Since the molecules can adopt any orientation in space, the polarizability, which normally has tensor character, is considered as a scalar α_L. Through relation (3.51), the incident wave couples to the molecules, which thereby become oscillating Hertzian dipoles. The response of the excited molecule follows from Maxwell’s equations [46]:

To generalize this equation to j particles, the position coordinate r_j and the retarded time t_ret are introduced according to [50]:

Here c denotes the speed of light and n the refractive index of the medium. The generalized field of particle j is therefore:

This rather complicated expression can be simplified by expanding and approximating the exponential function and introducing the Dirac delta function for the particle density (see [51]). The resulting expression for the scattered field is:

Here C is the constant specified in the original expression, and the subscript e denotes quantities associated with the incident wave. Although relation (3.55) follows from theoretical considerations, it does not yet provide direct access to information about the system, owing to limitations of the detector: electric fields at optical frequencies are technically very difficult to detect directly. Instead, the intensity is measured. A connection must therefore be established between (3.55) and the intensity I. The intensity is defined using an ensemble average:

5. Heinrich Hertz (1857–1894), physicist. 6. Direct electrical detection of fields at optical frequencies is technically very difficult.

Original mathematical typography retained. .