Orthonormal basis for nonparaxial focused fields in two dimensions, and its application to modeling scattering and optical manipulation of objects

Abstract

A new family of rigorous solutions to the two-dimensional Helmholtz equation is discussed. These solutions form a complete orthonormal basis in terms of which any focused field can be expressed. The directionality of each element of this basis is regulated by a parameter which is related to an imaginary displacement of the focus. The forces and torques that these fields and any linear combination of them exert on a homogeneous circular scatterer can be calculated analytically, regardless of the relative position between the scatterer and the focus.