The high-order toroidal moments and anapole states in all-dielectric photonics (1810.04945v1)

Abstract: All-dielectric nanophotonics attracts ever increasing attention nowadays due to the possibility to control and configure light scattering on high-index semiconductor nanoparticles. It opens a room of opportunities for the designing novel types of nanoscale elements and devices, and paves a way to advanced technologies of light energy manipulation. One of the exciting and promising prospects is associated with the utilizing so called toroidal moment being the result of poloidal currents excitation, and anapole states corresponding to the interference of dipole and toroidal electric moments. Here, we present and investigate in details via the direct Cartesian multipole decomposition higher order toroidal moments of both types (up to the electric octupole toroidal moment) allowing to obtain new near- and far-field configurations. Poloidal currents can be associated with vortex-like distributions of the displacement currents inside nanoparticles revealing the physical meaning of the high-order toroidal moments and the convenience of the Cartesian multipoles as an auxiliary tool for analysis. We demonstrate high-order nonradiating anapole states (vanishing contribution to the far-field zone) accompanied by the excitation of intense near-fields. We believe our results to be of high importance for both fundamental understanding of light scattering by high-index particles, and a variety of nanophotonics applications and light governing on nanoscale.

High-Order Toroidal Moments and Anapole States in All-Dielectric Photonics

The paper presents a comprehensive exploration of the role of high-order toroidal moments and anapole states in all-dielectric photonics, emphasizing the significance of nondispersive high-index dielectric nanoparticles such as Si, Ge, and TiO2. Through rigorous Cartesian multipole decomposition, the work investigates the contributions of these moments to the near- and far-field configurations of electromagnetic scattering.

Overview and Technical Contributions

The research focuses on novel toroidal moments derived from poloidal current configurations and their resultant anapole states. The authors provide a detailed breakdown of high-order toroidal moments extending up to electric octupole and magnetic quadrupole, facilitated by Cartesian multipole decomposition. This approach surpasses traditional Mie theory in analyzing scattering phenomena in optically large particles, which typically do not account for complex displacement current configurations.

By extending the Cartesian multipole expansion to higher orders, the authors capture additional optical effects enabled by the additional degrees of freedom from toroidal contributions. This advanced decomposition separates the radiating and nonradiating components of the multipoles, underscoring the analytical utility of irreducible Cartesian multipoles that observe the SO(3) symmetry.

Results and Implications

The paper reports an excellent correlation between the derived theoretical expressions and numerical stimulations performed using COMSOL Multiphysics and Mie theory. It is noted that while lower-order toroidal moments align well with spherical multipoles, higher-order toroidal configurations diverge—clarifying existing discrepancies in high-index material scattering descriptions.

A salient finding involves the characterization of high-order nonradiating anapole states, derived from interference patterns of traditional and toroidal multipoles. Such states arise from the constructive and destructive interference between electric, magnetic, and toroidal dipole moments, offering new insights into the manipulation of near-field enhancements and scattering nullification. Particularly, this leads to high local field concentrations, promising metrics for optoelectronic applications.

Additionally, the derivation illustrates the utility of toroidal moments to substantiate novel "hybrid anapole states," wherein simultaneous annihilation of different multipolarities is achieved.

Future Directions

The implications of this research are profound for both theoretical and applied nanophotonics. The accurate characterization of toroidal and anapole states will inform future designs of nanoscale optical devices and metasurfaces, potentially enhancing the efficacy of light manipulation at sub-wavelength scales. Beyond the immediate scope, extensions of these methodologies could address complex multipolar interactions in heterogeneous and anisotropic media.

Future work could further elaborate on the role of "hidden" toroidal moments in more complex geometries and explore the integration of these findings into metamaterials and photonic devices aiming for desired electromagnetic response traits. Moreover, given the rich insights provided into nonradiative field dynamics, applications in sensing, signaling, and energy transfer could benefit substantially from these explorations.

In summary, the paper provides an in-depth theoretical framework and experimental validation for high-order toroidal moments and anapole states, paving the way for innovative advances within the domain of all-dielectric photonics.