Nonlocal response in plasmonic waveguiding with extreme light confinement

We present a novel wave equation for linearized plasmonic response, obtained by combining the coupled real-space differential equations for the electric field and current density. Nonlocal dynamics are fully accounted for, and the formulation is very well suited for numerical implementation, allowing us to study waveguides with subnanometer cross-sections exhibiting extreme light confinement. We show that groove and wedge waveguides have a fundamental lower limit in their mode confine- ment, only captured by the nonlocal theory. The limita- tion translates into an upper limit for the corresponding Purcell factors, and thus has important implications for quantum plasmonics.