LASER

Laser technology is based on

Light Amplification by Stimulated Emission of Radiation

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Fig. 1: Spontaneous and induced incidents between a higher energy level m and a lower level n. Nm or Nn respectively denotes the number of atoms or molecules in the level.

With u(ν) as the spectral radiation density (details here ), the relative numbers of spontaneous to induced emission for thermal equilibrium is given by:

Within the visible range of the electromagnetic spectrum, e.g. for green light with a wavelength of λ = 500 nm = c ⋅&nu^-1 and a temperature of 300 Kelvin, this ratio becomes F = e⁹⁶ = 5⋅10⁴¹. Therefore, among 5⋅10⁴¹ incidents, only one is due to induced emission.

In contrast, for the microwave range with frequency ν = 1 GHz = 10⁹ Hz and the same temperature the expected ratio F is 1.6⋅10^-4. Therefore, nearly all incidents are induced. For a wavelength of 60 &my;m, spontaneous and induced processes contribute to the same (F = 1) extent to emission. Thus, it is not astonishing that the first laser produced microwaves. In the respective publication of 1954 by Townes et al., the experimental setup is described as NH₃-Maser. By the way, masers have existed for millions of years in the universe, especially in regions where new stars are formed. So far, OH-, H₂O- and an SiO-maser have been observed. The reaction H₂O (hν < 190 nm) → OH + H or collisions occuring in specific states come into question as the source for OH.

Fig. 2: Main components of a laser

Independent from the construction in detail, lasers are characterised by two energy levels. The number of species in the higher energy level exceeds the one in the lower level. Therefore all lasers have three components in common (Fig. 2): A pump, that charges the molecules in a laser cavity and a resonator, due to which a photon produced by the elementary process of induced emission is likely to initiate another event of the same kind.

 

Fig. 3:To realize an overpopulation of the upper energy level, at least three energy levels have to be present in the medium within laser cavity. a) Three level principle of a ruby laser, b) Four level principle.

The first laser system developed by Maiman in 1960 was a ruby laser based on the three level principle. Nowadays, the four level principle is fundamental for almost all lasers systems as, with this principle, a weakly populated lower energy level is easier to realize.

The properties of laser light:

Monochromatic (coherence respective time)
Laser light is confined to a narrow band Δν around the frequency ν_L. (Hänsch was able to reach a ratio Δν/ν_L≈ 10^-15). Therefore, lasers are used to to adjust high resolution spectroscopic appliances.

Non divergent (spatial coherence)
Due to coupling of the molecules or atoms within the resonator, an almost not divergent beam of light of diameter D is obtained. Ideally, the uncertainty principle is the limiting factor for the angle with which the beam widens.

Using a lens, it is possible to focus a laser beam on a spot of diameter d.

Here, f denotes the focal distance of the lens. As, for the best lenses, the ratio of focal lens to diameter is about 0.8, it is a rule of thumb that half the wavelength is the lower limit of the diameter of the spot.

Short light pulses:
Due to certain technical arrangements (Q-switch, coupled modes, pulse compression), the generation of light pulses of some nanoseconds duration is possible. (6 femtoseconds have been reached). This allows to observe chemical reactions in real-time.

High power output
In continous action, energy transformation rate of CO₂ lasers is around 100 kW. In pulsed action with integrated amplifiers, some 10⁹ or even 10¹² watts have been reached. Such lasers are able to initiate multiple photon processes.

Photon statistics
Assume a light source and a volumen element in which photons emitted by this source are counted. The probability for the case of detecting n photons is P(n). This probabiliy is shown for a thermal source of light and a laser source. (Here, <n> is the middle number of photons in our statistical approach, i.e. 50 photons for the 101 cases with n = 0 as the minimal number of photons and n = 100 as maximal number of photons.)

For thermal sources, this probability is decribed by the following distribution.
In contrast, for light emerging a laser, the probability distribution PL<n> is in accordance with Poisson's formula.

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