Light, magnetic vector

If the foregoing created the impression that the electric and magnetic vectors of a propagating electromagnetic field are confined to vibrate in fixed planes, that was unintentional. A field like that would be plane polarized and to create that requires a special device known as a polarizer. Ordinary unpolarized light consists of an array of plane waves that are randomly oriented with respect to a plane perpendicular to the directions of propagation. 

Figure 11.17 Calculated extinction by infinite cylinders for obliquely incident light = 90° corresponds to normally incident light. TE and TM denote light with the electric and magnetic vectors, respectively, perpendicular to the xz plane. From Lind and Greenberg (1966).

This dual nature of light appears puzzling to most students of this field, and cannot be resolved by any simple picture. From our point of view it is sufficient to consider that light is a stream of photons which travels in a straight line at constant velocity c (c = 3 X 108 ms-1). Each photon has an electric vector E and a magnetic vector H that allow interactions with electrons and nuclei through electric and magnetic forces. 

A beam of light is monochromatic if all photons have the same energy (the same frequency or wavelength in the wave picture). A beam of light is completely polarized if all the photons have parallel electric and magnetic vectors (E and H). 

Because the magnetic vector potential, A, is more naturally suited for including in the quantum-mechanical Hamiltonian [20, vll, pg 15-8], the incident light is represented mathematically by the magnetic vector potential ... 

Electromagnetic radiation has associated with it an electric vector E and a magnetic vector H. In linearly polarized light these vectors are mutually per-... 

It is worth recalling that the polarization plane is the one in which oscillations of the electric vector of light wave take place. The magnetic vector oscillates in a plane perpendicular to the latter... 

One usually considers the cross-sections by xOz plane, which coincides with the polarization plane of the incident beam, and by xOy plane, which is perpendicular to the former plane and in which oscillations of magnetic vector of primary wave lie. The scattered light intensity is usually viewed as a function of angle 0 between the directions of incident and scattered waves. For an indicatrix in the plane of polarization xOz, I, the angle 0 is related to the angle cp as 0 = 90° - cp. Consequently, taking into account eq. (V.39) one obtains... 

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