Abstract

When analyzing the two-dimensional multiple scattering of electromagnetic waves by cylinders, the incident, scattered, and transmitted fields need to be represented by infinite sums of cylindrical wave modes. These infinite sums need to be truncated to a finite limit in order to calculate the scattering matrix. The accuracy of the scattered field representation and the stability of the matrix inversion are both critically dependent on the truncation limit. The parameters involved in the scattering are analyzed to determine their effect on the upper and lower bounds of an appropriate modal truncation.

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References

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  1. H. A. Ragheb and M. Hamid, Int. J. Electron. 59, 407 (1985).
    [CrossRef]
  2. T. G. Tsuei and P. W. Barber, Appl. Opt. 27, 3375 (1988).
    [CrossRef] [PubMed]
  3. J. W. Young and J. C. Bertrand, J. Acoust. Soc. Am. 58, 1190 (1975).
    [CrossRef]
  4. S. J. Bever and J. P. Allebach, Appl. Opt. 31, 3524 (1992).
    [CrossRef] [PubMed]
  5. A. Z. Elsherbeni, Radio Sci. 29, 1023 (1994).
    [CrossRef]
  6. G. Olaofe, J. Opt. Soc. Am. 60, 1233 (1970).
    [CrossRef]

1994 (1)

A. Z. Elsherbeni, Radio Sci. 29, 1023 (1994).
[CrossRef]

1992 (1)

1988 (1)

1985 (1)

H. A. Ragheb and M. Hamid, Int. J. Electron. 59, 407 (1985).
[CrossRef]

1975 (1)

J. W. Young and J. C. Bertrand, J. Acoust. Soc. Am. 58, 1190 (1975).
[CrossRef]

1970 (1)

Allebach, J. P.

Barber, P. W.

Bertrand, J. C.

J. W. Young and J. C. Bertrand, J. Acoust. Soc. Am. 58, 1190 (1975).
[CrossRef]

Bever, S. J.

Elsherbeni, A. Z.

A. Z. Elsherbeni, Radio Sci. 29, 1023 (1994).
[CrossRef]

Hamid, M.

H. A. Ragheb and M. Hamid, Int. J. Electron. 59, 407 (1985).
[CrossRef]

Olaofe, G.

Ragheb, H. A.

H. A. Ragheb and M. Hamid, Int. J. Electron. 59, 407 (1985).
[CrossRef]

Tsuei, T. G.

Young, J. W.

J. W. Young and J. C. Bertrand, J. Acoust. Soc. Am. 58, 1190 (1975).
[CrossRef]

Appl. Opt. (2)

Int. J. Electron. (1)

H. A. Ragheb and M. Hamid, Int. J. Electron. 59, 407 (1985).
[CrossRef]

J. Acoust. Soc. Am. (1)

J. W. Young and J. C. Bertrand, J. Acoust. Soc. Am. 58, 1190 (1975).
[CrossRef]

J. Opt. Soc. Am. (1)

Radio Sci. (1)

A. Z. Elsherbeni, Radio Sci. 29, 1023 (1994).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Minimum accuracy mode limit M v is displayed for k a v factors that are (a) small, (b) medium, and (c) large.

Fig. 2
Fig. 2

Multiple scattering of a Gaussian beam from 11 perfectly conducting cylinders with broadside incidence.

Fig. 3
Fig. 3

Multiple scattering of a Gaussian beam from 11 conducting cylinders with in-line incidence.

Fig. 4
Fig. 4

Matrix condition number compared to the mode limit. The results are identical for broadside and in-line incidence.

Equations (6)

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E ( ρ v , θ v ) = n = j n exp ( j n θ v ) Z n ( k ρ v ) v b n ,
f n v = J n ( k a v ) H n ( 2 ) ( k a v ) ,
f n v = J n ( k a v ) J n ( ε v k a v ) ε v J n ( k a v ) J n ( ε v k a v ) ε v H n ( 2 ) ( k a v ) J n ( ε v k a v ) H n ( 2 ) ( k a v ) J n ( ε v k a v ) ,
M v 1.0302 k a v + 4.5585 10 k a v 200 M v 1.2174 k a v + 2.0578 0.5 k a v 10 ,
M v = 2 , 0.08125 k a v 0.5 1 , k a v 0.08125 .
C ext = 4 k Re [ n = v = 1 N b n v exp ( j k d 1 v cos ϕ 1 v ) ] ,

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