Polarisation is a property of transverse waves in which the direction of oscillation of the wave’s field vector is restricted to a particular orientation.
In a longitudinal wave the oscillations are parallel to the direction of propagation, so there is no independent direction that can be selected. In a transverse wave the oscillations are perpendicular to the direction of travel, providing a plane in which the direction can be fixed.
| Type | Oscillation pattern | Key characteristics |
|---|---|---|
| Linear | Oscillation occurs in a single plane | Electric field vector remains in a fixed direction |
| Circular | Electric field rotates at constant magnitude, tracing a circle | Phase difference of $90^\circ$ between orthogonal components |
| Elliptical | General case; tip of the field vector traces an ellipse | Arbitrary phase difference and amplitude ratio |
EM waves consist of mutually perpendicular electric ($\mathbf{E}$) and magnetic ($\mathbf{B}$) fields that are both transverse to the direction of propagation $\mathbf{k}$. The polarisation of an EM wave is defined by the direction of its electric field vector.
When linearly polarised light of initial intensity $I_0$ passes through a second polariser (analyser) whose transmission axis makes an angle $\theta$ with the incident polarisation direction, the transmitted intensity $I$ is
$$I = I_0 \cos^2\theta$$This relationship is fundamental for experiments that measure the degree of polarisation.
If $I_0 = 100\ \text{W m}^{-2}$ and the analyser is set at $\theta = 30^\circ$, the transmitted intensity is
$$I = 100 \cos^2 30^\circ = 100 \times \left(\frac{\sqrt{3}}{2}\right)^2 = 75\ \text{W m}^{-2}.$$