Multipole Decomposition of Open Systems

Multipole decomposition is one of the widely used techniques to analyze the scattering effect from spatially bounded systems such as a dielectric particle in vacuum.
In such systems, the particles` volume includes the charges and currents, the sources of radiation (scattering), thus, forming a closed system.
However, when considering a system in which charges and currents are not localized within the particles` integration volume, open systems, the contribution of currents leaking through the boundaries should be taken into account, otherwise, inaccuracy in multipole excitations is revealed.
Here, we review the classical multipole decomposition and reformulate it by 1) deriving amendments for each of multipole moments contributing to the scattering field and 2) proposing the calculation within a volume in which currents and charges remain unchanged. In addition, we proposed an intuitively simple domain merging approach based on the Babinet`s principle.
We envisage that our theoretical research opens up a new chapter in all-dielectric nano-photonics and plasmonics by paving a road toward theoretical analysis of large systems by means of multipole decomposition. Our formalism can be applied in studies of light scattering effect by small perturbations, such as chemical analytes, quantum dots, nanolasers and others, in large open systems, such as waveguides and cavities.