Abstract: Guidance characteristics in asymmetric left-handed material （LHM） slab waveguides are analyzed theoretically, Several lower-order transverse electric modes （TE） and transverse magnetic modes （TM） are calculated numerically and the dispersion curves are obtained. Some abnormal properties of guided modes in asymmetry left-handed material slab waveguides are discussed.

Key words: left-handed material （LHM）, negative refraction, guided modes