In nonlinear optics, '''B-Integral''' is a measure of the nonlinear optics phase shift of light. It calculates the exponential growth of the least stable spatial frequency in a 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 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
==References== {{reflist}}
{{Lasers}}
Category:Laser science Category:Nonlinear optics
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