# Filling factor

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{{Distinguish|Fill factor (disambiguation)}}
{{About|Fiber Optics|"Filling Factor" in Quantum Hall Effect|Quantum Hall Effect}}
{{Confusing|date=September 2007}}

'''Filling factor''', <math>~F,~</math> is a quantity measuring the efficiency of absorption of pump in the core of a [double-clad fiber](/source/double-clad_fiber).<ref>D. Kouznetsov, J. V. Moloney. Efficiency of pump in the double-clad fiber amplifiers. 2. Broken circular symmetry.
JOSA B, '''19''', No.6, p.1259-1263 (2002). [http://www.ils.uec.ac.jp/~dima/josa2f0.pdf] {{Webarchive|url=https://web.archive.org/web/20041102014946/http://www.ils.uec.ac.jp/~dima/josa2f0.pdf |date=2004-11-02 }}</ref><ref>D. Kouznetsov, J. V. Moloney. Efficiency of pump absorption in double-clad fibers amplifiers. 3. Calculation of modes. JOSA B, '''19''', No.6, p.1304-1309 (2002). [http://www.ils.uec.ac.jp/~dima/josa3f0.pdf] {{Webarchive|url=https://web.archive.org/web/20041102175218/http://www.ils.uec.ac.jp/~dima/josa3f0.pdf |date=2004-11-02 }}</ref><ref>D. Kouznetsov, J. V. Moloney. Highly efficient, high gain, short wavelength and power scalable incoherent diode slab-pumped fiber laser amplifier. [IEEE Journal of Quantum Electronics](/source/IEEE_Journal_of_Quantum_Electronics), v.39, No.11, p.1452-1461 (2003).
[http://www.ils.uec.ac.jp/~dima/01242365.pdf] {{Webarchive|url=https://web.archive.org/web/20041102155959/http://www.ils.uec.ac.jp/~dima/01242365.pdf |date=2004-11-02 }}</ref>

==Definition==
[[Image:FillingFactor.png|thumb|200px| Estimates of the pump efficiency in a [double-clad fiber](/source/double-clad_fiber) with <math>F=0.8
</math> (blue) and <math> F=0.9</math> (red), discussed in<ref name="Kouznetsov">{{Cite journal|title=Highly efficient, high-gain, short-length, and power-scalable incoherent diode slab-pumped fiber amplifier/laser| author= Kouznetsov, D.|author2=Moloney, J.V.| journal=[IEEE Journal of Quantum Electronics](/source/IEEE_Journal_of_Quantum_Electronics)|volume=39 | year=2003 | issue=11 | pages=1452–1461 | doi=10.1109/JQE.2003.818311|bibcode = 2003IJQE...39.1452K | citeseerx= 10.1.1.196.6031}}
</ref>
compared to the results of the ray tracing simulations<ref name="Liu">{{Cite journal|
title=The absorption characteristics of circular, offset, and rectangular double-clad fibers|
author=A. Liu|author2=K. Ueda|
journal=[Optics Communications](/source/Optics_Communications)|
volume=132|
year=1996|
pages= 511–518|
doi=10.1016/0030-4018(96)00368-9|
issue=5–6|bibcode = 1996OptCo.132..511A }}
</ref>(black curves).
]]
The efficiency of absorption of pumping energy in the fiber is an important parameter of a [double-clad fiber](/source/double-clad_fiber) laser. In many cases this efficiency can be approximated with<ref name="Kouznetsov" />
:<math>1- \exp\left(  - F \frac{\pi r^2}{S}\alpha L \right) ,</math>
where
:<math>~S~</math> is the cross-sectional area of the cladding
:<math>~r~</math> is the radius of the core (which is taken to be circular)
:<math>~\alpha~</math> is the [absorption coefficient](/source/absorption_coefficient) of pump light in the core
:<math>~L~</math> is the length of the double-clad fiber, and
:<math>~F~</math> is a [dimensionless](/source/dimensionless_number) adjusting parameter, which is sometimes called the "filling factor"; <math>~0<F<1~</math>.

The filling factor may depend on the initial distribution of the pump light, the shape of the cladding, and the position of the core within it.

==Application==
The large (close to unity) filling factor is important in double-clad amplifiers; it allows them to reduce the requirements for the [brightness](/source/brightness) of the pump and to reduce the length of the fiber laser.  Such a reduction is especially important for the [power scaling](/source/power_scaling) of various nonlinear processes, and  contributions of [stimulated scattering](/source/stimulated_scattering) to the degradation of signal. Use of the filling factor for the estimate of the efficiency of absorption of the pump in fiber lasers allows quick estimates without performing complicated numerical simulations.

==See also==
*[Double-clad fiber](/source/Double-clad_fiber)
*[Erbium Doped Fibre Amplifier (EDFA)](/source/Optical_amplifier)

==Notes==
<references/>

Category:Fiber optics

{{Engineering-stub}}

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Adapted from the Wikipedia article [Filling factor](https://en.wikipedia.org/wiki/Filling_factor) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Filling_factor?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.