Orientational imaging of single fluorescent molecules: What laser beam can provide azimuth-rotation-invariant image shape?

Abstract

In some areas of orientational fluorescence microscopy of single quantum emitters, exploiting tightly focused laser beams, the following property of single quantum emitter images is desirable: Rotations of an emitter’s transition dipole moment around a microscope objective axis leads to similar rotations of the emitter’s image but not to modifying a shape of this image. Here, we derive mathematically a generalized structure of an entrance laser beam that can provide this property. It was discovered that the only and the most possibly generalized kind of beam satisfying this requirement is a beam expressed mathematically as a linear complex superposition of a circularly polarized vortex beam with a spin angular momentum s=1 and an integer orbital angular momentum l and a circularly polarized vortex beam with a spin angular momentum s=−1 and an orbital angular momentum l+2.