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Since both metamaterials composed of artificial molecules (inclusions in a host material) and natural molecular materials at optical and greater frequencies can exhibit significant electric quadrupolarization as well as electric and magnetic dipolarization, we determine the passive, causal electric quadrupolarizability for a spherically symmetric molecule, namely a dielectric sphere subject to source-driven applied fields. For source-driven excitations, it is found that two electric quadrupolarizability constants are generally required to characterize the electric quadrupolar response of the sphere, with one of the constants multiplying the divergence of the applied electric field. For source-free fields, such as the fields of the eigenmodes of an electric quadrupolar array, the local electric field illuminating each inclusion is solenoidal, the constitutive relation is characterized by just one quadrupolarizability constant, and the electric quadrupolarization becomes traceless. It is also found that the electric quadrupolarization becomes very large and effectively traceless near the resonant frequencies of electrically small plasmonic spheres with negative permittivity and for somewhat larger spheres with positive permittivity.

ELECTRIC QUADRUPOLARIZABILITY OF A SOURCE-DRIVEN DIELECTRIC SPHERE