Surface polaritons in a circularly cylindrical interface: Surface plasmons

Abstract

A theoretical investigation of surface polaritons in the circularly cylindrical geometry is presented. The complete set of Maxwell's equations (retardation effects are not neglected) is solved with the simple dielectric function, $\ensuremath{\epsilon}(\ensuremath{\omega})=1\ensuremath{-}\frac{{\ensuremath{\omega}}_{p}^{2}}{{\ensuremath{\omega}}^{2}}$, where ${\ensuremath{\omega}}_{p}$ is the bulk plasma frequency. The resulting transcendental equation for the eigenfrequencies is solved via numerical methods for three representative values of the cylindricality constant, $\ensuremath{\alpha}=\frac{{\ensuremath{\omega}}_{p}a}{c}$, where $a$ is the cylinder radius and $c$ the velocity of light. In addition to the real nonradiative surface plasmons, various virtual radiative surface plasmons exist with properties depending rather strongly on $\ensuremath{\alpha}$. The results are compared with existing experimental data. Further experiments are proposed in order to reveal the most interesting features of the surface plasma modes.