Comprehensive quantitative analysis of vector beam states based on vector field reconstruction

Abstract

We demonstrate a comprehensive quantitative analysis of vector beam states (VBSs) by using a vector field reconstruction (VFR) technique integrating interferometry and imaging polarimetry, where the analysis is given by a cylindrically polarized Laguerre–Gaussian (LG) mode expansion of VBSs. From test examples of cylindrically polarized LG mode beams, we obtain the complex amplitude distributions of VBSs and perform their quantitative evaluations both in radial and azimuthal directions. The results show that we generated ( l , p ) = (1, 0) LG radially polarized state with a high purity of 98%. We also argue that the cylindrically polarized LG modal decomposition is meaningful for the detail discussion of experimental results, such as analyses of mode purities and mode contaminations. Thus the VFR technique is significant for analyses of polarization structured beams generated by lasers and converters.

Reference-free quantitative microscopic imaging of coherent arbitrary vectorial light beams

“…This capability, together with the high spatial resolution, constitute decisive advantages for this technique. In comparison to interferometric approaches [12][13][14], vectorial ptychography offers a referencefree design, ensuring experimental reproducibility and precision. Furthermore, it overcomes the main limitations of modal decomposition, thanks to its versatility.…”

“…To a large extent, this results from the mixing of phase and polarization space-variant features, the simultaneous investigations of which being tedious. Since phase is involved, most approaches are interferometric, and adapted to account for polarization [12][13][14]; however, the precision of the reconstructed field relies on the knowledge of a reference beam. Wavefront-analysis methods have been demonstrated using polarization-sensitive metalens arrays [15], to the price of the limited spatial resolution of the meta-pixel.…”

Supplementary document for Tailoring ultra-broadband vector beams via programming the electric field vector of light - 5944644.pdf

“…Furthermore, based on the principle of modal decomposition [2], we can quantitatively evaluate the polarization purity of generated vector beams by calculating the overlap integral between the transmitted optical field through TNLCs and the desired vector beam [3]. To be specific, since the cylindrical vector beam are one of the orthonormal bases for paraxial beams, an arbitrary light field can be regarded as a linear superposition among the orthogonal basis modes of vector beams with the respective polarization topological charge m. Correspondingly, the mode coefficient C m can be calculated using the overlap integral expressed as…”

Robust polarimetry via convex optimization

“…Having such a method is especially useful when dealing with other degrees of freedom in addition to polarization. For example, when measuring the polarization profile of a vector beam, we might have the result where only a few points are non-physical due to experimental errors [27]. Using our method, we can find the closest approximate physical coherency matrix for these points rather than invalidating all points and repeating the entire measurement.…”