plasmonic particles in near-field [@Park2014], which requires an increasingly large number of multipole order for accurate description [@Stout2008]. Still, the collective responses between plasmonic particles situated in a reasonably far distance and dielectric particles [@DeAbajo1999] can be efficiently and accurately described under the multipole approach.

Importantly, the multipole approach has superior computational efficiency compared to the traditional numerical methods, such as finite-difference time-domain and finite-element methods. Noticeably, this approach has shown significant potentials for rigorously studying electromagnetic problems involving disordered, aperiodic [@Rahimzadegan2019; @Jenkins2018; @Pinheiro2017], and multi-scale systems with a large number of particles ($N$&gt;10,000) over a large volume [@Pattelli2018]. Especially, aperiodic metasurfaces [@MahdiSalary2017; @Rahimzadegan2019; @Jenkins2018] and random media [@Pinheiro2017] could be accurately studied using this method, and optimization [@Forestiere2012] and dataset construction for deep-learning neural networks [@So2019] would significantly benefit from this approach. In addition, the multipole approach can implement localized shaped beams from simple Gaussian beams [@Novotny2009] to highly focused [@AlvaroRanhaNeves2006] and helical beams [@Wu2015; @Wang2017], providing a versatile framework to rigorously study spin-orbit interactions. Therefore, the multipole approach could be used to rigorously study electromagnetic phenomena arising in complex, disordered media consisting of discrete scattering objects.

Toy models
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![(a,b) Completely decoupled dipolar dual particles at (a) LCP 