The purpose of this work is to investigate theoretically the characteristics of confined electromagnetic modes propagating along the interfaces of a multilayer device. This one dimensional (1D) sensor is formed by stacking a left-handed material (LHM) layer between a SiO₂-glass prism and a dielectric gap layer in contact with gold (Au). The results indicate that the total thickness of the LHM layer and dielectric gap, in optimum conditions, give the ability of tuning significantly the characteristics of the resonant modes correlated to surface plasmons (SPs) propagation along the interfaces of the designed device. By considering two arrangements between LHM and Au, two opposite resonant behaviors observed in p-reflectance spectra are analyzed in the angular interrogation mode and discussed thoroughly.