2 exp ( - i n β ) i l H n + l ( δ ) exp ( - i l β ) ] 1 b l , b 2 n = b n exp ( i δ cos β ) + l = 1 N [ ( - 1 ) n b n i n + 2 × exp ( i n β ) i - l H - n - l ( δ ) exp ( i l β ) ] 1 b - l + [ ( - 1 ) n b n i n + 2 exp ( i n β ) H n ] 1 b 0 + l = 1 N [ ( - 1 ) n b n i n + 2 exp ( i n β ) i l H - n + l ( δ ) exp ( - i l β ) ] 1 b l ,
L = ( I - C ) - 1 F .
( I - C ) - 1 = I + C + C 2 + .
Q ext = 2 k a n = - Re [ b 1 n + b 2 n exp ( i δ cos β ) ] .
Q bsca = 2 k a | n = - ( - 1 ) n [ b 1 n + b 2 n exp ( i δ cos β ) ] | 2 ,

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