  We propose a scheme to study the nonlinear propagation properties of
nonlinear surface plasmon polaritons (SPPs) in a three level $\Lambda$ type
electromagnetically induced transparency (EIT) system with modulation of a
rectangular barrier. Based on the multi scale method, the nonlinear
Schr\"odinger equation (NLSE) describing nonlinear propagation of SPPs is
derived, and the rectangular barrier affecting propagation of nonlinear SPPs is
provided by an off-resonance Stark field. For the single nonlinear SPPs
incident case, by adjusting the height and half width of the barrier, we can
realize transmission, trapping and reflection of the nonlinear SPPs. For two
nonlinear SPPs symmetrical incident case, we find that a periodic intensity
distribution in transverse direction mode can be excited in the rectangular
barrier, and we study the relationship between propagation properties of such
excited modes in the barrier with nonlinearity, half width of the barrier and
phase difference of the initial nonlinear SPPs. In addition, we design an
optical switch of nonlinear SPPs based on the above results. The results
obtained here not only provide a theoretical basis for the study of the
interaction between nonlinear SPPs and external potentials, but also have broad
application prospects in the field of optical information at micro/nano scale.
