Mie scattering of purely azimuthal Laguerre-Gauss beams: Angular-momentum-induced transparency

The Mie scattering of a circularly polarized, purely azimuthal Laguerre-Gauss beam carrying orbital angular momentum from a particle small compared with the incident wavelength is treated analytically. Using the vector spherical harmonics, we show angular momentum conservation leads to two physical mechanisms that cause vanishingly small scattering intensity when the dipole moment dominates the response of the particle. The application of this angular-momentum-induced transparency is discussed in the case of a plasmonic crystal whose collective modes possess a well-defined angular momentum content.

Figure 1

Linear-log comparison of the waist-independent magnitude of scattering from the lowest order electric multipole moment, $\beta$, from Eqs. (9b) and (12b) taken in the limit $k_{d}a\ll 1$ excited by an incident circularly polarized $p=0$, $l=1$ LG beam (solid line) to that of an incident circularly polarized plane wave (dashed line) for cases when $k_{d}a$ scales from $0.05$ to $0.5$ for ${\epsilon }_r={\epsilon }_p/{\epsilon }_d={(k_p/k_d)}^2=2.25$. For the incident plane wave the lowest order term is $\beta (m=1)$, while for the incident purely azimuthal LG beam the lowest order term is $\beta (m=2)$.