Single-particle light scattering: imaging and dynamical fluctuations in the polarization and spectral response

A theoretical framework for light scattering from individual nanoscale particles or structures is developed. The main considerations distinguishing the present treatment from the theories developed for conventional light-scattering experiments are the experimental requirements for the detection of the limited light from a single scatterer. These requirements include use of a high numerical aperture microscope objective, annular illumination, and the reduced linear dichroism instead of depolarization ratio. It is shown how these issues are considered in relating the microscopic polarizability tensor to the far-field experimental observables. The approach is further extended to include the dynamical response in the scattering polarization and spectrum and discussed in the context of the particle's rotational diffusion. For dynamic light scattering, analytical expressions are derived to elucidate the interrelationship between the experimental configuration, the observable, the polarizability tensor, and the diffusion tensor. Specific examples including static imaging and dynamic correlation for rodlike and spheroidal scatterers are discussed to illustrate the application of the theory.