Linear polarization

Linear polarization, also referred to as plane polarization, describes a state of electromagnetic radiation in which the electric field vector (and consequently the magnetic field vector) oscillates within a single, fixed plane along the direction of wave propagation. The term "linear polarization" (or, in French, polarisation rectiligne) was introduced by the physicist Augustin-Jean Fresnel in 1822. The orientation of such a wave is defined by the direction of its electric field vector; for instance, a wave whose electric field alternates vertically is described as vertically polarized.

Mathematically, a classical sinusoidal plane wave solution to the electromagnetic wave equation can be expressed for both the electric and magnetic fields. The wave's behavior in a given plane, such as the x-y plane, is often described using a Jones vector, which captures the amplitude and phase of the field components. A wave is linearly polarized when the phase angles of its two orthogonal components (for example, along the x and y axes) are equal. In this case, the resulting electric field oscillates along a line at a specific angle relative to the x-axis.

The Jones vector for such a wave can be written to reflect this single direction of oscillation. The special cases of pure x-polarization or pure y-polarization are subsets of this general linear state. By defining unit vectors along the x and y axes, the polarization state can be represented in this "x-y basis" as a combination of those two orthogonal, in-phase components. This confinement of the field to a single plane distinguishes linear polarization from other forms, such as circular or elliptical polarization.