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nonlinear term on the right hand side is called Kerr effect, and is multiplied by -j according to the engineer's notation used in the definition of Fourier transform.

The power of the electric field is invariant along z, since:
:

with * denoting conjugation.

Since the power is invariant, the Kerr effect can manifest only as a phase rotation. In polar coordinates, with , it is:
:

such that:
:

The phase ? at coordinate

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