The Dielectric Bowtie Effect: Classical Electromagnetic Edge Singularities in Subwavelength Cavities

Abstract

Dielectric bowtie nanocavities can concentrate light into subwavelength regions without the ohmic losses of plasmonic metals. We show that this enhancement is the finite-geometry realization of a classical electromagnetic edge singularity. Unlike an isolated dielectric wedge, the scaling in a bowtie is governed by an exponent determined by a collective four-sector singularity. In a finite structure, this scale-free singular field is regularized by the gap size, while the bowtie length sets the outer scale. The tip radius, gap, and bowtie length therefore play distinct physical roles: curvature cuts off the local wedge singularity, the gap cuts off the collective bowtie singularity, and the outer length sets the range over which the field can build up. Electrostatic simulations confirm the predicted scaling laws, while three-dimensional quasinormal-mode simulations show how the same near-field mechanism is accessed and limited by realistic dielectric nanocavities.