What is Polarization states? — Physics

Definition 13.3 University Physics — Year 2 · Chapter 13 — Plane Electromagnetic Waves and Polarization

For a PPH wave along $z$ the field in a plane $z =$ const is

\vect E = E_{0x}\cos(\omega t - kz)\,\vect e_x + E_{0y}\cos(\omega t - kz - \varphi)\,\vect e_y ,

and the tip of $\vect E$ describes, in general, an ellipse: elliptical polarization. Two special cases: $\varphi = 0$ or $\pi$ , linear polarization along a fixed direction at angle $\arctan(\pm E_{0y}/E_{0x})$ from $x$ ; $E_{0x} = E_{0y}$ and $\varphi = \pm\pi/2$ , circular polarization, $\vect E$ of constant modulus turning at $\omega$ (right or left according to its sense of rotation, seen facing the oncoming wave). Natural (unpolarized) light, from a lamp or the Sun, is a succession of short wave trains with random, rapidly changing polarizations: no direction is preferred on average. Any polarization decomposes into two linear (or two circular) components.

Left: natural light through three polarizers at 0, 45 and 90 — the middle one lets an eighth through a pair that alone would block everything. Right: Malus’s law. — Left: natural light through three polarizers at $0^\circ$ , $45^\circ$ and $90^\circ$ — the middle one lets an eighth through a pair that alone would block everything. Right: Malus’s law.

Examples

Example 13.5 (Sunglasses, screens, photographs)

Light reflected at a glancing angle from water or asphalt is largely polarized horizontally (Brewster’s angle, Chapter 15): sunglasses with a vertical transmission axis cut the glare and keep the rest. A liquid-crystal screen emits polarized light: through a polarizer at $90{}^{\circ}$ it goes black. A photographer’s polarizing filter darkens the sky (scattered light is partly polarized, Chapter 17) and removes reflections from glass.

Example 13.7 (Where plates are used)

A quarter-wave plate between a polarizer and a mirror makes an optical isolator: the light goes out circular, comes back circular of the opposite handedness, is turned by the plate into linear light at $90{}^{\circ}$ from the polarizer and is absorbed — no reflection returns to the laser. The two eyes’ images of a 3D film are projected in opposite circular polarizations and sorted by the quarter-wave–polarizer sandwiches of the glasses, which still work when you tilt your head (linear polarizers would not). A transparent ruler between crossed polarizers shows coloured fringes: stress makes plastic birefringent, and engineers read the stresses of a model from the pattern.

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