In recent years, various optical measurement technologies such as far-infrared spectroscopy, low-frequency Raman spectroscopy, optical Kerr effect spectroscopy, and two-dimensional Raman-terahertz spectroscopy have developed vigorously. By comparing the complementary aspects detected by various linear and nonlinear spectroscopic techniques, a coherent picture emerges from studies of dynamics in water. Numerous molecular dynamics experiments and theoretical investigations have demonstrated low-frequency molecular motions in liquid water. For example, intermolecular hydrogen bond vibration, molecular reorientation motion, and the interaction between molecule/ionic solute and hydrogen bond all occur in the THz region, which are closely related to their physical/chemical properties and structural dynamics. However, precise probing of various modes of motion is difficult due to the complexity of the collective and cooperative motion of molecules and the spectral overlap of related modes. With the development of THz optical technology, current state-of-the-art THz sources can generate pulsed electric fields with peak intensities on the order of ~MV/cm. Such strong fields make it possible to use THz waves as the driving light source for nonlinear polarization of the medium, which in turn leads to the development of the emerging terahertz Kerr effect (TKE) spectroscopy technique. Many low-frequency molecular motion modes, such as the collective directional motion of molecules and the cooperative motion under the constraint of weak intermolecular interactions, are resonantly excited to unprecedentedly strong amplitudes driven by the THz electric field. Thereby the collected responses are increased. The TKE technique thus creates an interesting prospect for investigating low-frequency dynamics in these media. In view of this, this paper firstly summarizes the research work on the measurement mechanism of TKE spectroscopy by taking the solid material without low-frequency molecular dynamics process as an example. Starting from the principle of TKE technology and the exploration of the properties of solid matter using this technology, its application in the exploration of low-frequency molecular dynamics of liquid water and aqueous solutions is introduced. Liquid water is considered the building block of life and possesses many extraordinary physical and biochemical properties. Its hydrogen bonding network plays a crucial role in these properties. It is generally believed that the ability of water to form complex hydrogen-bonding networks is the main reason for its various kinetic and thermodynamic properties that are different from other liquids. However, the exact structure of the hydrogen-bonding network, the spatial extent of its existence, and the associated timescale are not known. And the relevant spectral information of the basic properties of the reaction water is still not known. Therefore, it is of great significance to evaluate the hydrogen bond-related kinetic properties of liquid water by optical means.

As a novel layered noble metal dichalcogenide material, palladium diselenide (PdSe₂) has attracted wide interest due to its excellent optical and electronic properties. In this work, a strong third-order nonlinear optical response of 2D PdSe₂ films is reported. We conduct both open-aperture (OA) and closed-aperture (CA) Z-scan measurements with a femtosecond pulsed laser at 800 nm to investigate the nonlinear absorption and nonlinear refraction, respectively. In the OA experiment, we observe optical limiting behaviour originating from large two photo absorption (TPA) in the PdSe₂ film of β = 3.26 ×10^-8 m/W. In the CA experiment, we measure a peak-valley response corresponding to a large and negative Kerr nonlinearity of n₂ = -1.33×10^-15 m²/W – two orders of magnitude larger than bulk silicon. In addition, the variation of n₂ as a function of laser intensity is also characterized, with n₂ decreasing in magnitude when increasing incident laser intensity, becoming saturated at n₂ = -9.96×10^-16 m²/W at high intensities. Our results show that the extraordinary third-order nonlinear optical properties of PdSe₂ have strong potential for high-performance nonlinear photonic devices. Keywords: 2D materials, PdSe₂ films, Z-scan technique, Kerr nonlinearity, nonlinear photonics.

We demonstrate a photonic RF integrator based on an integrated soliton crystal micro-comb source. By multicasting and progressively delaying the input RF signal using a transversal structure, the input RF signal is integrated discretely. Up to 81 wavelengths are provided by the microcomb source, which enable a large integration time window of ~6.8 ns, together with a time resolution as fast as ~84 ps. We perform signal integration of a diverse range of input RF signals including Gaussian pulses with varying time widths, dual pulses with varying time intervals and a square waveform. The experimental results show good agreement with theory. These results verify our microcomb-based integrator as a competitive approach for RF signal integration with high performance and potentially lower cost and footprint.

