We investigate nonlinear transmission in a layered structure consisting of a
slab of positive index material (PIM) with Kerr-type nonlinearity and a
sub-wavelength layer of linear negative index material (NIM) sandwiched between
semi-infinite linear dielectrics. We find that a thin layer of NIM leads to
significant changes in the hysteresis width when the nonlinear slab is
illuminated at an angle near that of total internal reflection. Unidirectional
diode-like transmission with enhanced operational range is demonstrated. These
results may be useful for NIMs characterization and for designing novel NIMs
based devices
