Gain
Author: the photonics expert Dr. Rüdiger Paschotta (RP)
Definition: a measure of the strength of optical amplification
Categories: 
- gain
Related: Tutorial on Fiber Amplifiers
Part 2: Gain and Pump Absorptionlaser gain mediagain bandwidthgain clampingoptical amplifiersfiber amplifiersgain saturationgain narrowinggain switchinggain efficiencyhomogeneous saturationinhomogeneous saturation
Units: %, [[decibel|dB]] or dimensionless number
Formula symbol: ($g$), ($G$)
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DOI: 10.61835/6uh Cite the article: BibTex BibLaTex plain textHTML Link to this page! LinkedIn
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What is Gain in Photonics?
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
($g = N_\textrm{exc} \: \sigma_\textrm{em}$)where ($g$) is in units of 1/m, ($N_\textrm{exc}$) is the density of laser ions in the upper state (which generally depends on pump and signal intensities and may be time-dependent), and ($\sigma_\textrm{em}$) 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 not 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 logarithmic 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.
Fiber Amplifiers
Part 2: Gain and Pump Absorption
We explain how the local gain and pump absorption depend on the degree of excitation of the laser-active ions.
Frequently Asked Questions
This FAQ section was generated with AI based on the article content and has been reviewed by the article’s author (RP).
What is optical gain?
In photonics, gain quantifies the amplification in devices like optical amplifiers or laser gain media. It is most simply defined as the ratio of the output optical power to the input power.
In what units is gain expressed?
Gain can be expressed as a simple power amplification factor, as a percentage for small values (e.g., 3% for a factor of 1.03), or in decibels (dB) for large values (e.g., 40 dB for a factor of 10,000). There are also logarithmic gain coefficients, often per unit length.
What determines the gain in a laser medium?
The local gain coefficient ($g$) depends on the density of excited ions ($N_\textrm{exc}$) and the emission cross-section ($\sigma_\textrm{em}$), based on the equation ($g = N_\textrm{exc} \\cdot \sigma_\textrm{em}$). The total gain over a certain length also depends on reabsorption and other propagation losses.