TY - JOUR

T1 - Analytical model of resonant electromagnetic dipole-quadrupole coupling in nanoparticle arrays

AU - Babicheva, Viktoriia E.

AU - Evlyukhin, Andrey B.

N1 - Funding information: The work has the support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy within the Cluster of Excellence PhoenixD (EXC 2122, Project ID 390833453) and from the Air Force Office of Scientific Research under Grant No. FA9550-19-1-0032.

PY - 2019/5/15

Y1 - 2019/5/15

N2 - An analytical model for investigations of multipole coupling effects in the finite and infinite nanoparticle arrays supporting electromagnetic resonances is presented and discussed. This model considers the contributions of both electric and magnetic modes excited in the nanoparticles, including electric and magnetic dipoles and electric and magnetic quadrupoles. The magnetic quadrupole propagator (Green's tensor) that describes the electromagnetic field generated by a point magnetic quadrupole source in all wave zones is derived. As an example, we apply the developed model to study infinite two-dimensional rectangular periodic arrays of spherical silicon nanoparticles supporting the dipole and quadrupole resonant responses. The correctness and accuracy of the analytical model are confirmed by the agreement of its results with the results of full-wave numerical simulations. Using the developed model, we show the electromagnetic coupling between electric dipole and magnetic quadrupole moments as well as between magnetic dipole and electric quadrupole moments even for the case of an infinite rectangular periodic array of spherical nanoparticles. The strong suppression of the dipole or quadrupole moment due to the coupling effects is demonstrated and discussed for spherical nanoparticle arrays. The analytical expressions for the reflection and transmission coefficients written with the effective dipole and quadrupole polarizabilities are derived for normal light incidences and zero-order diffraction. The derived expressions are applied to explain the lattice anapole (invisibility) states when the incident light is transmitted unperturbed through the silicon nanoparticle array. The important role of dipole and quadrupole excitations in scattering compensation resulting in the lattice anapole effect is explicitly demonstrated. The presented approach can be used for designing metasurfaces and further utilizing them in developing ultrathin functional optical elements.

AB - An analytical model for investigations of multipole coupling effects in the finite and infinite nanoparticle arrays supporting electromagnetic resonances is presented and discussed. This model considers the contributions of both electric and magnetic modes excited in the nanoparticles, including electric and magnetic dipoles and electric and magnetic quadrupoles. The magnetic quadrupole propagator (Green's tensor) that describes the electromagnetic field generated by a point magnetic quadrupole source in all wave zones is derived. As an example, we apply the developed model to study infinite two-dimensional rectangular periodic arrays of spherical silicon nanoparticles supporting the dipole and quadrupole resonant responses. The correctness and accuracy of the analytical model are confirmed by the agreement of its results with the results of full-wave numerical simulations. Using the developed model, we show the electromagnetic coupling between electric dipole and magnetic quadrupole moments as well as between magnetic dipole and electric quadrupole moments even for the case of an infinite rectangular periodic array of spherical nanoparticles. The strong suppression of the dipole or quadrupole moment due to the coupling effects is demonstrated and discussed for spherical nanoparticle arrays. The analytical expressions for the reflection and transmission coefficients written with the effective dipole and quadrupole polarizabilities are derived for normal light incidences and zero-order diffraction. The derived expressions are applied to explain the lattice anapole (invisibility) states when the incident light is transmitted unperturbed through the silicon nanoparticle array. The important role of dipole and quadrupole excitations in scattering compensation resulting in the lattice anapole effect is explicitly demonstrated. The presented approach can be used for designing metasurfaces and further utilizing them in developing ultrathin functional optical elements.

UR - http://www.scopus.com/inward/record.url?scp=85066403004&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.99.195444

DO - 10.1103/PhysRevB.99.195444

M3 - Article

AN - SCOPUS:85066403004

VL - 99

JO - Physical Review B

JF - Physical Review B

SN - 2469-9950

IS - 19

M1 - 195444

ER -