# B Integral

> Mediated Wiki article. Canonical URL: https://mediated.wiki/source/B_Integral
> Markdown URL: https://mediated.wiki/source/B_Integral.md
> Source: https://en.wikipedia.org/wiki/B_Integral
> Source revision: 1225018773
> License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/)

In [nonlinear optics](/source/nonlinear_optics), '''B-Integral''' is a measure of the [nonlinear optics](/source/nonlinear_optics) phase shift of light. It calculates the exponential growth of the least stable [spatial frequency](/source/spatial_frequency) in a [laser beam](/source/laser_beam), and is the numerical equivalent of the nonlinear phase shift along the laser system's optical axis.

In a multipass laser system as a cumulative measure of the nonlinear interaction,<ref>{{Cite web|url=http://www.rp-photonics.com/b_integral.html|title=B Integral|publisher=Encyclopedia of Laser Physics and Technology}}</ref> this [integral](/source/integral) is given by:

: <math>B=\frac{2\pi}{\lambda}\int \! n_2I(z)\,dz \,</math>

where <math>I(z)</math> is the optical intensity along the beam axis, <math>z</math> the position in beam direction, and <math>n_2</math> the nonlinear index quantifying the Kerr nonlinearity. As <math>n_2I(z)</math> is the nonlinear change in the refractive index, one easily recognizes the B integral to be the total on-axis nonlinear phase shift accumulated in a passage through the device.
The B integral is frequently used in the context of ultrafast amplifiers, e.g. for optical components such as the Pockels cell of a regenerative amplifier.

==See also==
* [Kerr effect](/source/Kerr_effect)

==References==
{{reflist}}

{{Lasers}}

Category:Laser science
Category:Nonlinear optics

{{optics-stub}}

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