Nonlinear phase shift without cascaded second-order processes and third   order nonlinearity
  The new mechanism for obtaining a nonlinear phase shift has been proposed and the schemes are described for its implementation. As it is shown, the interference of two waves with intensity-dependent amplitude ratio coming from the second harmonic generation should produce the nonlinear phase shift. The sign and amount of nonlinear distortion of a beam wavefront is dependent of the relative phase of the waves that is introduced by the phase element. Calculated value of $n_2^{eff}$ exceeds that connected with cascaded quadratic nonlinearity, at the same conditions. 
V.P. Drachev, S.V. Perminov (Institute of Semiconductor Physics,   Russian Academy of Sciences, Novosibirsk, Russia)