The fundamental polarization singularities of monochromatic light are normally associated with invariance under coordinated rotations: symmetry operations that rotate the spatial dependence of an electromagnetic field by an angle θ and its polarization by a multiple γθ of that angle. These symmetries are generated by mixed angular momenta of the form J_γ = L + γS, and they generally induce Möbius-strip topologies, with the coordination parameter γ restricted to integer and half-integer values. In this work we construct beams of light that are invariant under coordinated rotations for arbitrary rational γ, by exploiting the higher internal symmetry of ‘bicircular’ superpositions of counter-rotating circularly polarized beams at different frequencies. We show that these beams have the topology of a torus knot, which reflects the subgroup generated by the torus-knot angular momentum J_γ, and we characterize the resulting optical polarization singularity using third- and higher-order field moment tensors, which we experimentally observe using nonlinear polarization tomography.

We show that an optical vortex beam, implemented classically, can be transferred to the transverse amplitude of a heralded single photon. For this purpose we have relied on the process of spontaneous parametric downconversion (SPDC) for the generation of signal and idler photon pairs, using a pump in the form of a Bessel-Gauss (BG) beam with orbital angular momentum (specifically, with topological charge l = 1 and l = 2). We have designed our source so that it operates within the short SPDC crystal regime for which, the amplitude and phase of the pump may be transferred to a heralded single photon. In order to verify the vortex nature of our heralded single photon, we have shown that the conditional angular spectrum and the transverse intensity at the single-photon level match similar measurements carried out for the pump. In addition, we have shown that when our heralded single photon is diffracted through a triangular aperture, the far-field single-photon transverse intensity exhibits the expected triangular arrangement of intensity lobes associated with the presence of orbital angular momentum.

Insights gained from quantum physics can inspire novel classical technologies. These quantum-inspired technologies are protocols that aim at mimicking particular features of quantum algorithms. They are generally easier to implement and make use of intense beams. Here we demonstrate in a proof-of-concept experiment a quantum-inspired protocol based on the idea of quantum fingerprinting (Phys. Rev. Lett. 87, 167902, 2001).The carriers of information are optical beams with orbital angular momentum (OAM). These beams allow the implementation of a Fredkin gate or polarization-controlled SWAP operation that exchanges data encoded on beams with different OAM. We measure the degree of similarity between waveforms and strings of bits without unveiling the information content of the data.

In this work, we propose to design a liquid crystal–based modular and extendable platform of cutting-edge optical technologies for studying materials based on the analysis of polarization and wavefront of light in the wavelength range of 10–50 μm, which is considered to work even in the longer wavelengths range. This platform will be driven by the future THz-FEL source TerRa@BriXSinO that produces high power radiation in THz-range from 6 THz up to 30 THz (Mid-/Far-IR). The lack of optical infrastructures in this range has been tackled by fabricating liquid crystal–based geometric phase components that have been specifically designed for this purpose. This is in order to optimally exploit all the source’s potential for maximum accuracy and efficiency in determining polarization- and wavefront-sensitive properties of materials. We present an overview of a few experiments for characterizing bulk inhomogeneities, dielectric anisotropy, surface roughness, cracks, impact damages, and stress and strain effects with special emphasis on non-destructive tests on composite structures. The tools for wavefront shaping developed within our platform will be exploited to add a further degree of freedom, i.e., orbital angular momentum, to nonlinear optics techniques, such as Terahertz Hyper-Raman spectroscopy, for investigating chiral agents’ properties.

We present an experimental and theoretical study of type I, frequency-degenerate spontaneous parametric down-conversion (SPDC) with a Bessel-Gauss pump in which we include both paraxial and nonparaxial pump beam configurations. We present measurements of the SPDC angular spectrum (AS), of the conditional angular spectrum (CAS) of signal-mode single photons as heralded by the detection of an idler photon, and of the transverse wave-vector signal-idler correlations (TWC). We show that as the pump is made increasingly nonparaxial, the AS acquires a nonconcentric double-cone structure, with the CAS shape depending on the azimuthal location of the heralding detector, while the signal-idler wave-vector correlation region splits into characteristic doublet stripes, representing as yet unexplored nontrivial, nonlocal quantum correlations between the signal and idler photons. Our work provides further understanding of SPDC with a particular class of structured pump beams, and we believe that the controlled presence of double wave-vector correlations represents an interesting resource for photon-pair quantum-state engineering.

We introduce a wide class of singular inhomogeneously polarized beams characterized by a nonuniform rotation rate of the local polarization azimuth about a C- or a V-point. They are obtained by adding an extra phase modulation with an m-fold rotational symmetry to the helical wavefronts underpinning Poincaré beams. The resulting modulated Poincaré beams have been theoretically studied and experimentally generated using tailored space-varying-axis plates based on liquid crystals.