Physics: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, this integral is given by:

[math]\displaystyle{ B=\frac{2\pi}{\lambda}\int \! n_2I(z)\,dz \, }[/math]

where [math]\displaystyle{ I(z) }[/math] is the optical intensity along the beam axis, [math]\displaystyle{ z }[/math] the position in beam direction, and [math]\displaystyle{ n_2 }[/math] the nonlinear index quantifying the Kerr nonlinearity. As [math]\displaystyle{ 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