Scattering Matrix -- from Eric Weisstein's World of Physics

Scattering Matrix

The linearity of the boundary conditions imposed by the Maxwell equations allows the relationship between incident and scattered electric field of a plane wave scattered from an arbitrary particle to be expressed concisely in matrix form

(1)

where the matrix is known as the "amplitude scattering matrix" (van de Hulst 1957, Bohren and Huffman 1983, and Goody and Yung 1989). Note that the labeling of the matrix elements is the same as in Hansen and Travis (1974),

(2)

except that Hansen and Travis (1974) use r and l to stand for perpendicula and paralle, respectively, switch the order of the electric field orientations in the vector, and have a minus sign in the complex exponential (which eliminates the minus sign in front). The matrix equation will be valid for all distances, as long as they are sufficiently far from the origin.

References

Abhyankar, K. D. and Fymat, A. L. "Relations Between the Elements of the Phase Matrix for Scattering." J. Math. Phys. 10, 1935-1938, 1969.

Bohren, C. F. and Huffman, D. R. Absorption and Scattering of Light by Small Particles. New York: Wiley, pp. 57-65, 1983.

Goody, R. M. and Yung, Y. L. Atmospheric Radiation: Theoretical Basis, 2nd ed. New York: Oxford University Press, p. 291, 1989.

Hansen, J. E. and Travis, L. D. "Light Scattering in Planetary Atmospheres." Space Sci. Rev. 16, 527-610, 1974.

van de Hulst, H. C. Light Scattering by Small Particles. New York: Dover, p. 34, 1981.