TPDSci Scattering vector

Scattering vector

The concept of the scattering vector arises in light scattering by tenuous dispersions and particles, i.e. where the local electromagnetic field can be approximated by that of the incident wave. This can be done if the contribution to the electromagnetic field at a region of the medium (or a particle) by waves scattered by other regions can be neglected. Such an approach is know in physics as the Born approximation (for example, http://en.wikipedia.org/wiki/Born_approximation). In light scattering theory it is also known as the Rayleigh-Gans-Debye (RGD) approximation (for example, Bohren and Huffman 1983, p. 158).

The change in the direction of a wave vector after the wave encounters a scattering center, can be expressed in vector notation and in reference to Fig. 1 as follows:

k_s = k_i + q

(1)

where k_s and k_i are the scattered and incident wave vectors and q is the scattering vector. The scattered wave direction should be understood as the observation direction of the scattered light, because the scattered wave is spherical, with a direction-dependent amplitude.

The wave vector, k, can be expressed as a product of its magnitude, k, and a direction unit vector, u. As we consider here only the elastic scattering, the wave vector changes only its direction. Hence Eq. 1 can be rephrased as follows:

q = k ( u_s - u_i )

(2)

It follows from Eq. 2 that a ratio q/k represents a purely geometric relation between the scattered and incident wave directions. The magnitude |q| = q of the scattering vector can be expressed (in reference to Fig. 1) as follows:

q = 2k sin( θ / 2 )

(3)

The scattering angle is sometimes defined as 2θ, which leads to a definition of q = 2ksinθ instead of that given by Eq. 3.

CITATION:
Jonasz M. 2006. Scattering vector (www.tpdsci.com/Tpc/ScaVct.php). In: Top. Part. Disp. Sci. (www.tpdsci.com).

HISTORY:
Published: 15-Jun-2006
Modified: 05-Feb-2008
Reviewed: PENDING

Topics in Particle and Dispersion Science