## 12 Summary and Discussion
Nevertheless the symmetry allows to decouple the BSC at least with some particular continua. 1. The symmetry protected BSCs constitute the vast majority of BSCs which are symmetrically mismatched with the first diffraction continuum \(m=0,n=0\) of both polarizations. The EM field configurations of such BSCs presented in Figure 2 show hybridizations of a few orbital numbers \(l=2,4,6,\ldots\) which specify the BSCs as multipoles of high order. Therefore the BSC solutions can not be obtained by the use of the dipole approximation [20; 21]. The most remarkable property from experimental viewpoint is the robustness of the BSCs relative to choice of the material parameters of the dielectric spheres. We present in Figure 3 an example of the BSC which is symmetry protected relative to the TM diffraction continuum but a zero coupling to the TE continuum obtained through variation of the sphere radius. 2. We demonstrated that the BSC can be accessed not only by variation of the material parameters but also by variation of Bloch wave vector \(\beta\) along the array axis. Patterns of the Bloch BSCs are presented in Figure 3.
3. By tuning of the radius of the spheres we found BSCs in the next sectors of continua with \(m\
eq 0\). These BSCs shown in Figure 4 are remarkable by that they carry the OAM with spinning Poynting vectors. 4. The most sophisticated Bloch BSCs with OAM demonstrate spiralling Poynting vector as shown in Figures 24 and 25. The advantage of dielectric structures is a high quality factor and a wide range of BSC wavelengths from microns (photonics) to centimeter (microwave) as dependent on the choice of the radius of the spheres. Although the BSCs exist only in selected points in the parametric space there is a nearest vicinity of the BSC point where the BSC predominantly contributes into the cross-section and the EM field in the near field zone as seen from Figures 10 and 11. That leads to extremely efficient light harvesting capabilities [83]. The far zone EM fields can also show abundant features related to the BSCs. In particular Figure 11a demonstrates the effect of antenna when the BSC with azimuthal number \(m=2\) converts the EM energy into the perpendicular directions. The BSCs with OAM \(m=\pm 1\) emerge in the response of the array to incident plane waves with circular polarization. A transfer of the SAM of the incident plane wave into the OAM of EM field takes place for any frequency and wave vector of the incident wave as shown in Figure 13. The transfer results in the power current spinning around the array. The most remarkable is that as seen from Figures 13 and 16 in the nearest vicinity of the BSCs with \(m\
eq 0\) the array supports giant vortical power currents which are directly related to the extremal enhancement of the scattered field. The value of the current is also sensitive to the distance from the array. It rapidly goes down away from spheres as shown in Figure 19.  
Theoretically the value of the circulating currents can grow up to infinity in the BSC point. However there is a difference between the present theory and possible experimental realization of the transfer of SAM into OAM, that is (1) a finite number of the spheres and (2) there are always some losses when the waves transport through the sample because of material for spheres. The most profound effect of finite arrays is that the BSCs become quasi-BSCs because, unlike a plasmonic sphere, finite dielectric systems can not support BSCs [101; 102; 103]. Therefore the effect of giant vortical currents around the array can be suppressed. Indeed, as our calculations show in Figure 27 for finite number \(N\) the currents decay for approaching to ends of the array. However with since \(N\geq 100\) at middle of the array the BSC is restoring. The next problem which can seriously damage the effect of giant spinning currents is the complex dielectric permittivity \(\epsilon=\epsilon^{\prime}+i\epsilon^{\prime\prime}\).