The singular nature of a non-integer spiral phase plate allows easy manipulation of spatial degrees of freedom of photon states. Using two such devices, we have observed very high dimensional (D > 3700) spatial entanglement of twin photons generated by spontaneous parametric downconversion.

By analyzing entangled photon states in terms of high-dimensional spatial mode superpositions, it becomes feasible to expose high-dimensional entanglement, and even the nonlocality of twin photons. To this end, a proper analyzer should be designed that is capable of handling a large number of spatial modes, while still being convenient to use in an experiment. We compare two variants of a high-dimensional spatial mode analyzer on the basis of classical and quantum considerations. These analyzers have been tested in classical optical experiments.

The special spiral phase structure of an optical vortex leads to an intriguing study in modern singular optics. This paper proposes a real-time phase measurement method of vortex beam based on pixelated micropolarizer array (PMA). Four phase-shifting fringe images can be obtained from a single interference image, thus the vortex beam phase can be obtained in real-time. The proposed method can achieve full-field phase measurement of the vortex beam with the advantages of lower computation and vibration resistance. In the experiments, the typical phases of vortex with different topological charges are loaded on a spatial light modulator (SLM) to generate diffraction vortex beam, and the phase distribution of vortex beam is obtained in real-time, which confirm the robustness of this method. This method is of great significance in promoting the study of optical vortices.

The combination of diffractive and refractive elements in hybrid optical systems allows for precise control of the longitudinal chromatic aberration. We provide comprehensive design strategies for hybrid hyperchromatic lenses that maximise the longitudinal chromatic aberrations. These lenses are mainly used in chromatic confocal sensor systems for efficient non-contact profilometry as well as for measurements of distances and wall thicknesses of transparent materials. Our design approach enables the tailoring of the sensor properties to the specific measurement problem and assists designers in finding optimised solutions for industrial applications. We, for example, demonstrate a hybrid system that significantly exceeds the longitudinal chromatic aberration of purely diffractive elements.

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