Plane of polarization

Lore & Background

The plane of polarization was originally defined by Étienne-Louis Malus in 1811, based on his experiments with light reflected from surfaces. Malus, adhering to the corpuscular theory of light, defined it as the plane containing the direction of propagation (the ray direction) and the magnetic vector, though this was not understood at the time. Augustin-Jean Fresnel, in his wave-theory explanation of double refraction from 1822 onward, redefined the plane of polarization to contain the wave-normal direction and the magnetic vectors, ensuring that the supposed vibrations of the medium were perpendicular to this plane. Fresnel admitted that, had he not been constrained by existing terminology, it would have been more natural to define the plane of polarization as the plane containing the vibrations and the direction of propagation—a plane that became known as the plane of vibration, perpendicular to Fresnel's plane but identical to the modern convention.

Physics of the term

In modern literature, the term plane of polarization, if used, typically refers to the plane containing the direction of propagation and the electric vector, because the electric field interacts more strongly with matter. This convention is used in the online Encyclopædia Britannica and in Feynman's lectures on polarization, and it describes the polarization of radio signals and antennas. For waves in birefringent crystals, the ray direction and wave-normal direction generally differ, and both are perpendicular to the magnetic vector, leading to three possible planes: the plane containing both electric vectors and both propagation directions (normal to the magnetic vectors), the plane containing the magnetic vectors and the wave-normal (normal to D), and the plane containing the magnetic vectors and the ray (normal to E). In isotropic media, these reduce to a single plane.

Malus's choice

The discovery of polarization is attributed to Christiaan Huygens, who observed double refraction in calcite (Iceland spar) and published his findings in his Treatise on Light (1690). Huygens noted that when two calcite crystals are aligned, the ordinary and extraordinary rays from the first crystal behave predictably in the second, but rotating the second crystal interchanges their roles. He defined a principal section of calcite as a plane normal to a natural surface and parallel to the axis of the obtuse solid angle.

Reader's Guide

The plane of polarization is significant primarily because of its historical ambiguity, which has led to persistent confusion in optics and related fields. The term was coined by Malus in 1811, but its meaning shifted with Fresnel's wave theory, and modern usage often favors the electric-field convention due to the greater propensity of the electric field to interact with matter. This convention is standard for describing radio signals and antennas, as seen in the example of a vertically polarized parabolic-grid microwave antenna where the polarization refers to the alignment of the electric field.

In birefringent crystals, the distinction between ray and wave-normal directions adds further complexity, making the term even more problematic. It has been argued that the term plane of polarization should be avoided in original writing because of its historical ambiguity; one can instead specify the orientation of a particular field vector, and even the term plane of vibration carries less risk of confusion. The legacy of the term is that it encapsulates the evolution of electromagnetic theory from Huygens's early observations through Malus's discovery to Maxwell's later unification, but its continued use requires careful attention to which convention is intended.