Electromagnetic Casimir–Polder Interaction for a Conducting Cone

Abstract

Using the formulation of the electromagnetic Green’s function of a perfectly conducting cone in terms of analytically continued angular momentum, we compute the Casimir–Polder interaction energy of a cone with a polarizable particle. We introduce this formalism by first reviewing the analogous approach for a perfectly conducting wedge, and then demonstrate the calculation through numerical evaluation of the resulting integrals.

Keywords

• Casimir–Polder interaction
• Kontorovich–Lebedev transformation
• electromagnetic Green’s function