• Source: B Integral

      • 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


      References

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