  Metamaterials with simultaneous negative permittivity and negative
permeability (also called left-handed materials) open new avenues to achieving
unprecedented physical properties and functionality unattainable with naturally
occurring materials. It has been predicted that a metamaterial slab waveguide
can slow down light significantly (even to zero velocity) as the thickness of
the core layer approaches a critical thickness. Here we show that coupling
between the forward and backward modes becomes significant near the critical
thickness due to the good matching of the wavevectors and modal profiles of the
two modes. Physical explanation and impact of this coupling are given.
