Orbital angular momentum (OAM) modes have their phase distribution as exp (jlθ), which resembles the plane wave in the Cartesian coordinates. Like the traditional lens, which can focus the plane wave on the focal plane, the angular lens can focus the OAM beam in the angular domain, albeit with a relatively long tail due to the unsatisfied angular focal condition for the non-ring shape beams. In this paper, a hybrid lens in the angular domain and the radial domain is proposed. The radial lens with the specific radially distributed phase guarantees the angular focal condition is met for the beams with an arbitrary beam waist or radial field distribution, which significantly improves the performance for the OAM modes sorting by the angular lens. The discrimination of the different OAM modes can be achieved efficiently based on such a single optical component, i.e., the proposed hybrid radial-angular lens, with the OAM modes inter-mode crosstalk as 3.7% when the topological charge difference is 3.

A diffractive deep neural network (D2NN) is proposed to distinguish the inverse nonlinear Fourier transform (INFT) symbols. Different from other recently proposed D2NNs, the D2NN is fiber based, and it is in the time domain rather than the spatial domain. The D2NN is composed of multiple cascaded dispersive elements and phase modulators. An all-optical back-propagation algorithm is proposed to optimize the phase. The fiber-based time domain D2NN acts as a powerful tool for signal conversion and recognition, and it is used in a receiver to recognize the INFT symbols all optically. After the symbol conversion by the D2NN, simple phase and amplitude measurement will determine the correct symbol while avoiding the time-consuming NFT. The proposed device can not only be implemented in the NFT transmission system, but also in other areas which require all optical time domain signal transformation and recognition, like sensing, signal coding and decoding, beam distortion compensation and image recognition.

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In this work, a simple phase retrieval method is proposed by observing two intensity patterns on a single plane, which are generated with and without a lens. Rigorous theoretical derivations show that the two fields constitute the Fourier transform pairs, and a modified Gerchberg–Saxton algorithm is proposed to recover the phase patterns from the Fourier pairs. The proposed method does not require the intensity patterns to be measured on two different planes along the propagation distance, and this is quite beneficial in a system with a phase tuning element like a spatial light modulator, which can form a virtual lens by creating a parabola-like phase distribution. Experiments are conducted to demonstrate the effectiveness of the proposed phase retrieval method.

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