Abstract
Nonlocal effects have been shown to be responsible for a variety of non-trivial optical effects in small-size plasmonic nanoparticles, beyond classical electrodynamics. However, it is not clear whether optical mode descriptions can be applied to such extreme confinement regimes. Here, we present a powerful and intuitive quasinormal mode description of the nonlocal optical response for three-dimensional plasmonic nanoresonators. The nonlocal hydrodynamical model and a generalized nonlocal optical response model for plasmonic nanoresonators are used to construct an intuitive modal theory and to compare to the local Drude model response theory. Using the example of a gold nanorod, we show how an efficient quasinormal mode picture is able to accurately capture the blueshift of the resonances, the higher damping rates in plasmonic nanoresonators, and the modified spatial profile of the plasmon quasinormal modes, even at the single mode level. We exemplify the use of this theory by calculating the Purcell factors of single quantum emitters, the electron energy-loss spectroscopy spatial maps, as well as the Mollow triplet spectra of field-driven quantum dots with and without nonlocal effects for different size nanoresonators. Our nonlocal quasinormal mode theory offers a reliable and efficient technique to study both classical and quantum optical problems in nanoplasmonics.
Highlights
Fundamental studies of light-matter interactions using plasmonic devices continue to make considerable progress and offer a wide range of applications [1,2,3,4,5,6,7]
We show that, somewhat surprisingly, quasinormal modes (QNMs) can be obtained and used to construct the full system Green function (GF) for complex 3D plasmonic nanoresonators with nonlocal effects, and even a single mode description is accurate over a wide range of frequencies and spatial positions
We start by redefining the Helmholtz equation that is usually solved to obtain the local QNMs [37], and we extend this approach to the case of nonlocal systems using a generalized Helmholtz equation, which is applicable to both hydrodynamical model (HDM) and generalized nonlocal optical response (GNOR) models
Summary
Fundamental studies of light-matter interactions using plasmonic devices continue to make considerable progress and offer a wide range of applications [1,2,3,4,5,6,7]. In contrast to “normal modes,” which are solutions to Maxwell’s equations subjected to (usually) fixed or periodic boundary conditions, QNMs are obtained with open boundary conditions [21], and they are associated with complex frequencies whose imaginary parts quantify the system losses These QNMs require a more generalized normalization [21,22,23,24,25,26], allowing for accurate mode quantities to be obtained such as the effective mode volume or Purcell factor [27], that is, the enhanced spontaneous emission (SE) factor of a dipole emitter. To more rigorously show the benefit of our nonlocal modal picture for use in quantum theory of lightmatter interaction, we study the behavior of the Mollow triplets of field-driven quantum dots (QDs) coupled to plasmonic resonators [52], under the influence of nonlocal effects
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