Geometric Phase-Driven Scattering Evolutions

We explore the classical topic of scattering manipulation, from a different perspective of controlled excitations and interferences of quasi-normal modes (QNMs). Scattered waves can be expanded as coherent additions of radiations from the QNMs excited, and thus relative amplitudes and phases among them are crucial factors to engineer for scattering shaping. Here relying on the electromagnetic reciprocity, we provide full geometric representations based on the Poincar\'e sphere for those factors, and identify the hidden underlying geometric phases that drive the scattering evolutions. Further synchronous exploitations of the incident polarization-dependent geometric phases and excitation amplitudes enable efficient manipulations of both scattering intensities and polarizations. Continuous geometric phase spanning 2π is directly manifest through scattering variations, even in the rather elementary configuration of an individual particle scattering waves of varying polarizations. We have essentially merged three vibrant fields of geometric phase, Mie scattering and QNM, and unlocked an extra dimension of geometric phase for scattering manipulations, which will greatly broaden the horizons of many disciplines associated with not only electromagnetic scatterings, but also scatterings of waves in other forms.