Classical interface modes of quantum dots

The classical surface and interface modes of dotlike microstructures and the optical absorption corresponding to them are studied within a dielectric continuum approach. Explicit results are given mainly for the interface phonons of ionic materials, and it is noted that the same formalism applies to the surface plasmons of conducting materials. Analytical results for the modes are given for dots having the shapes of spheres and ellipsoids of revolution. An integral-equation approach is introduced to treat dots having arbitrary shapes. The dependence of the mode frequencies and eigenmodes on the dot shape and the dependence of the optical absorption on its shape and on the light polarization are discussed. An interesting feature that emerges is that the number of optically active modes increases as the dot shape becomes less symmetric. Dots with sharp tips are found to support interface modes which are strongly enhanced in the vicinity of the tip, a fact relevant to phenomena involving electric fields near the tip of a scanning microscope probe.