  An exceptional surface wave can propagate in an isolated direction, when
guided by the planar interface of two homogeneous dielectric partnering mediums
of which at least one is anisotropic, provided that the constitutive parameters
of the partnering mediums satisfy certain constraints. Exceptional surface
waves are distinguished from unexceptional surface waves by their localization
characteristics: the fields of an exceptional surface wave in the anisotropic
partnering medium decay as a combined linear-exponential function of distance
from the interface, whereas the decay is purely exponential for an
unexceptional surface wave. If both partnering mediums are anisotropic then a
doubly exceptional surface wave can exist for an isolated propagation
direction. The decay of this wave in both partnering mediums is governed by a
combined linear-exponential function of distance from the interface.
