# What is temporal coherence

## The coherence of light

(Course level > The wave properties of light)

Why can the detection of interference of light waves with light from incandescent lamps only be realized with relatively complicated experimental set-ups and with laser light is it very easy? The light from a laser seems to have different properties than that of an incandescent lamp.

If you use the light of an incandescent lamp to operate the Michelson interferometer, you can see that the path difference between the two partial beams must not be too great. From a path difference of approx.

The light of a laser is characterized by the fact that it

• has only one wavelength (color) ("temporal coherence") and
• all wave fronts have the same direction of propagation ("spatial coherence")

The light from incandescent lamps, on the other hand, is nowhere coherent because it is

• is a mixture of many wavelengths and
• will be sent out in any directions.
• temporally and spatially coherent

• temporally coherent, but not spatially

• spatially coherent, but not temporally

• neither temporally nor spatially coherent

This has to do with the different ways in which the light is generated.

The filament of the lamp is heated electrically. Due to the high temperature, the atoms of the metal thread "wobble" very strongly. The electron shells are raised to higher energy levels. After a certain time, the electron shell returns to the lower-energy position. The shell vibrates and emits an electromagnetic wave, which transports away the excitation energy. This is called "spontaneous emission".
Depending on the strength of the excitation and the type of spontaneous reverse transition, the electron shell vibrates differently, which means that em waves of different frequencies are emitted.
Because the emission is spontaneous, i.e. random, the waves of the many different atoms are not coordinated.
Because the emission only takes a short period of time, short wave trains of approx. [Math] 1000 \, \ rm nm-10,000 \, \ rm nm [/ math][1] that do not have a constant frequency but a small frequency spectrum.

This creates a "mixture" of different wave trains with different frequencies.

Interference experiments with incandescent lamp light are therefore only possible with single wave trains of an atom. Each wave train creates a low-intensity pattern. The spatial coherence is achieved by using suitable diaphragms.

LASER is the abbreviation for: "Light Amplification by Stimulated Emission of Radiation". With a laser, the emission of the em wave from an atom is not spontaneous. The atoms that are permanently excited from the outside emit when they are excited to do so by another em wave. As a result, the wave trains "hang together". The light emitted is coherent.

### Footnotes

1. ↑ See Wikipedia: Coherence length, Michelson interferometer (Matthias Lütgens, April 9, 2005) and experimental physics for biologists, script 10, p.5 (Humboldtuni Berlin winter semester 2011)