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Three-layer slab waveguide with left-handed materials (LHM) is discussed using the Maxwells equations and their equations of dispersion relation for TM modes are obtained. By seeking the power of the slab waveguide, their equations of effective thickness for TM modes are obtained. Furthermore, the interrelated equations for right-handed materials (RHM)slab waveguide are introduced and their curves plotted. To find new properties for LHM slab waveguide, the equations and their curves for the LHM and RHM slab waveguide are compared respectively.