  We present an experimental study of the nonlinear optical absorption of the
eutectic mixture E7 at the nematic-isotropic phase transition by the Z-scan
technique, under a continuos wave excitation at 532 nm. In the nematic region,
the effective nonlinear optical coefficient \beta for an extraordinary beam is
negative and for an ordinary beam is positive, being null in the isotropic
phase. The parameter S_{NL} defined in terms of the nonlinear absorption
coefficients in a similar way than the optical order parameter from the linear
dichoic ratio behavies like an order parameter with a critical exponent
0.22+-0.05, in good agreement with the tri-critical hipothesis of the N-I
transition.
