## 2 Results
### Expressions of Polarizability in the Rayleigh Limit  
In the Rayleigh limit of electromagnetically small spheres \(x\ll 1\), only the dipole terms of [PERSON]'s theory are retained. For \(l,\ u=1\), \(g_{MN}^{\alpha}=g_{ML}^{\alpha}=g_{NM}^{\alpha}=0\) and the E- and H-fields, Equations (7) and (8) can be written as  
\[E=\sum_{mv}M_{1v}^{1}\big{(}g_{MM^{\prime}}^{\alpha_{ED}}g_{MM}^{\alpha_{EB}} \big{)}_{m,v}\bigg{(}f_{1 km}^{DM}\bigg{)}+\sum_{mv}N_{1v}^{1}\big{(}g_{NN^{ \prime}}^{\alpha_{ED}},g_{NN}^{\alpha_{EB}}\big{)}_{m,v}\bigg{(}f_{1 km}^{DN} \bigg{)}+\sum_{mv}L_{1v}^{1}\big{(}g_{NN^{\prime}}^{\alpha_{ED}},g_{NL}^{ \alpha_{EB}}\big{)}_{m,v}\bigg{(}f_{1 km}^{DN}\bigg{)} \tag{27}\]  
\[H=\sum_{mv}M_{1v}^{1}\big{(}g_{MM^{\prime}}^{\alpha_{HD}},g_{MM}^{\alpha_{HB}} \big{)}_{m,v}\bigg{(}f_{1 km}^{DM}\bigg{)}+\sum_{mv}N_{1v}^{1}\big{(}g_{NN^{ \prime}}^{\alpha_{HD}},g_{NN}^{\alpha_{HB}}\big{)}_{m,v}\bigg{(}f_{1 km}^{DN} \bigg{)}+\sum_{mv}L_{1v}^{1}\big{(}g_{NN}^{\alpha_{HD}},g_{NL}^{\alpha_{HB}} \big{)}_{m,v}\bigg{(}f_{1 km}^{DN}\bigg{)} \tag{28}\]  
Applying [PERSON]'s equation to the E- and H-fields of Equations (20) and (21), we can obtain  
\[-i(\mathbf{k}_{0}/\mathbf{k})\mathbf{D}=\sum_{\mathbf{1}m,\mathbf{1}v}N_{\mathbf{1}v}^{1}\cdot\big{(} g_{MM^{\prime}}^{\alpha_{HD}}g_{MM}^{\alpha_{HB}}\big{)}_{m,v}\cdot\bigg{(}f_{1 km}^{ DM}\bigg{)}+\sum_{\mathbf{1}m,\mathbf{1}v}M_{\mathbf{1}v}^{1}\cdot\big{(}g_{NN^{ \prime}}^{\alpha_{HD}},g_{NN}^{\alpha_{HB}}\big{)}_{m,v}\cdot\bigg{(}f_{1 km}^{ DN}\bigg{)}\]  
\[i(\mathbf{k}_{0}/\mathbf{k})\mathbf{B}=\sum_{\mathbf{1}m,\mathbf{1}v}N_{\mathbf{1}v}^{1}\cdot\big{(}g_{ MM^{\prime}}^{\alpha_{ED}}g_{MM}^{\alpha_{EB}}\big{)}_{m,v}\cdot\bigg{(}f_{1 km}^{ DM}\bigg{)}+\sum_{\mathbf{1}m,\mathbf{1}v}M_{\mathbf{1}v}^{1}\cdot\big{(}g_{NN^{ \prime}}^{\alpha_{ED}},g_{NN}^{\alpha_{EB}}\big{)}_{m,v}\cdot\bigg{(}f_{1 km}^{ DN}\bigg{)}\]  
Figure 4: Reduced scattering cross-section \(Q_{s}/\left(\pi R^{2}\right)\) for all incidence angles \(\theta\) and \(\phi\) for a bianisotropic sphere with the effective material parameters color-coded in Figure 1b and with \(x=k_{0}R=1\). In panel (**a**), the incidence polarization angle is \(\alpha=0\); in (**b**) \(\alpha=\pi/2\). The color of the surface corresponds to the magnitude of \(Q_{s}/\left(\pi R^{2}\right)\). This translates into a system of equations  
\[\hat{G}_{M}F_{Mq}=i(k_{0}/k_{q})\hat{U}F_{Nq} \tag{29}\]  
\[\hat{G}_{N}F_{Nq}=i(k_{0}/k_{q})\hat{V}F_{Mq} \tag{30}\]  
where \(F_{Mq}=\left(f_{1-1q^{\prime}}^{DM}f_{1-1q^{\prime}}^{BM}f_{10q}^{DM}f_{10q}^{ RM}f_{11q^{\prime}}^{DM}f_{11q}^{BM}\right)^{T}\), \(F_{Mq}=\left(f_{1-1q^{\prime}}^{DN}f_{1-1q^{\prime}}^{BN}f_{10q}^{DN}f_{10q}^{ DN}f_{11q}^{DN}\right)^{T}\), and the matrices \(\hat{G}_{M}\) and \(\hat{G}_{N}\) are composed of the coefficients \(\hat{G}_{M}\) and \(\hat{G}_{NN}\)  
\[\hat{G}_{M}= \begin{pmatrix}g_{SMM-}^{A_{HD}}&g_{SMM-}^{A_{HB}}&g_{SMM-}^{A_{HD} }&g_{SMM-}^{A_{HB}}&g_{SMM-}^{A_{HB}}&g_{SMM-}^{A_{HB}}\\ g_{ED}^{A_{EB}}&g_{EB}^{A_{EB}}&g_{ED}^{A_{EB}}&g_{ED}^{A_{EB}}&g_{ED}^{A_{EB}}&g _{ED}^{A_{EB}}\\ g_{MM-}^{A_{HD}}&g_{MM-}^{A_{HB}}&g_{MM-}^{A_{HD}}&g_{MM-}^{A_{HB}}&g_{MM-}^{A_{ HD}}&g_{MM-}^{A_{HD}}&g_{MM-}^{A_{HD}}\\ g_{MDM-}^{A_{HD}}&g_{MM-}^{A_{HD}}&g_{MM0}^{A_{HD}}&g_{MM0}^{A_{HD}}&g_{MM0}^{A_{ HD}}&g_{MM+0}^{A_{HB}}&g_{MM+0}^{A_{HB}}\\ g_{ED}^{A_{ED}}&g_{ED}^{A_{EB}}&g_{ED}^{A_{ED}}&g_{ED}^{A_{EB}}&g_{ED}^{A_{EB}}&g _{ED}^{A_{EB}}&g_{ED}^{A_{EB}}\\ g_{MMM-+}^{A_{HD}}&g_{MM-+}^{A_{HD}}&g_{MM0+}^{A_{HB}}&g_{MM++}^{A_{HD}}&g_{MM+ }^{A_{HD}}&g_{MM+}^{A_{HB}}\\ g_{MDM-+}^{A_{HD}}&g_{MM-+}^{A_{HB}}&g_{MMM+}^{A_{HD}}&g_{MM+}^{A_{HB}}&g_{MM+ }^{A_{HD}}&g_{MM+}^{A_{HB}}\\ \end{pmatrix} \]  
\[\hat{G}_{N}=