Polarisation of EM waves

So far we have treated the plane EM wave with $\vec{E}$ oscillating along one fixed direction (say $y$) and $\vec{B}$ along another fixed direction ($z$): a wave of this type is said to be linearly polarised. The direction of oscillation of $\vec{E}$ defines the polarisation of the wave.

Polarisation of an EM wave

Polarisation is the direction of the electric field $\vec{E}$. The magnetic field $\vec{B}$ is always at $90^\circ$ to $\vec{E}$: once $\vec{E}$ is chosen, $\vec{B}$ is determined too.

Depending on how the tip of the vector $\vec{E}$ moves in the plane transverse to the direction of propagation, three cases are distinguished:

• Linear polarisation: $\vec{E}$ oscillates along a fixed straight line.
• Circular polarisation: $\vec{E}$ has constant magnitude and rotates on a circle (sum of two orthogonal linear polarisations, out of phase by $\pi/2$, with the same amplitude).
• Elliptical polarisation: sum of two orthogonal linear polarisations with different amplitudes and/or phases; the tip of $\vec{E}$ traces an ellipse. This is the general case, of which linear and circular are limiting cases.

The three types of polarisation, seen looking the wave “in the face”: trajectory of the tip of $\vec{E}$ in the transverse plane.

Historical context — Unpolarised light

Sunlight is unpolarised: a disordered superposition of waves with random polarisations, because each atom in the photosphere emits independently of the others. Incandescent bulbs, candle flames, old cathode-ray-tube screens likewise emit unpolarised light. LCD screens, lasers, and light reflected off shiny surfaces at certain angles, on the other hand, are polarised sources (Walker 2013).

Links

Topics: Electromagnetic waves Concepts: Polarisation and Malus’s law · Electromagnetic wave · Electric field

Related exercises: Problem — TV antennas and polarisation · Problem — Microwave oven · Problem — Amplitudes of the solar wave