The Kerr nonlinear optical performance of silicon nanowire waveguides integrated with 2D layered graphene oxide (GO) films is theoretically studied and optimized based on experimentally measured linear and nonlinear optical parameters of the GO films. The strong mode overlap between the silicon nanowires and highly nonlinear GO films yields a significantly enhanced Kerr nonlinearity for the hybrid waveguides. A detailed analysis for the influence of waveguide geometry and GO film thickness on the propagation loss, nonlinear parameter, and nonlinear figure of merit (FOM) is performed. The results show that the effective nonlinear parameter and nonlinear FOM can be increased by up to ≈52 and ≈79 times relative to bare silicon nanowires, respectively. Self-phase modulation (SPM)-induced spectral broadening of optical pulses is used as a benchmark to evaluate the nonlinear performance, examining the trade-off between enhancing Kerr nonlinearity and minimizing loss. By optimizing the device parameters to balance this, a high spectral broadening factor of 27.6 can be achieved ‒ more than 6 times that achieved in previous experiments. Finally, the influence of pulse chirp, material anisotropy, and the interplay between saturable absorption and SPM is also discussed. These results provide useful guidance for optimizing the Kerr nonlinear optical performance of silicon waveguides integrated with 2D layered GO films.

We consider the Dirac electron as a nonperturbative particle-like solution consistent with its own Kerr-Newman (KN) gravitational and electromagnetic field. We develop the earlier models of the KN electron regularized by Israel and López, and consider the non-perturbative electron model as a bag model formed by Higgs mechanism of symmetry breaking. The López regularization determines the unique shape of the electron in the form of a thin disk with a Compton radius reduced by 4π. In our model this disk is coupled with a closed circular string which is placed on the border of the disk and creates the caused by gravitation frame-dragging string tension produced by the vector potential of the Wilson loop. Using remarkable features of the Kerr-Schild coordinate system, which linearizes the Dirac equation, we obtain solutions of the Dirac equation consistent with the KN gravitational and electromagnetic field, and show that this solution takes the form of a massless relativistic string. Parallelism of this model with quantum representations in Heisenberg and Schrodinger pictures explains remarkable properties of the stringy electron model in the relativistic scattering processes.

The Schwarzschild metric describes a non-rotating and charge-free celestial body, and it results in things stopping at the event horizon of a black hole and spending infinite time across the event horizon by the observer far away from the black hole. The analysis of the particle’s behavior at the event horizon tells us that this solution predicts an un-expanded black hole which violates the astronomical observations and our knowledge about the black hole. Although some alternative metrics have been proposed, the singularity problem is still unsolved. In this research, the degenerate Fermi electron gas is used to reveal that the Fermi electron gas cannot shrink to a point no matter how large energy it obtains, so the singularity exists at the center very unreasonably. In order to avoid these problems, a finite-size nucleus of the black hole is proposed and reasonably explained by the behaviors of the Fermi electron gas and the Fermi neutron gas there. On the other hand, the Kerr-Newman metric is the one describing the rotating and charged black hole and the equation of the light velocity at each space point can be obtained. It tells us that there are two real and non-imaginary solutions for the radial speed of light at the position larger than the Schwarzschild radius.

We report a 92 channel RF channelizer based on a 48.9 GHz integrated micro-comb that operates via soliton crystals, together with a passive high-Q ring resonator that acts as a periodic filter with an optical 3dB bandwidth of 121.4 MHz. We obtain an instant RF bandwidth of 8.08 GHz and 17.55 GHz achieved through temperature tuning. These results represent a major advance to achieving fully integrated photonic RF spectrum channelizers with reduced low complexity, size, and high performance for digital-compatible signal detection and broadband analog signal processing.

We review recent work on broadband RF channelizers based on integrated optical frequency Kerr micro-combs combined with passive micro-ring resonator filters, with microcombs having channel spacings of 200GHz and 49GHz. This approach to realizing RF channelizers offers reduced complexity, size, and potential cost for a wide range of applications to microwave signal detection.

