 Encyclopedia … combined with a great Buyer's Guide!

# Gain

Definition: a measure of the strength of optical amplification

More specific terms: small-signal gain, laser gain, Raman gain

German: Verstärkung, Verstärkungsfaktor

Units: %, dB or dimensionless number

Formula symbol: <$g$>, <$G$>

Author:

In photonics, the term gain is usually used to quantify the amplification of optical amplifiers or of a laser gain medium. Different meanings occur in the literature:

• The gain can simply be an amplification factor, i.e., the ratio of output power and input power.
• Particularly for small gains, the gain is often specified as a percentage. For example, 3% correspond to a power amplification factor of 1.03.
• Particularly large gains are often specified in decibels (dB), i.e., as 10 times the logarithm (to base 10) of the amplification factor. For example, a fiber amplifier may have a small-signal gain of 40 dB, corresponding to an amplification factor of 104 = 10 000.
• One also often specifies a gain per unit length, or more precisely the natural logarithm of the amplification factor per unit length, or alternatively the decibels per unit length.

Apart from its magnitude, important properties of gain are its spectral bandwidth and its saturation characteristics.

The gain achieved e.g. in a fiber amplifier or the gain medium of a laser depends on the population densities in different electronic levels, which themselves depend on the optical intensities. Rate equation modeling may be used for calculating the gain and investigating its dependence on various influences. A basic equation for the local gain coefficient in an excited laser gain medium is

$$g = N_{\rm exc} \: \sigma_{\rm em}$$

where <$g$> is in units of 1/m, <$N_{\rm exc}$> is the density of laser ions in the upper state (which generally depends on pump and signal intensities and may be time-dependent), and <$\sigma_{\rm em}$> is the emission cross-section at the relevant signal wavelength. If there are reabsorption and/or other propagation losses, these must be subtracted. In an optical fiber, where the excitation density applies to the fiber core only, an additional overlap factor may be included to take into account that now all signal light propagates in the fiber core. For the gain over some propagation length, that gain coefficient can be integrated, resulting in a dimensionless exponential gain factor. Applying the natural exponential function to that, one obtains the power amplification factor.

Other equations need to be used for other mechanisms of providing amplification, for example for parametric amplification.

### Bibliography

  R. Paschotta, tutorial on "Fiber Amplifiers", part 2 on gain and pump absorption

## Questions and Comments from Users

Here you can submit questions and comments. As far as they get accepted by the author, they will appear above this paragraph together with the author’s answer. The author will decide on acceptance based on certain criteria. Essentially, the issue must be of sufficiently broad interest.

Spam check:

(Please enter the sum of thirteen and three in the form of digits!)

By submitting the information, you give your consent to the potential publication of your inputs on our website according to our rules. (If you later retract your consent, we will delete those inputs.) As your inputs are first reviewed by the author, they may be published with some delay. Share this with your friends and colleagues, e.g. via social media:   These sharing buttons are implemented in a privacy-friendly way!

## Code for Links on Other Websites

If you want to place a link to this article in some other resource (e.g. your website, social media, a discussion forum, Wikipedia), you can get the required code here.

<a href="https://www.rp-photonics.com/gain.html">Article on Gain</a>in the <a href="https://www.rp-photonics.com/encyclopedia.html">RP Photonics Encyclopedia</a>
<a href="https://www.rp-photonics.com/gain.html"><img src="https://www.rp-photonics.com/previews/gain.png" alt="article" style="width:400px"></a>
* [https://www.rp-photonics.com/gain.htmlarticle on 'Gain' in the RP Photonics Encyclopedia]