Nonlinear Excitation of Ideal Anapoles

An ideal anapole is a localized excitation of electromagnetic fields that does not produce any far-field radiation. In practice, anapoles are not ideal due to the parasitic scattered fields associated with higher-order multipoles.

Here, we use the recently established exact current multipole expansion and the exact anapole condition to design an ideal anapole in which radiation due to the multipole orders up to the electric and magnetic octupoles is either eliminated or strongly suppressed, reducing the total radiated power by orders of magnitude. We also propose and study realistic photonic structures in which such anapoles can be excited by a uniform linearly polarized plane wave through second-harmonic generation that involves the off-diagonal elements of the second-order susceptibility tensor.