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The coherence length can be measured using a Michelson interferometer and is the optical path length difference of a self-interfering laserbeam which corresponds to a 1 / e = 37% fringe visibility, where the fringe visibility is defined as

where I is the fringe intensity. Multimode helium-neon lasers have a typical coherence length of 20 cm, while semiconductor lasers reach some 100 m. Fiber lasers can have coherence lengths exceeding 100 km.

Population inversion

In physics, specifically statistical mechanics, a

population inversion occurs when a system (such as a group of atoms or molecules) exists in state with more members in an excited state than in lower energy states. The concept is of fundamental importance in laser science because the production of a population inversion is a necessary step in the workings of a laser.

Boltzmann distributions and thermal equilibrium

To understand the concept of a population inversion, it is necessary to understand some thermodynamics and the way that light interacts with matter. To do so, it is useful to consider a very simple assembly of atoms forming a laser medium.

Assume there are a group of N atoms, each of which is capable of being in one of two energy states, either

1. The ground state , with energy E

1 ; or 2. The excited state , with energy E

2 , with

E

2 > E

1 .

The number of these atoms which are in the ground state is given by N

1 , and the number in the excited state N

2 . Since there are N atoms in total,

N

1

+ N

2

= N

The energy difference between the two states, given by

Δ E

12

= E

2

− E

1 ,

determines the characteristic frequency ν

12 of light which will interact with the atoms; This is given by the relation

E

2

− E

1

= Δ E = h ν

12 ,

h being Planck's constant.

If the group of atoms is in thermal equili-brium, it can be shown from thermodynamics that the ratio of the number of atoms in each state is given by a Boltzmann distribution:

,

where T is the thermodynamic temperature of the group of atoms, and k is Boltzmann's constant.

We may calculate the ratio of the populations of the two states at room temperature ( T ≈ 300 K) for an energy difference Δ E that