Continuity of field patterns for exceptional surface waves and exceptional compound waves

Surface waves guided by the planar interface of two dissimilar mediums or compound waves guided by two such parallel planar interfaces are classified as unexceptional or exceptional, depending upon their localization characteristics to the planar interfaces. The localization of unexceptional waves is governed by functions that vary exponentially with distance from an interface, whereas the localization of exceptional waves involves functions that vary as the product of a linear function and an exponential function of the same distance. Numerical studies based on the corresponding canonical boundary-value problems were undertaken in order to characterize the transitions from unexceptional surface and unexceptional compound waves to exceptional surface and exceptional compound waves. Both Dyakonov surface waves and surface-plasmon-polariton waves, as well as compound plasmon-polariton waves, were investigated. Our studies revealed that the transitions involve smooth variations in the electric and magnetic field phasors, as well as in the time-averaged Poynting vector. Therefore, in terms of spatial profile, an exceptional surface wave or an exceptional compound wave is practically indistinguishable from a corresponding unexceptional surface wave or unexceptional compound wave propagating along directions in the immediate neighborhood of the exceptional wave.