Waveguiding in air with left-handed material

Symmetric air waveguide and antisymmetric air waveguide made with left-handed material (LHM) cladding are constructed. Guided modes in the two kinds of air waveguides are studied on condition that the permittivity and permeability of LHM are simultaneously negative. When absolute value of refraction of cladding is less than that of air, fast modes and slow modes are possible to exist at the same time; when absolute value of refraction of cladding is more than that of air, only slow modes could exist.