Gain saturation

Gain saturation ( English gain saturation ), and saturation of the gain , gain saturation and gain saturation called, is a term used in quantum optics . He describes the dependence of the gain (Engl. Gain ) of the intensity of the laser light field within the laser cavity .

Gain saturation occurs because an increased laser intensity tends to reduce the population inversion through increased stimulated emission .

definition

The intensity dependency of the gain coefficient at saturation is: ${\displaystyle g(\nu )}$

${\displaystyle g(\nu )={\frac {g_{0}(\nu )}{1+\Phi /\Phi _{\mathrm {sat} }}}}$

It stands

• ${\displaystyle \nu }$for the frequency of the light
• ${\displaystyle g_{0}(\nu )}$for small signal amplification (see below)
• ${\displaystyle \Phi }$for the photon flux, i.e. for the number of photons that cross a unit area of ​​1 m² within one second:

${\displaystyle \Phi =cq/V}$

With

• the speed of light ${\displaystyle c}$
• the number of photons ${\displaystyle q}$
• the resonator volume ${\displaystyle V}$

• ${\displaystyle \Phi _{\mathrm {sat} }}$ for the saturation flow.

Photon flux and intensity are therefore linked via

${\displaystyle I=h\nu \Phi }$

with Planck's quantum of action h .

Small signal amplification

The small-signal gain ( English small-signal gain ) corresponds to the gain of the laser medium in the limit , so in the case of a vanishing light field. ${\displaystyle \Phi \rightarrow 0}$

The value for the small-signal gain of a three-level laser :

${\displaystyle g_{0}(\nu )={\frac {P-\Gamma }{P+\Gamma }}\cdot \sigma (\nu )\cdot N_{T}}$

depends on

• the pumping power ${\displaystyle P}$
• the transition rate of the laser transition ${\displaystyle \Gamma }$
• the absorption cross section ${\displaystyle \sigma (\nu )}$
• the threshold inversion and represent the number of atoms in the upper or lower laser level . To simplify matters, it was assumed that both levels show the same degeneracy . ${\displaystyle N_{\mathrm {T} }=(N_{2}-N_{1})_{\text{Threshold}};}$ ${\displaystyle N_{2}}$ ${\displaystyle N_{1}}$

While the formula for the intensity dependency of the amplification for a four-level laser is the same as stated above, the formula for the small-signal amplification for a four-level laser is a little different, since the transition between the lower laser level and the basic level must also be taken into account.

Individual evidence

1. ^ Jürgen Eichler, Hans Joachim Eichler: Laser. Designs, beam guidance, applications. 7th, updated edition. Springer, Berlin et al. 2010, ISBN 978-3-642-10461-9 , p. 40 ( limited preview in the Google book search).
2. ^ ^{A b} Bahaa EA Saleh, Malvin Carl Teich: Fundamentals of Photonics. 2nd, completely revised and expanded edition. Wiley-VCH, Weinheim 2008, ISBN 978-3-527-40677-7 , p. 666 ( limited preview in the Google book search).
3. ^ ^{A b} Peter W. Milonni, Joseph H. Eberly: Lasers. John Wiley & Sons, New York NY et al. 1988, ISBN 0-471-62731-3 , p. 312.
4. ^ ^{A b} Peter W. Milonni, Joseph H. Eberly: Lasers. John Wiley & Sons, New York NY et al. 1988, ISBN 0-471-62731-3 , p. 298.