page_title: Plane of polarization
section_title: Malus's choice
hierarchical_section_title: Plane of polarization / History of the term / Malus's choice
context_page_description: The term plane of polarization refers to the direction of polarization of linearly-polarized light or other electromagnetic radiation. Unfortunately the term is used with two contradictory meanings. As originally defined by Étienne-Louis Malus in 1811, the plane of polarization coincided with the plane containing the direction of propagation and the magnetic vector. In modern literature, the term plane of polarization, if it is used at all, is likely to mean the plane containing the direction of propagation and the electric vector, because the electric field has the greater propensity to interact with matter.
  For waves in a birefringent crystal, under the old definition, one must also specify whether the direction of propagation means the ray direction or the wave-normal direction, because these directions generally differ and are both perpendicular to the magnetic vector. Malus, as an adherent of the corpuscular theory of light, could only choose the ray direction.
context_section_description: 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.  In 1808, in the midst of confirming Huygens' geometric description of double refraction (while disputing his physical explanation), Malus had discovered that when a ray of light is reflected off a non-metallic surface at the appropriate angle, it behaves like one of the two rays emerging from a calcite crystal. 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." That definition is identical with Malus's.
caption: Étienne-Louis Malus (1775–1812).
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