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, this integral is given by:
B
=
2
π
λ
∫
n
2
I
(
z
)
d
z
where
I
(
z
)
is the optical intensity along the beam axis,
z
the position in beam direction, and
n
2
the nonlinear index quantifying the Kerr nonlinearity. As
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.
