$(\alpha_{e2}^{e1})_{xy}^{z}$ and $(\alpha_{e1}^{e2})_{z}^{xy}$ are necessary for this anisotropic CD; they constructively contribute to CD for $\mathbf{k \parallel y}$ (red line, Fig. \[fig:TDB\]d), whereas destructively for $\mathbf{k \parallel x}$ and pretty much eliminating the total CD (black line, Fig. \[fig:TDB\]d). We do not explicitly show this, but we mention that their contributions can be quantified by directly calculating CD from their retrieved $\boldsymbol{\alpha}$-tensor. Here, TDB clearly shows that higher-order multipole transition is necessary for describing plasmonic meta-atoms and reconstructing ansotropic chiral responses even in far-fields, as well as in near-fields [@Mun2019].

![(a) The schematics of Si quadrumer. (b) The retrieved $\boldsymbol{\alpha}$-tensor at $\lambda$ = 520 nm. (c) Multipole-decomposed scattering cross-sections at $\mathbf{E}_\mathrm{inc} = \hat{x}e^{ikz}$. (d) Spectra of $(\alpha_{m2}^{m2})_{xx}^{xx}$, $(\alpha_{m2}^{m2})_{xy}^{xy}$, $(\alpha_{m2}^{m2})_{xz}^{xz}$, $(\alpha_{m2}^{m2})_{xz}^{xx}$, and $(\alpha_{e1}^{m2})_{x}^{yz}$.[]{data-label="fig:HDQ"}](Fig_HRI.png)

Finally, we briefly discuss high-refractive-index nanoparticles, which are actively researched topic due to their higher-order multipolar modes. In general, subwavelength plasmonic nanoparticles exhibit dominant ED mode, but high-refractive-index nanoparticles often exhibit dominant higher-order modes. For instance, Si quadrumer exhibits strong MD mode exceeding ED near 520 nm (Fig. \[fig:HDQ\]c). In addition, broad MQ response was observed between 420 and 520 nm. We analyzed the origin of MQ response from the $\boldsymbol{\alpha}$-tensor components that can contribute to the MQ 