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Light beams with Orbital Angular Momentum (OAM) are explored in applications from microscopy to quantum communication, while the Talbot effect revives in applications from atomic systems to x-ray phase contrast interferometry. We evidence the topological charge of an OAM carrying THz beam in the near-field of a binary amplitude fork-grating by means of the Talbot effect, which we show to persist over several fundamental Talbot lengths. We measure and analyze the evolution of the diffracted beam behind the fork grating in Fourier domain to recover the typical donut-shaped power distribution, and we compare experimental data to simulations. We isolate the inherent phase vortex using the Fourier phase retrieval method. To complement the analysis, we assess the OAM diffraction orders of a fork grating in the far-field using a cylindrical lens.

The Talbot effect has been revived in many fields of modern optics. As a key number of self-imaging, the fundamental Talbot length plays a crucial role in many applications. However, the inspection of the Talbot carpet for determining the Talbot length is applicable only if the 2D field distribution behind the grating is represented by a 1D cross section. In this Letter, we show an effective way to overcome this limitation to explore the self-imaging of gratings with complex 2D periodicities. For that purpose, the near-field diffraction is analyzed using the Pearson correlation coefficient of the intensity distribution in Fourier space. We report results on linear, ring, and spiral gratings.

Optical beams with helical phase fronts carry orbital angular momentum (OAM). To exploit this property in integrated photonics, micrometer-scale devices that generate beams with well-defined OAM are needed. Consequently, lasers based on microring resonators decorated with azimuthal grating elements have been investigated. However, future development of such devices requires better methods to determine their OAM, as current approaches are challenging to implement and interpret. If a simple and more sensitive technique were available, OAM microring lasers could be better understood and further improved. In particular, despite most devices being pulsed, their OAM output has been assumed to be constant. OAM fluctuations, which are detrimental for applications, need to be quantified. Here, we fabricate quantum-dot microring lasers and demonstrate a simple measurement method that can straightforwardly determine the magnitude and sign of the OAM down to the level of individual laser pulses. We exploit a Fourier microscope with a cylindrical lens and then investigate three types of microring lasers: with circular symmetry, with "blazed" grating elements, and with unidirectional rotational modes. Our results confirm that previous measurement techniques obscured key details about the OAM generation. For example, while time-averaged OAM from our unidirectional laser is very similar to our blazed grating device, single-pulse measurements show that detrimental effects of mode competition are almost entirely suppressed in the former. Nevertheless, even in this case, the OAM output exhibits shot-to-shot fluctuations. Thus, our approach reveals important details in the underlying device operation that can aid in the improvement of micrometer-scale sources with pure OAM output.