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# B Integral

In nonlinear optics, **B-Integral** is a measure of the nonlinear 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,^{[1]} 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

## References

- ↑ "B Integral". Encyclopedia of Laser Physics and Technology.

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