Rayleigh Scattering – EM Wave Direction After Rayleigh Scattering

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I have a problem in figuring out where and how a beam of light is scattered by a molecule (Rayleigh scattering), in the two pictures I posted two different situations seem to be illustrated: in the first picture the incident wave after scattering is spread out in all the space with different intensity depending on the angle while in the second image the incident beam is scattered in just one direction. Now my questions:

1. What is the right image? What happens once the incident beam is scattered? Does it become a spherical wave that spread all over the space? Does it have a definite propagation direction?

2. Since the scattered light is due to the induced electric dipole, does an oscillating electric dipole always radiate spherical waves? If yes, is it possible to have a spherical wave with different inesities in different points of its wave-front like in the first image?

3. Should I think of the first image as the possible scenario of a Rayleigh scattering i.e.: illustrates the various intensities the scattered light will have depending on the angle at which it is emitted?

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Best Answer

  1. The second image is a reasonable picture. The first could be possible but would need qualification and explanation.

Rayleigh scattering occurs when the electric dipole moment of the molecule is made to oscillate in the direction of the electric field of the incoming wave. The oscillating electric dipole then emits "dipole radiation", which has a dipole antenna pattern $\propto \sin^2 \theta$; the intensity of dipole radiation is not spherically symmetric and there is no radiation along the axis of the oscillating dipole.

However, all depends on the polarisation state of the incoming light. If it is plane polarised, then the intensity of the scattered light has a dipolar anisotropy (but the wavefronts would still be spherical) as described above. If it is unpolarized, then there is no preferred axis for the molecular dipole oscillations, but no dipole oscillation in the same direction as the incident light - the scattered light would then have an intensity $\propto 1 + \cos^2 \theta$.

  1. Yes, see above. The "spherical" waves will be anisotropic in intensity, especially if the incoming light has any linear polarisation.

  2. Yes. The arrows could represent the Poynting vector of the scattered light, which can vary with the scattering angle.

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