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.

本文利用亚波长硅圆柱组成的超表面设计了用于太赫兹探测器的聚焦透镜，通过改变硅柱的直径，实现对太赫兹波传输相位0~2π的调控。在1 THz频率下，所设计的单面超表面透镜，太赫兹波电场能量密度提升到入射平面波的32倍。基于工艺制备可行性和抗反射考虑，提出了一种双面超表面透镜，将电场能量密度提升到入射平面波的44倍。对比于传统超半球太赫兹硅透镜，超表面透镜具有厚度薄，体积小的优点，有利于太赫兹探测器组件的小型化，为实现与太赫兹探测器的集成提供了可能性。

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.

In the process of high-harmonic generation with a Laguerre-Gaussian (LG) mode, it was well established that the topological charge could be of an N-fold increase due to angular momentum conservation. Here, by mimicking the effect of high-harmonic generation, we devise a simple algorithm to generate optical vortex arrays carrying arbitrary topological charges with a single phase-only spatial light modulator. By initially preparing a coaxial superposition of suitable low-order LG modes, we demonstrate experimentally that the topological charges of the embedded vortices can be multiplied and transformed into arbitrarily high orders on demand, while the array structure remains unchanged. Our algorithm offers a concise way to efficiently manipulate the structured light beams and holds promise in optical micromanipulation and remote sensing.