Orbital angular momentum (OAM), emerging as an inherently high-dimensional property of photons, has boosted information capacity in optical communications. However, the potential of OAM in optical computing remains almost unexplored. Here, we present a highly efficient optical computing protocol for complex vector convolution with the superposition of high-dimensional OAM eigenmodes. We used two cascaded spatial light modulators to prepare suitable OAM superpositions to encode two complex vectors. Then, a deep-learning strategy is devised to decode the complex OAM spectrum, thus accomplishing the optical convolution task. In our experiment, we succeed in demonstrating 7-, 9-, and 11-dimensional complex vector convolutions, in which an average proximity better than 95% and a mean relative error <6 % are achieved. Our present scheme can be extended to incorporate other degrees of freedom for a more versatile optical computing in the high-dimensional Hilbert space.

While the uncertainty principle for linear position and linear momentum, and more recently for angular position and angular momentum, is well established, its radial equivalent has so far eluded researchers. Here we exploit the logarithmic radial position, lnr, and hyperbolic momentum, PH, to formulate a rigorous uncertainty principle for the radial degree of freedom of transverse light modes. We show that the product of their uncertainties is bounded by Planck’s constant, Δlnr·ΔPH≥ℏ/2, and identify a set of radial intelligent states that satisfy the equality. We illustrate the radial uncertainty principle for a variety of intelligent states, by preparing transverse light modes with suitable radial profiles. We use eigenmode projection to measure the corresponding hyperbolic momenta, confirming the minimum uncertainty bound. Optical systems are most naturally described in terms of cylindrical coordinates, and our radial uncertainty relation provides the missing piece in characterizing optical quantum measurements, providing a new platform for the fundamental tests and applications of quantum optics.

We demonstrated an efficient scheme of measuring the angular velocity of a rotating object with the detection light working at the infrared regime. Our method benefits from the combination of second-harmonic generation (SHG) and rotational Doppler effect, i.e., frequency upconversion detection of rotational Doppler effect. In our experiment, we use one infrared light as the fundamental wave (FW) to probe the rotating objects while preparing the other FW to carry the desired superpositions of orbital angular momentum. Then these two FWs are mixed collinearly in a potassium titanyl phosphate crystal via type II phase matching, which produces the visible second-harmonic light wave. The experimental results show that both the angular velocity and geometric symmetry of rotating objects can be identified from the detected frequency-shift signals at the photon-count level. Our scheme will find potential applications in infrared monitoring.

We demonstrate the full vectorial feature of second-harmonic generation (SHG), i.e., from infrared full Poincaré beams to visible full Poincaré beams, based on two cascading type I phase-matching beta barium borate crystals of orthogonal optical axes. We visualize the structured features of the vectorial SHG wave by using Stokes polarimetry and show the interesting doubling effect of the polarization topological index, i.e., a low-order full Poincaré beam is converted to a high-order one. However, the polarization singularities of both C points and L lines are found to keep invariant during the SHG process. Our scheme could offer a deeper understanding on the interaction of vectorial light fields with media and can be generalized to other nonlinear optical effects.

Developing a low-cost, room-temperature operated and complementary metal-oxide-semiconductor (CMOS) compatible visible-blind short-wavelength infrared (SWIR) silicon photodetector is of interest for security, telecommunications, and environmental sensing. Here, we present a silver-supersaturated silicon (Si:Ag)-based photodetector that exhibits a visible-blind and highly enhanced sub-bandgap photoresponse. The visible-blind response is caused by the strong surface-recombination-induced quenching of charge collection for short-wavelength excitation, and the enhanced sub-bandgap response is attributed to the deep-level electron-traps-induced band-bending and two-stage carrier excitation. The responsivity of the Si:Ag photodetector reaches 504 mA· W 1 at 1310 nm and 65 mA ·W 1 at 1550 nm under 3 V bias, which stands on the stage as the highest level in the hyperdoped silicon devices previously reported. The high performance and mechanism understanding clearly demonstrate that the hyperdoped silicon shows great potential for use in optical interconnect and power-monitoring applications.

The generation and manipulation of optical vortices are of fundamental importance in a variety of promising applications. Here, we develop a nonlinear optical paradigm to implement self- and cross-convolution of optical vortex arrays, demonstrating the features of a vortex copier and regenerator. We use a phase-only spatial light modulator to prepare the 1064 nm invisible fundamental light to carry special optical vortex arrays and use a potassium titanyl phosphate crystal to perform type II second-harmonic generation in the Fourier domain to achieve 532 nm visible structured vortices. Based on pure cross-convolution, we succeed in copying arbitrary-order single vortices as well as their superposition states onto a prearranged array of fundamental Gaussian spots. Also, based on the simultaneous effect of self- and cross-convolutions, we can expand the initial vortex lattices to regenerate more vortices carrying various higher topological charges. Our presented method of realizing an optical vortex copier and regenerator could find direct applications in optical manipulation, optical imaging, optical communication, and quantum information processing with structured vortex arrays.