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Abstract
A unique guided mode with a zero transverse wave number is shown to be supported by a slab of Left-Handed Material (LHM). Unlike the known guided modes with trigonometric and hyperbolic profiles, this unique guided mode has a linear profile, which was never reported before. It is a transitional mode between the sine and the sinh modes when the mode is anti-symmetric, however the transitional mode between the cosine and the cosh modes only exists in a special case as a TEM mode when it is symmetric. The properties of this unique guided mode are discussed and demonstrated by numerical examples in this paper.