  A nonlinear Helmholtz equation (NLH) with high wave number and Sommerfeld
radiation condition is approximated by the perfectly matched layer (PML)
technique and then discretized by the linear finite element method (FEM).
Wave-number-explicit stability and regularity estimates and the exponential
convergence are proved for the nonlinear truncated PML problem. Preasymptotic
error estimates are obtained for the FEM, where the logarithmic factors in h
required by the previous results for the NLH with impedance boundary condition
are removed in the case of two dimensions. Moreover, local quadratic
convergences of the Newton's methods are derived for both the NLH with PML and
its FEM. Numerical examples are presented to verify the accuracy of the FEM,
which demonstrate that the pollution errors may be greatly reduced by applying
the interior penalty technique with proper penalty parameters to the FEM. The
nonlinear phenomenon of optical bistability can be successfully simulated.
