Correction to 'Electromagnetic Wave Scattering by Assemblies of Particles in the RayleighApproximation'Author(s): A. R. JonesSource: Proceedings of the Royal Society of London. Series A, Mathematical and PhysicalSciences, Vol. 375, No. 1762 (Mar. 31, 1981), pp. 453-454Published by: The Royal SocietyStable URL: http://www.jstor.org/stable/2990317 .

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Proc. R. Soc. Lond. A 375, 453-454 (1981)

Printed in Great Britain

Correction to 'Electromagnetic wave scattering by assemblies of particles in the Rayleigh approximation't

BY A. R. JONES

Department of Chemical Engineering and Chemical Technology, Imperial College, London SW7 2BY, U.K.

(Communicated by A. G. Gaydon, E.R.S. - Received 6 November 1980)

In a previous paper (Jones I979a) a theory was developed for scattering by chains of small spheres. However, certain of the results were questionable as they did not satisfy the reciprocity theorem (Saxon I955). The reason for this has now been traced to an error in the computer program.

The orientation angle X of the chain was given by

cosX = (Zj-Z1)/D1j

but in the original calculations the order of the two Z-terms was reversed. Super- ficially this merely rotates the chain by i and should make no difference. Indeed altering X to X + i yields identical results. However, the error effectively changed the sign of Z and, combined with the phase term exp (-ikr1 cos,8/), was significant for certain intensities.

The correction makes no difference to the components Vv and VH, for the scatter- ing angles 0 = lni, or if the chain is aligned along one of the primary axes. A typical example of the change in HH is shown in figure 1. For random orientation the effect on HH is negligible, as it is for the scattering and absorption efficiencies

(Jones I979b).

0/cleg

-180 -90 0_ 90 180

-20L FIGURE 1. Scattered intensity HE, against angle for a chain of ten equal spheres.

kR = 0. 1, mn = 1.6 -0.8 i. X = 450, 3b = 0?; ---, uncorrected.

t Appeared in Proc. R. Soc. Lond. A 366, 111-127 (1980). [ 453 1

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454 A. R. Jones

The most important factor is the ratio HV/VH for random orientation. This is now found to be unity to within less than about 6 0. An example is seen in figure 2. This deviation can be attributed to rounding error, so that we may conclude that reciprocity is satisfied.

1.2 - \

/ \

~ 1.0 \ 1 0 60 120 o '180 0/deg

0.8 X

1'

0.6 '

FIGURE 2. Comparison of Hv with VH against angle for a chain of ten equal spheres in random orientation. kR = 0.2, m = 1.6-0.8 i; ---, uncorrected.

REFERENCES

Jones, A. R. I979a Proc. R. Soc. Lond. A 366, 111-127. Jones, A. R. I979b J. Phys. D 12, 1661-1672. Saxon, D. S. I955 Phys. Rev. 100, 1771-1775.

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