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Guided by the planar interface of two dissimilar partnering mediums, a surface wave can be exceptional if at least one of the partnering mediums is anisotropic. Exceptional surface waves propagate in isolated directions parallel to the interfacial plane, whereas unexceptional (i.e., garden-variety) surface waves propagate for a non-degenerate angular interval of directions parallel to the interfacial plane. Also, exceptional surface waves have localization characteristics different from those of unexceptional surface waves: the decay of fields for an exceptional surface wave has a combined linear-exponential dependency on distance from the interface in an anisotropic partnering medium, whereas the decay is purely exponential for an unexceptional surface wave. In order for exceptional surface waves to exist, the constitutive parameters of that anisotropic partnering medium must satisfy certain constraints. Exceptional surface waves of different types have been reported: (a) If both partnering mediums are dielectric, at least one of the two is anisotropic, then exceptional surface waves classified as Dyakonov-Voigt surface waves can exist, whether or not the partnering mediums are dissipative. Whereas the planar interface of an isotropic dielectric medium and a uniaxial dielectric medium can guide one exceptional surface wave in each quadrant of the interface plane, the planar interface of an isotropic dielectric medium and a biaxial dielectric medium can guide two exceptional surface waves in each quadrant of the interface plane. Furthermore, doubly exceptional Dyakonov-Voigt surface waves, which exhibit a combined linear-exponential dependency on distance from the interface on both sides of the interface, have been reported on for the planar interface of a biaxial dielectric medium and a uniaxial dielectric medium. (b) If one of the partnering mediums is metallic and the other is dielectric, and at least one of them is anisotropic, then exceptional surface waves classified as surface plasmon-polariton-Voigt waves can exist. The notion of exceptional surface waves guided by a single planar interface has been extended to compound waves that are guided by a pair of parallel planar interfaces, provided that the distance between the two interfaces is not too great. For example, if a thin film of metal is embedded within an anisotropic dielectric medium, the two planar interfaces can guide exceptional compound-plasmon-polariton waves.
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