Abstract

Scattering from two neighboring parallel circular cylinders is generalized to the case of an arbitrary ensemble of parallel, nonoverlapping, circular cylinders of arbitrary sizes. An exact solution of Maxwell’s equations is given in terms of a transverse magnetic, and a transverse electric, scalar-potential function, from which the extinction, backscattering, and total-scattering cross sections are obtained, each as an infinite linear sum of the scattering-amplitude coefficients.

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  1. D. S. Jones, The Theory of Electromagnetism (Pergamon, London, 1964), Ch. 8.
  2. G. N. Watson, Theory of Bessel Functions (Cambridge University Press, Cambridge, 1966), p. 361, Eqs. (4) and (5).
  3. V. Twersky, J. Appl. Phys. 23, 407 (1952).
  4. R. V. Row, J. Appl. Phys. 26, 666 (1955).
  5. R. F. Millar, Can. J. Phys. 38, 272 (1960).
  6. N. Zitron and S. N. Karp, J. Math. Phys. 2, 394 (1961).
  7. R. F. Millar, Can. J. Phys. 41, 2106, 2135 (1963); 42, 1149, 2395 (1964); 44, 2839 (1966).
  8. V. Twersky, J. Math. Phys. 8, 589 (1967).
  9. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  10. R. W. Hart and R. A. Farrell, J. Opt. Soc. 59, 766 (1969).
  11. In their investigation of the light scattering from the ensemble of collagen fibrils of the stomal region of the cornea of the eye, Hart and Farrell10 chose a theoretical model that consists of identical "soft," random, parallel, circular cylinders. In our notation, their model corresponds to the case al = a and ml = m (→ 1) for all l = 1, 2, . . ., N.

Farrell, R. A.

R. W. Hart and R. A. Farrell, J. Opt. Soc. 59, 766 (1969).

Hart, R. W.

R. W. Hart and R. A. Farrell, J. Opt. Soc. 59, 766 (1969).

Jones, D. S.

D. S. Jones, The Theory of Electromagnetism (Pergamon, London, 1964), Ch. 8.

Karp, S. N.

N. Zitron and S. N. Karp, J. Math. Phys. 2, 394 (1961).

Millar, R. F.

R. F. Millar, Can. J. Phys. 41, 2106, 2135 (1963); 42, 1149, 2395 (1964); 44, 2839 (1966).

R. F. Millar, Can. J. Phys. 38, 272 (1960).

Row, R. V.

R. V. Row, J. Appl. Phys. 26, 666 (1955).

Twersky, V.

V. Twersky, J. Math. Phys. 8, 589 (1967).

V. Twersky, J. Appl. Phys. 23, 407 (1952).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Watson, G. N.

G. N. Watson, Theory of Bessel Functions (Cambridge University Press, Cambridge, 1966), p. 361, Eqs. (4) and (5).

Zitron, N.

N. Zitron and S. N. Karp, J. Math. Phys. 2, 394 (1961).

Other

D. S. Jones, The Theory of Electromagnetism (Pergamon, London, 1964), Ch. 8.

G. N. Watson, Theory of Bessel Functions (Cambridge University Press, Cambridge, 1966), p. 361, Eqs. (4) and (5).

V. Twersky, J. Appl. Phys. 23, 407 (1952).

R. V. Row, J. Appl. Phys. 26, 666 (1955).

R. F. Millar, Can. J. Phys. 38, 272 (1960).

N. Zitron and S. N. Karp, J. Math. Phys. 2, 394 (1961).

R. F. Millar, Can. J. Phys. 41, 2106, 2135 (1963); 42, 1149, 2395 (1964); 44, 2839 (1966).

V. Twersky, J. Math. Phys. 8, 589 (1967).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

R. W. Hart and R. A. Farrell, J. Opt. Soc. 59, 766 (1969).

In their investigation of the light scattering from the ensemble of collagen fibrils of the stomal region of the cornea of the eye, Hart and Farrell10 chose a theoretical model that consists of identical "soft," random, parallel, circular cylinders. In our notation, their model corresponds to the case al = a and ml = m (→ 1) for all l = 1, 2, . . ., N.

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