Three candidates Whether by accident or by design, the plane of polarization has always been defined as the plane containing a field vector and a direction of propagation. In Fig.1, there are three such planes, to which we may assign numbers for ease of reference: :(1) the plane containing both electric vectors and both propagation directions (i.e., the plane normal to the magnetic vectors); :(2a) the plane containing the magnetic vectors and the wave-normal (i.e., the plane normal to
D); :(2b) the plane containing the magnetic vectors and the ray (i.e., the plane normal to
E). In an isotropic medium,
E and
D have the same direction, so that the ray and wave-normal directions merge, and the planes (2a) and (2b) become one: :(2) the plane containing both magnetic vectors and both propagation directions (i.e., the plane normal to the electric vectors).
Malus's choice Polarization was discovered — but not named or understood — by
Christiaan Huygens, as he investigated the double refraction of "Iceland crystal" (transparent
calcite, now called
Iceland spar). The essence of his discovery, published in his
Treatise on Light (1690), was as follows. When a ray (meaning a narrow beam of light) passes through two similarly oriented calcite crystals at normal incidence, the ordinary ray emerging from the first crystal suffers only the ordinary refraction in the second, while the extraordinary ray emerging from the first suffers only the extraordinary refraction in the second. But when the second crystal is rotated 90° about the incident rays, the roles are interchanged, so that the ordinary ray emerging from the first crystal suffers only the extraordinary refraction in the second, and vice versa. At intermediate positions of the second crystal, each ray emerging from the first is doubly refracted by the second, giving four rays in total; and as the crystal is rotated from the initial orientation to the perpendicular one, the brightnesses of the rays vary, giving a smooth transition between the extreme cases in which there are only two final rays. Huygens defined a
principal section of a calcite crystal as a plane normal to a natural surface and parallel to the axis of the obtuse
solid angle. This axis was parallel to the axes of the
spheroidal
secondary waves by which he (correctly) explained the directions of the extraordinary refraction. The term
polarization was coined by
Étienne-Louis Malus in 1811. As this behavior had previously been known only in connection with double refraction, Malus described it in that context. In particular, he defined the
plane of polarization of a polarized ray as the plane, containing the ray, in which a principal section of a calcite crystal must lie in order to cause only
ordinary refraction. This definition was all the more reasonable because it meant that when a ray was polarized by reflection (off an isotopic medium), the plane of polarization was the
plane of incidence and reflection — that is, the plane containing the incident ray, the normal to the reflective surface, and the polarized reflected ray. But, as we now know, this plane happens to contain the
magnetic vectors of the polarized ray, not the electric vectors. The plane of the ray and the magnetic vectors is the one numbered
(2b) above. The implication that the plane of polarization contains the
magnetic vectors is still found in the definition given in the online Merriam-Webster dictionary. Even
Julius Adams Stratton, having said that "It is customary to define the polarization in terms of
E", promptly adds: "In optics, however, the orientation of the vectors is specified traditionally by the 'plane of polarization,' by which is meant the plane normal to
E containing both
H and the axis of propagation." Supposing that light waves were analogous to
shear waves in
elastic solids, and that a higher
refractive index corresponded to a higher
density of the
luminiferous aether, he found that he could account for the partial reflection (including polarization by reflection) at the interface between two transparent isotropic media, provided that the vibrations of the aether were perpendicular to the plane of polarization. Thus the polarization, according to the received definition, was "in" a certain plane if the vibrations were
perpendicular to that plane! Fresnel himself found this implication inconvenient; later that year he wrote: ::Adopting this hypothesis, it would have been more natural to have called the plane of polarisation that in which the oscillations are supposed to be made: but I wished to avoid making any change in the received appellations. But he soon felt obliged to make a less radical change. In his successful model of double refraction, the displacement of the medium was constrained to be tangential to the wavefront, while the force was allowed to deviate from the displacement and from the wavefront. Hence, if the vibrations were perpendicular to the plane of polarization, then the plane of polarization contained the wave-normal but not necessarily the ray. In his "Second Memoir" on double refraction, Fresnel formally adopted this new definition, acknowledging that it agreed with the old definition in an isotropic medium such as air, but not in a birefringent crystal. But it could not be extended to birefringent crystals — in which at least one refractive index varies with direction — because density is not directional. Hence his explanation of refraction required a directional variation in
stiffness of the aether
within a birefringent medium, plus a variation in density
between media.
James MacCullagh and
Franz Ernst Neumann avoided this complication by supposing that a higher refractive index corresponded always to the same density but a greater elastic
compliance (lower stiffness). To obtain results that agreed with observations on partial reflection, they had to suppose, contrary to Fresnel, that the vibrations were
within the plane of polarization. The question called for an experimental determination of the direction of vibration, and the challenge was answered by
George Gabriel Stokes. He defined the
plane of vibration as "the plane passing through the ray and the direction of vibration" (in agreement with Fig.1). Now suppose that a fine
diffraction grating is illuminated at normal incidence. At large angles of diffraction, the grating will appear somewhat edge-on, so that the directions of vibration will be crowded towards the direction parallel to the plane of the grating. If the planes of polarization coincide with the planes of vibration (as MacCullagh and Neumann said), they will be crowded in the same direction; and if the planes of polarization are
normal to the planes of vibration (as Fresnel said), the planes of polarization will be crowded in the normal direction. To find the direction of the crowding, one could vary the polarization of the incident light in equal steps, and determine the planes of polarization of the diffracted light in the usual manner. Stokes performed such an experiment in 1849, and it found in favor of Fresnel. In 1852, Stokes noted a much simpler experiment that leads to the same conclusion. Sunlight scattered from a patch of blue sky 90° from the sun is found, by the methods of Malus, to be polarized in the plane containing the line of sight and the sun. But it is obvious from the geometry that the vibrations of that light can only be perpendicular to that plane. There was, however, a sense in which MacCullagh and Neumann were correct. If we attempt an analogy between shear waves in a non-isotropic elastic solid, and EM waves in a magnetically isotropic but electrically non-isotropic crystal, the density must correspond to the magnetic
permeability (both being non-directional), and the compliance must correspond to the electric
permittivity (both being directional). The result is that the velocity of the solid corresponds to the
H field, so that the mechanical vibrations of the shear wave are in the direction of the
magnetic vibrations of the EM wave. But Stokes's experiments were bound to detect the
electric vibrations, because those have the greater propensity to interact with matter. In short, the MacCullagh-Neumann vibrations were the ones that had a mechanical analog, but Fresnel's vibrations were the ones that were more likely to be detected in experiments.
Modern practice The electromagnetic theory of light further emphasized the
electric vibrations because of their interactions with matter, == Remaining uses ==