title: Spatial and temporal variations in vector fields.
abstract: We introduce a new metric to characterise spatial variations occurring in a time varying vector field, and we derive a rotationally invariant formula that quantifies temporal fluctuations within a consistent framework. So as to highlight the physics behind these metrics, both are derived from a well-known experiment in polarimetry. The derivation yields a set of expressions in a two-dimensional space, which is subsequently expanded to n-dimensions for special cases. The resulting expressions of the temporal and spatial metrics are incorporated into the electromagnetic theory of coherence and polarisation. Examples are given in the context of single molecule detection when measuring asymmetrically and radially polarised beams.
authors.affiliation: Imperial College London, London SW7 2BZ, UK. cm1105@ic.ac.uk
authors.forename: C
authors.initials: C
authors.lastname: Macías-Romero
authors.forename: M R
authors.initials: MR
authors.lastname: Foreman
authors.forename: P
authors.initials: P
authors.lastname: Török
mesh_terms: D003198:Computer Simulation; D008027:Light; D008962:Models, Theoretical; D009391:Nephelometry and Turbidimetry / Q000379:methods*; D012542:Scattering, Radiation