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, this integral is given by:
B = 2 π λ ∫ n 2 I ( z ) d z {\displaystyle B={\frac {2\pi }{\lambda }}\int \!n_{2}I(z)\,dz\,}
where I ( z ) {\displaystyle I(z)} is the optical intensity along the beam axis, z {\displaystyle z} the position in beam direction, and n 2 {\displaystyle n_{2}} the nonlinear index quantifying the Kerr nonlinearity. As n 2 I ( z ) {\displaystyle n_{2}I(z)} 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
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