We report enhanced nonlinear optics in complementary metal-oxide-semiconductor (CMOS) compatible photonic platforms through the use of layered two-dimensional (2D) graphene oxide (GO) films. We integrate GO films with silicon-on-insulator nanowires (SOI), high index doped silica glass (Hydex) and silicon nitride (SiN) waveguides and ring resonators, to demonstrate an enhanced optical nonlinearity including Kerr nonlinearity and four-wave mixing (FWM). The GO films are integrated using a large-area, transfer-free, layer-by-layer method while the film placement and size are controlled by photolithography. In SOI nanowires we observe a dramatic enhancement in both the Kerr nonlinearity and nonlinear figure of merit (FOM) due to the highly nonlinear GO films. Self-phase modulation (SPM) measurements show significant spectral broadening enhancement for SOI nanowires coated with patterned films of GO. The dependence of GO’s Kerr nonlinearity on layer number and pulse energy shows trends of the layered GO films from 2D to quasi bulk-like behavior. The nonlinear parameter of GO coated SOI nanowires is increased 16 folds, with the nonlinear FOM increasing over 20 times to FOM > 5. We also observe an improved FWM efficiency in SiN waveguides integrated with 2D layered GO films. FWM measurements for samples with different numbers of GO layers and at different pump powers are performed, achieving up to ≈7.3 dB conversion efficiency (CE) enhancement for a uniformly coated device with 1 layer of GO and ≈9.1 dB for a patterned device with 5 layers of GO. These results reveal the strong potential of GO films to improve the nonlinear optics of silicon, Hydex and SiN photonic devices.

Convolutional neural networks (CNNs), inspired by biological visual cortex systems, are a powerful category of artificial neural networks that can extract the hierarchical features of raw data to greatly reduce the network parametric complexity and enhance the predicting accuracy. They are of significant interest for machine learning tasks such as computer vision, speech recognition, playing board games and medical diagnosis [1-7]. Optical neural networks offer the promise of dramatically accelerating computing speed to overcome the inherent bandwidth bottleneck of electronics. Here, we demonstrate a universal optical vector convolutional accelerator operating beyond 10 Tera-FLOPS (floating point operations per second), generating convolutions of images of 250,000 pixels with 8-bit resolution for 10 kernels simultaneously — enough for facial image recognition. We then use the same hardware to sequentially form a deep optical CNN with ten output neurons, achieving successful recognition of full 10 digits with 900 pixel handwritten digit images with 88% accuracy. Our results are based on simultaneously interleaving temporal, wavelength and spatial dimensions enabled by an integrated microcomb source. This approach is scalable and trainable to much more complex networks for demanding applications such as unmanned vehicle and real-time video recognition.

Layered two-dimensional (2D) graphene oxide (GO) films are integrated with micro-ring resonators (MRRs) to experimentally demonstrate enhanced nonlinear optics in the form of four-wave mixing (FWM). Both uniformly coated and patterned GO films are integrated on CMOS-compatible doped silica MRRs using a large-area, transfer-free, layer-by-layer GO coating method together with photolithography and lift-off processes, yielding precise control of the film thickness, placement, and coating length. The high Kerr nonlinearity and low loss of the GO films combined with the strong light-matter interaction within the MRRs results in a significant improvement in the FWM efficiency in the hybrid MRRs. Detailed FWM measurements are performed at different pump powers and resonant wavelengths for the uniformly coated MRRs with 1−5 layers of GO as well as the patterned devices with 10−50 layers of GO. The experimental results show good agreement with theory, achieving up to ~7.6-dB enhancement in the FWM conversion efficiency (CE) for an MRR uniformly coated with 1 layer of GO and ~10.3-dB for a patterned device with 50 layers of GO. By fitting the measured CE as a function of pump power for devices with different numbers of GO layers, we also extract the dependence of GO’s third-order nonlinearity on layer number and pump power, revealing interesting physical insights about the evolution of the layered GO films from 2D monolayers to quasi bulk-like behavior. These results confirm the high nonlinear optical performance of integrated photonic resonators incorporated with 2D layered GO films.

