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We predict theoretically that surface plasmon polaritons propagating toward the tip of a tapered plasmonic waveguide are slowed down and asymptotically stopped when they tend to the tip, never actually reaching it (the travel time to the tip is logarithmically divergent). This phenomenon causes accumulation of energy and giant local fields at the tip. There are various prospective applications in nano-optics and nanotechnology.
Mark I. Stockman (Thu,) studied this question.