Abstract
We describe a powerful and intuitive theoretical technique for modeling light–matter interactions in classical and quantum nanoplasmonics. Our approach uses a quasinormal mode (QNM) expansion of the photon Green function within a metal nanoresonator of arbitrary shape, together with a Dyson equation, to derive an expression for the spontaneous decay rate and far field propagator from dipole oscillators outside resonators. For a single QNM, at field positions outside the quasi-static coupling regime, we give a closed form solution for the Purcell factor and generalized effective mode volume. We augment this with an analytic expression for the divergent local density of optical states very near the metal surface, which allows us to derive a simple and highly accurate expression for the electric field outside the metal resonator at distances from a few nanometers to infinity. This intuitive formalism provides an enormous simplification over full numerical calculations and fixes several pending problems in QNM theory.
Highlights
High-index-contrast dielectric cavities and metallic nano-resonators both facilitate control of light-matter interaction by engineering the local density of optical states (LDOS)
While some authors believe that it is unnatural to work with modes in a lossy system [21], we argue that quasinormal modes (QNMs) have enormous intuitive appeal in metallic nanoparticles (MNPs) geometries, and that they help to accurately explain the underlying physics of light-matter coupling in a remarkably clear and transparent way
The use of QNMs in the field of nanoplasmonics is made difficult by a number of challenges: (i) techniques developed in quantum optics for lossy inhomogeneous structures suggest that traditional mode expansion techniques do not work [22]; (ii) proper calculations of localized surface plasmons as QNMs are non-trivial; (iii) because QNMs diverge in space, it is impossible to directly use them in calculations of the electromagnetic propagator to positions far away from the resonators; and (iv): the LDOS is known to diverge near a metal surface due to quasi-static coupling so at these positions a single QNM expansion is not expected to work
Summary
High-index-contrast dielectric cavities and metallic nano-resonators both facilitate control of light-matter interaction by engineering the local density of optical states (LDOS). The use of QNMs in the field of nanoplasmonics is made difficult by a number of challenges: (i) techniques developed in quantum optics for lossy inhomogeneous structures suggest that traditional mode expansion techniques do not work [22]; (ii) proper calculations of localized surface plasmons as QNMs are non-trivial; (iii) because QNMs diverge in space, it is impossible to directly use them in calculations of the electromagnetic propagator to positions far away from the resonators; and (iv): the LDOS is known to diverge near a metal surface due to quasi-static coupling (e.g., causing Ohmic heating) so at these positions a single QNM expansion is not expected to work.
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