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 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.

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.

Einstein’s field equation is a highly general equation. However, the equation itself provides limited information about the universe unless it is solved with different boundary conditions. Multiple solutions have been utilized to predict cosmic scales, and among them, the Friedmann-Lemaître-Robertson-Walker solution that is the back-bone of the development into todays standard model of modern cosmology: the Λ-CDM model. However this is naturally not the only solution to Einsteins field equation. We will investigate the extremal solutions of the Reissner-Nordström, Kerr, and Kerr-Newman metrics. Interestingly, in their extremal cases, these solutions yield identical predictions for horizons and escape velocity. These solutions can be employed to formulate a new cosmological model that resembles the Friedmann equation. However, a significant distinction arises in the extremal universe solution, which does not necessitate the ad hoc insertion of the cosmological constant; instead, it emerges naturally from the derivation itself. To the best of our knowledge, all other solutions relying on the cosmological constant do so by initially ad hoc inserting it into Einstein’s field equation. This clarification unveils the true nature of the cosmological constant, suggesting that it serves as a correction factor for strong gravitational fields, accurately predicting real-world cosmological phenomena only within the extremal solutions of the discussed metrics, all derived strictly from Einstein’s field equation.

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.

In this article, we review about the nature of Kerr Blackhole, Kerr metric and express kerr metric in Boyer-Lindquist co-ordinates.

High-quality optical Fano resonances, which exist in a spherical dielectric microparticle in the spatial configurations of the "whispering-gallery modes" (WGMs) and recently are referred to as the “super-resonances”, possess extremal sensitivity not only to the micro-cavity size and shape but also to the optical properties of the particulate material. The increase in the power of light radiation coupling into a super-resonance can lead to the manifestation of strong optical nonlinearity of the resonator material due to the cubic nonlinearity (optical Kerr effect) and generation of free electron plasma in certain regions of the spherical microcavity. In fact, an optically linear medium of the resonance cavity transforms into a Drude-Kerr-type medium with a strong dependence on input laser intensity. With the help of the finite-elements numerical simulations, we theoretically analyze the transformations of the resonant contour for a number of high-quality WGMs excited in a lanthanum-glass microsphere exposed to an optical radiation of different intensity. We show that in a certain input intensity range, the competition of Kerr and plasma optical nonlinearities can stop and even reverse the Stokes shift of the super-resonance observed in a pure Kerr medium. Additionally, optical ionization and plasma generation within the mode volume significantly reduce the strength of the magnetic super-resonance and lead to its spoiling and frequency splitting.

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 deterministic generation of robust soliton comb has significant meaning for the optical frequency combs to be widely used in various applications. As a novel form of microcomb, Soliton crystal holds the advantages of easy generation, high conversion efficiency, and excellent thermal robustness. Here, we report the turnkey deterministic generation of ‘Palm-like’ soliton crystal with a free-running scheme. The robustness of the turnkey soliton crystal generation is also investigated in multiple aspects, including the success rate, the thermal robustness, and the long-term stability. The experiment results reveal our turnkey soliton crystal can achieve nearly a 100% success rate with a power variation less than ±1.5 dB over one hundred trials of two samples, is insensitive to thermal effects, and is robust to the environment during four-hour laboratory time.

Axions can be stimulated to decay to photons by ambient photons of the right frequency or by photons from decay of neighboring axions. If the axion density is high enough the photon intensity can be amplified, which is a type of lasing or an axion maser. Here we review the astrophysical situations where axion lasing can appear and possibly be detected.

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.

Although some alternative metrics have been proposed in classical gravity, the singularity problem remains unresolved perfectly. To satisfy the super-gravitational requirement of a black hole without singularities, we propose some possible finite-size structure to avoid the confused one. In this research, the degenerate Fermi electron gas is first used to reveal that the Fermi electron gas cannot shrink to a point regardless of how much energy it obtains; therefore, the singularity existing at the center becomes very unreasonable. To avoid these problems, a finite-size nucleus of the black hole is proposed and explained by the behaviors of the Fermi electron gas and Fermi neutron gas for this finite-size nuclear model. We construct the Kerr-Newman black hole by using a non-rotating but charged finite-size nucleus, a compact-like star, which is surrounded by counter-rotating and corotating electrons. Based on this model, the super-gravity the same as the one from a black hole is presented, and the speed of light observed at far-away places can be nonzero at the event horizon.

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.

The aim of this work is a comprehensive study of the effect of variable atomic composition and structural-phase state of (CoFeZr)x(MgF2)100-x nanocomposites (NCs) on their nonlinear electronic and magnetic/magneto-optical properties. Micrometer-thick nanocomposites layers on the glass substrates were obtained by ion-beam sputtering of a composite target in the argon atmosphere in a wide range of compositions x=9-51at.% The value of the resistive percolation threshold xper=34 at.%, determined from the concentration dependences of the electrical resistance of NCs, coincides with the beginning of nucleation of metallic nanocrystals CoFeZr in MgF2 dielectric matrix. The absolute value of maximum magnetoresistance of NCs is 2.4 % in a magnetic field of 5.5 kOe at x=25 at.%, up to the percolation threshold. Two maxima appear in the concentration dependences of magneto-optical transversal Kerr effect, one of which at x = 34 at.% corresponds to the formation of CoFeZr alloy nanocrystals of a hexagonal structure, and the second one at x=45 at.% corresponds to the phase transition of nanocrystals from a hexagonal to a cubic body-centered structure. The magnetic percolation threshold in (CoFeZr)x(MgF2)100-x system at xfm=34 at.% with the appearance of a hysteresis loop and a coercive force of Hc≈ 8 Oe, coincides with the resistive percolation threshold xper=34 at.%. Concentration dependence of the coercive force showed that at low contents of metallic alloy x<30 at.% NCs are superparamagnetic (Hc=0). With an increase of the alloy content, in the region of magnetic and resistive percolation thresholds NCs exhibit a magnetically soft ferromagnetic character and do not change it far beyond the percolation threshold with the maximum value of the coercive force Hc< 30 Oe. Decrease in magnetic order and soft ferromagnetic are influenced by the diamagnetic phase FeF2 that we discovered at the interface of magnetic nanocrystals CoFeZr with a dielectric matrix MgF2 by the Mössbauer spectroscopy.

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.

Scattering resonances play a crucial role in understanding wave behavior in various physical systems. While significant progress has been made in analyzing resonances in high-contrast and nonlinear media, a general characterization of resonances in small, high-contrast nonlinear media with the Kerr effect, particularly in layered configurations, has remained an open problem. In this paper, we present a novel asymptotic approach that addresses this gap by providing an approximation for resonances in terms of material properties, geometry, and nonlinearity. Our results offer new insights into the dependence of resonances on these factors, particularly for complex multilayered structures, making this the first general characterization of its kind.

In synthetic diamond plate, the intrapulse correlated dynamics of self-phase modulation and spontaneous Raman scattering by optical phonons were for the first time directly investigated for tightly focused (focusing numerical aperture NA = 0.25) positively-chirped visible-range ultrashort laser pulses with variable durations (0.3-9.5 ps) and energies, transmitted through the sample. The observed modulation of the transmitted light spectra and Stokes Raman scattering spectra for the different pulse durations were related to nonthermal excitation of nonlinear phonon polarization and its eventual picosecond-scale suppression due to thermal decay of optical phonons on the timescale of electron-phonon thermalization in the material.

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.