The nonlinear optical features of surface plasmon resonance (SPR) wave propagating along the metallic interface (SPR-mode) of a nanoslit array are presented. The SPR resonance wavelength is decided by the nanoslit period (P) and the refractive index (RI) of the sensing medium (n). Approximate analytic formulas and fit equations are derived and compared with the exact numerical results. The real part of gold dielectric function is fit to a quadratic equation which covers wider range of the SPR resonance wavelength
(600-4000 nm) than the prior linear fit (600-1000 nm). A nonlinear fit RI sensitivity (M) is found to be M = P + 7.46n which is much more accurate than the first order approximation, M=P. The figure of merit defined by the ratio of M and the spectrum broadening is also calculated and showing an optimal period.