Superfocusing modes of surface plasmon polaritons in a wedge-shaped geometry obtained by quasi-separation of variables

Analytic solutions to the superfocusing modes of surface plasmon polaritons in the wedge-shaped geometry are theoretically studied by solving the Helmholtz wave equation for the magnetic field using quasi-separation of variables in combination with perturbation methods. The solutions are described as a product of radial and extended angular functions and are obtained for a lossless metallic wedge and V-groove by determining the separation quantities that satisfy the boundary conditions. For the metallic wedge and V-groove, we show that the radial functions of the zeroth order are approximately described by the imaginary Bessel and modified Whittaker functions, respectively, and that the extended angular functions have odd and even symmetries, respectively, for reflection in the central plane of the wedge-shaped geometry. Importantly, we show that the wave numbers of superfocusing surface plasmon polaritons in the metallic wedge and V-groove are clearly different in their radial dependence.