27.8 Polarization

Polarization of Electromagnetic Waves

Polarization describes the direction in which an electromagnetic wave's electric field oscillates. This property only exists in transverse waves, where the oscillation is perpendicular to the direction the wave travels. Understanding polarization explains everyday technology like glare-reducing sunglasses and LCD screens, and it shows up throughout optics problems.

Polarization of Electromagnetic Waves

In any electromagnetic wave, the electric field oscillates perpendicular to the direction the wave is moving, and the magnetic field is perpendicular to both the electric field and the propagation direction. Polarization refers to the specific orientation of that electric field oscillation.

Unpolarized light has electric fields oscillating in all random directions perpendicular to the wave's travel. Most common light sources produce unpolarized light: sunlight, incandescent bulbs, and fluorescent lights all fall into this category.

When light is polarized, the electric field oscillates in a predictable pattern. There are three types:

• Linear polarization: The electric field oscillates back and forth in a single plane (for example, purely vertical or purely horizontal). This is the most common type you'll encounter in this course.
• Circular polarization: The electric field vector rotates in a circle as the wave moves forward. It can be right-handed (clockwise) or left-handed (counterclockwise) when viewed head-on.
• Elliptical polarization: The electric field vector traces out an ellipse, which is the most general case. Linear and circular are really just special cases of elliptical.

Methods of Producing Polarized Light

There are several ways to turn unpolarized light into polarized light.

Polarizing filters selectively transmit only one orientation of the electric field. The most common type is a dichroic polarizer, like a Polaroid filter. These contain long-chain molecules (polyvinyl alcohol with embedded iodine crystals) that absorb the electric field component parallel to the chains while transmitting the perpendicular component. Birefringent polarizers, such as calcite crystals or Nicol prisms, work differently: they split incoming light into two beams with perpendicular polarizations, and one beam is selected.

Reflection can also polarize light. When unpolarized light hits a surface like water or glass at a specific angle called Brewster's angle, the reflected light becomes completely polarized (horizontally, parallel to the surface). Brewster's angle is found using:

$\tan \theta_B = \frac{n_2}{n_1}$

where $n_1$ is the refractive index of the medium the light is coming from (often air, $n \approx 1.00$) and $n_2$ is the refractive index of the reflecting surface. For water ($n_2 = 1.33$), Brewster's angle is about $53°$.

Scattering by small particles can partially polarize light. This is why the blue sky is partially polarized: air molecules scatter sunlight through Rayleigh scattering, and the scattered light has a preferred polarization direction. The polarization is strongest at $90°$ from the sun.

Birefringent (anisotropic) materials have optical properties that depend on direction. Light entering these materials splits into two polarized components that travel at different speeds, which can be used to produce polarized light.

Applications of Polarization Principles

Polaroid sunglasses contain polarizing filters oriented to block horizontally polarized light. Glare from flat surfaces like water, snow, and roads is predominantly horizontally polarized (because of reflection near Brewster's angle), so these filters cut glare dramatically while still letting most other light through.

Liquid Crystal Displays (LCDs) sandwich liquid crystal molecules between two polarizing filters with perpendicular transmission axes. Normally, the liquid crystals twist the polarization of light by $90°$ so it can pass through both filters. When a voltage is applied, the molecules realign and stop rotating the polarization, blocking light at that pixel. This is how individual pixels in smartphones, monitors, and televisions are switched on and off.

Optical activity is a property of certain materials that rotate the plane of linearly polarized light passing through them. Solutions of chiral molecules (like sugar or amino acids) do this, and the rotation angle depends on the concentration of the solution and the path length the light travels. This is actually used in medicine to measure glucose concentration in biological samples.

Photoelasticity uses polarized light to reveal stress patterns in transparent materials. When a stressed material is placed between crossed polarizers, colorful fringe patterns appear that map out where stress is concentrated. Engineers use this to analyze structural components.

Polarization and Wave Interactions

Because polarized light is still a wave, superposition applies. Two polarized waves can interfere with each other, but only the components along the same polarization direction will interfere. Waves polarized at $90°$ to each other don't interfere at all.

Malus's Law is the key quantitative relationship for polarization problems. When linearly polarized light with intensity $I_0$ passes through a polarizer whose transmission axis is at angle $\theta$ relative to the light's polarization direction, the transmitted intensity is:

$I = I_0 \cos^2 \theta$

When $\theta = 0°$, all the light gets through ($I = I_0$). When $\theta = 90°$, no light gets through ($I = 0$). For unpolarized light hitting a single ideal polarizer, exactly half the intensity is transmitted: $I = \frac{1}{2}I_0$.

A common exam setup involves stacking multiple polarizers. To find the final intensity, apply Malus's Law at each polarizer in sequence, using the angle between each successive pair of transmission axes.