A three-layer waveguide structure sensor consists of LHMs (left-handed materials) film surrounded by dielectric cladding and antiferromagnetic substrate is proposed. LHMs known as MTMs (metamaterials) have simultaneous negative permeability and permittivity. The dispersion relation for the structure is derived for TE guided modes. Two ranges of frequencies are chosen such that Voigt permeability, μ v , either negative or positive. The sensitivity is proven to be affected by different parameters including the film thickness, LHM parameters, and Voigt frequency.