and (b) RCP incidences. Inset spectra are absorption by LDP (red) and RDP (blue). (c) Randomly dispersed dual particles at LCP incidence. Inset spectra are the sums of absorption by LDP (red) and RDP (blue). The positions of LDPs and RDPs are denoted by circled letters L and R, respectively.[]{data-label="fig:dual"}](Fig_dual.png)

In previous examples, $\boldsymbol{\alpha}$-tensors of realistic particles were considered, but it is also possible to consider $\boldsymbol{\alpha}$-tensors of arbitrary particles without information on their physical geometric parameters. Recently, Fernandez-Corbaton, et al. proposed the concept of dual particles, which are excited by light with one helicity, re-radiates light with the same helicity, and are completely transparent to light with the opposite helicity. They also proposed that two oppositely dual particles are completely uncoupled to each other, and a media consisting of dual particles with a single handedness will be completely transparent to one helicity and opaque to the other helicity [@Fernandez-Corbaton2016]. Demonstration of this concept is difficult, because purely dual particles have not been discovered, although approximately dual particles have been studied [@Fernandez-Corbaton2016; @Fruhnert2017]. Still, we can theoretically investigate the concepts above using $\boldsymbol{\alpha}$-tensors and MST, because arbitrary $\boldsymbol{\alpha}$-tensors without physical parameters can be devised, which cannot be done using the 