In this paper, we study the weak gravitational deflection angle of relativistic massive particles by the Kerr-like black hole in the bumblebee gravity model. In particular, we focus on weak field limits and calculate the deflection angle for a receiver and source at a finite distance from the lens. To this end, we use the Gauss-Bonnet theorem of a two-dimensional surface defined by a generalized Jacobi metric. The spacetime is asymptotically non-flat due to the existence of a bumblebee vector field. Thus the deflection angle is modified and can be divided into three parts: the surface integral of the Gaussian curvature, the path integral of a geodesic curvature of the particle ray and the change in the coordinate angle. In addition, we also obtain the same results by defining the deflection angle. The effects of the Lorentz breaking constant on the gravitational lensing are analyzed. We then consider the finite-distance correction for the deflection angle of massive particles.

Advanced image processing will be crucial for emerging technologies such as autonomous driving, where the requirement to quickly recognize and classify objects under rapidly changing, poor visibility environments in real time will be needed. Photonic technologies will be key for next-generation signal and information processing, due to their wide bandwidths of 10’s of Terahertz and versatility. Here, we demonstrate broadband real time analog image and video processing with an ultrahigh bandwidth photonic processor that is highly versatile and reconfigurable. It is capable of massively parallel processing over 10,000 video signals simultaneously in real time, performing key functions needed for object recognition, such as edge enhancement and detection. Our system, based on a soliton crystal Kerr optical micro-comb with a 49GHz spacing with >90 wavelengths in the C-band, is highly versatile, performing different functions without changing the physical hardware. These results highlight the potential for photonic processing based on Kerr microcombs for chip-scale fully programmable high-speed real time video processing for next generation technologies.

The weakness of the dispersion-managed link combined with optical phase conjugation to compensate for optical signal distortion caused by chromatic dispersion and nonlinear Kerr effect of standard single mode fiber is its limited structural flexibility. We propose dispersion map that can simultaneously compensate for the distorted wavelength division multiplexed signal while increasing the configurational flexibility. Each residual dispersion per span (RDPS) in the former half of the proposed link is randomly determined, and in the latter half, the arrangement order of RDPS is the same as or inverted in the former half. We confirm that the dispersion maps in which the RDPS distribution pattern in the latter half is opposite to the arrangement order in the former half are more effective in compensation, and rather, the compensation effect is better than in the dispersion map of the conventional scheme. The notable result of this paper is that the increase of flexibility can be achieved through random arrangement of RDPS in the former half, and the compensation improvement can be achieved by through inverse arrangement in the latter half which make the distribution profile of each half link roughly symmetric with respect to the midway optical phase conjugator.

This paper discusses approaches to the numerical integration of the coupled nonlinear Schrödinger equations system in case of few-mode wave propagation. The wave propagation assumes the propagation of up to nine modes of light in an optical fiber. In this case, the light propagation is described by the non-linear coupled Schrödinger equation system, where propagation of each mode is described by own Schrödinger equation with other modes interactions. In this case, the non-linear coupled Schrödinger equation system solving becomes increasingly complex, because each mode affects the propagation of other modes. The suggested solution is based on the direct numerical integration approach, which is based on a finite-difference integration scheme. The well-known explicit finite-difference integration scheme approach fails, due to the non-stability of the computing scheme. Due to this fact, the combined explicit/implicit finite-difference integration scheme, based on the implicit Crank–Nicolson finite-difference scheme, is used. It allows ensuring the stability of the computing scheme. Moreover, this approach allows separating the whole equation system on the independent equation system for each wave mode at each integration step. Additionally, the algorithm of numerical solution refining at each step and the integration method with automatic integration step selection are used. The suggested approach has performance gains (or resolutions) up to three or more orders of magnitude in comparison with the split-step Fourier method due to the fact that there is no need to produce direct and inverse Fourier transforms at each integration step. The main advantage of the proposed method is the ability to calculate the propagation of an arbitrary number of modes in the fiber.