Identifying plasmonic modes in a circular paraboloidal geometry by quasi-separation of variables

Analytic solutions for surface plasmon polaritons in a circular paraboloidal geometry are theoretically studied by solving the wave equation for the magnetic field in paraboloidal coordinates, using the quasi-separation of variables in combination with perturbation methods. It is found that solutions do not exist for a metallic solid paraboloid, but they can be obtained for a metallic hollow paraboloid in the form of standing waves. This paper provides the zeroth- and first-order approximate solutions of plasmonic modes for a metallic hollow paraboloid and graphically represents the zeroth-order solution in electric field-line patterns.