Spatiotemporal diffractive deep neural networks.

A spatiotemporal diffractive deep neural network (STD2NN) is proposed for spatiotemporal signal processing. The STD2NN is formed by gratings, which convert the signal from the frequency domain to the spatial domain, and multiple layers consisting of spatial lenses and space light modulators (SLMs), which conduct spatiotemporal phase modulation. An all-optical backpropagation (BP) algorithm for SLM phase tuning is proposed, with the gradient of the loss function computed by the inner product of the forward propagating optical field and the backward propagating conjugated error field. As a proof of concept, a spatiotemporal word "OPTICA" is generated by the STD2NN. Afterwards, a spatiotemporal optical vortex (STOV) beam multiplexer based on the STD2NN is demonstrated, which converts the spatially separated Gaussian beams into the STOV wave-packets with different topological charges. Both cases illustrate the capability of the proposed STD2NN to generate and process the spatiotemporal signals.

Analytical expressions for the crosstalk of super-modes in the tightly bounded multicore fibers.

In this paper, an analytical approach for the super-modes in the tightly bounded multicore fibers is proposed. The method considers deterministic and random inter-core coupling, and the analytical analysis is based on the ordinary differential equations (ODEs), which are derived from the stochastic differential equations (SDEs). It is theoretically found that the crosstalk level is directly proportional to the square of the ratio for the random inter-core coupling strength over the deterministic coupling strength, and is inversely proportional to the random coupling correlation length. The ODEs for the variance and the super-mode power correlations are also provided to further facilitate the analysis for the tightly bounded multicore fibers. Simple and explicit formulas for the super-mode crosstalk power and power covariance evaluation are provided in the weak super-mode crosstalk scenario.

Nonlinear Fourier transform receiver based on a time domain diffractive deep neural network.

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.

Orbital angular momentum mode sorting based on a hybrid radial-angular hybrid lens.

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.

Analytical study on the evolutionary behavior of transfer matrix element moments in strongly coupled multimode systems.

In this paper, the evolutionary behavior of the transfer matrix element moments in strongly coupled multimode systems is studied analytically. The randomly coupled multimode system is modeled by a set of coupled stochastic differential equations (SDEs), which can be used to find the coupled ordinary differential equations (ODEs) for the arbitrary order moments of the matrix elements. Since the ODEs are with the constant coefficients, it is possible to obtain the analytical solutions. The asymptotic behaviors of the solutions are investigated by comparing with the existing results derived from the property of the Haar matrix, and a perfect agreement is observed. The evolutionary behaviors of the transfer matrix element moments computed by the analytical formulas have excellent match with the Monte Carlo simulation results. The analytical method can be highly beneficiary for the multimode system design and analysis.

Simple phase retrieval method based on two intensity measurements on a single plane.

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.