Basis-independent tomography and nonseparability witnesses of pure complex vectorial light fields by Stokes projections

Abstract

Complex vectorial light fields, non-separable in their polarization and spatial degree of freedom, are of relevance in a wide variety of fields encompassing microscopy, metrology, communication and topological studies. Controversially, they have been suggested as analogues to quantum entanglement, raising fundamental questions on the relation between non-separability in classical systems, and entanglement in quantum systems. Here we propose and demonstrate basis-independent tomography of arbitrary vectorial light fields by relating their concurrence to spatially resolved Stokes projections. We generate vector fields with controllable non-separability using a novel compact interferometer that incorporates a digital micro-mirror device (DMD), thus offering a holistic toolbox for the generation and quantitative analysis of arbitrary vectorial light fields.

Paraxial skyrmionic beams

“…The Skyrmion number for a beam can change on free space propagation, however, if Skyrmion field lines escape radially out of the beam towards regions of negligible intensity. Demonstrating these properties requires the preparation of vector vortex beams and measurement of the polarization or spin in planes perpendicular to the beam axis [57]. We shall report on such experiments elsewhere.…”

Structured Light in Turbulence

“…where r denotes the coordinates, a and b are complex coefficients while u R,L (r) are spatial components of the field and are solutions of the scalar Helmholtz equation. In general such fields have spatially inhomogeneous polarisation distributions [64][65][66], which can be quantified by a measure of nonseparability of the spatial mode and its polarisation [67][68][69]. This class of spatial modes, called vector modes, has received a great deal of attention [70], [71].…”

Measuring the non-separability of spatially disjoint vectorial fields

“…This time our toolkit is quantum-inspired, returning a vector quality factor (the vectorial equivalent to the M 2 parameter), but with some shortcomings that require continual improvement. The first was to alter the measurement from basis dependent [46] to a basis independent [49], removing the requirement of knowledge of the field to be probed. But here we have highlighted that even though these techniques perform very well at characterising vector modes whose spatial and polarisation degrees of freedom are shape-invariant upon propagation, it fails at characterising beams that do not satisfy such condition, whose constituting spatial modes separate from each other upon propagation, becoming path-like separable.…”

“…As stated earlier, the degree of concurrence or nonseparability of spatially disjoint vector fields, cannot be quantified using traditional methods, such as a basis independent tomography, as exhibited in [49]. In other words, traditional methods can only quantify the global behaviour of vector fields, but not the local behaviour exhibited by spatially disjoint vector fields.…”

“…Conversely, characterisation techniques are still somewhat limited. These include filtering [41][42][43] and deterministic detection [44] of the mode, as well as quantitative analysis by a quantum toolkit, for a full decomposition via tomographic projections [45] and a reduced measurement set for determining the non-separability [46][47][48][49]. Both quantitative techniques rely on the similarities between the vector modes and quantum-entangled states, for example, the latter being the classical equivalent to the well-known concurrence, C, for qubits [50,51].…”