PT-symmetric solitons and parameter discovery in self-defocusing saturable nonlinear Schrödinger equation via LrD-PINN.

We propose a physical information neural network with learning rate decay strategy (LrD-PINN) to predict the dynamics of symmetric, asymmetric, and antisymmetric solitons of the self-defocusing saturable nonlinear Schrödinger equation with the PT-symmetric potential and boost the predicted evolutionary distance by an order of magnitude. Taking symmetric solitons as an example, we explore the advantages of the learning rate decay strategy, analyze the anti-interference performance of the model, and optimize the network structure. In addition, the coefficients of the saturable nonlinearity strength and the modulation strength in the PT-symmetric potential are reconstructed from the dataset of symmetric soliton solutions. The application of more advanced machine learning techniques in the field of nonlinear optics can provide more powerful tools and richer ideas for the study of optical soliton dynamics.

Deep neural network for modeling soliton dynamics in the mode-locked laser.

Integrating the information of the first cycle of an optical pulse in a cavity into the input of a neural network, a bidirectional long short-term memory (Bi_LSTM) recurrent neural network (RNN) with an attention mechanism is proposed to predict the dynamics of a soliton from the detuning steady state to the stable mode-locked state. The training and testing are based on two typical nonlinear dynamics: the conventional soliton evolution from various saturation energies and soliton molecule evolution under different group velocity dispersion coefficients of optical fibers. In both cases, the root mean square error (RMSE) for 80% of the test samples is below 15%. In addition, the width of the conventional soliton pulse and the pulse interval of the soliton molecule predicted by the neural network are consistent with the experimental results. These results provide a new insight into the nonlinear dynamics modeling of the ultrafast fiber laser.

Propagation and interaction between special fractional soliton and soliton molecules in the inhomogeneous fiber.

INTRODUCTION: Fractional nonlinear models have been widely used in the research of nonlinear science. A fractional nonlinear Schrödinger equation with distributed coefficients is considered to describe the propagation of pi-second pulses in inhomogeneous fiber systems. However, soliton molecules based on the fractional nonlinear Schrödinger equation are hardly reported although many fractional soliton structures have been studied. OBJECTIVES: This paper discusses the propagation and interaction between special fractional soliton and soliton molecules based on analytical solutions of a fractional nonlinear Schrödinger equation. METHODS: Two analytical methods, including the variable-coefficient fractional mapping method and Hirota method with the modified Riemann-Liouville fractional derivative rule, are used to obtain analytical non-travelling wave solutions and multi-soliton approximate solutions. RESULTS: Analytical non-travelling wave solutions and multi-soliton approximate solutions are derived. The form conditions of soliton molecules are given, and the dynamical characteristics and interactions between special fractional solitons, multi-solitons and soliton molecules are discussed in the periodic inhomogeneous fiber and the exponential dispersion decreasing fiber. CONCLUSION: Analytical chirp-free and chirped non-traveling wave solutions and multi-soliton approximate solutions including soliton molecules are obtained. Based on these solutions, dynamical characteristics and interactions between special fractional solitons, multi-solitons and soliton molecules are discussed. These theoretical studies are of great help to understand the propagation of optical pulses in fibers.

Holographic and speckle encryption using deep learning: publisher's note.

This publisher's note contains a correction to Opt. Lett.46, 5794 (2021)10.1364/OL.443398.

Holographic and speckle encryption using deep learning.

Vulnerability analysis of optical encryption schemes using deep learning (DL) has recently become of interest to many researchers. However, very few works have paid attention to the design of optical encryption systems using DL. Here we report on the combination of the holographic method and DL technique for optical encryption, wherein a secret image is encrypted into a synthetic phase computer-generated hologram (CGH) by using a hybrid non-iterative procedure. In order to increase the level of security, the use of the steganographic technique is considered in our proposed method. A cover image can be directly diffracted by the synthetic CGH and be observed visually. The speckle pattern diffracted by the CGH, which is decrypted from the synthetic CGH, is the only input to a pre-trained network model. We experimentally build and test the encryption system. A dense convolutional neural network (DenseNet) was trained to estimate the relationship between the secret images and noise-like diffraction patterns that were recorded optically. The results demonstrate that the network can quickly output the primary secret images with high visual quality as expected, which is impossible to achieve with traditional decryption algorithms.

Existence, symmetry breaking bifurcation and stability of two-dimensional optical solitons supported by fractional diffraction.

We study existence, bifurcation and stability of two-dimensional optical solitons in the framework of fractional nonlinear Schrödinger equation, characterized by its Lévy index, with self-focusing and self-defocusing saturable nonlinearities. We demonstrate that the fractional diffraction system with different Lévy indexes, combined with saturable nonlinearity, supports two-dimensional symmetric, antisymmetric and asymmetric solitons, where the asymmetric solitons emerge by way of symmetry breaking bifurcation. Different scenarios of bifurcations emerge with the change of stability: the branches of asymmetric solitons split off the branches of unstable symmetric solitons with the increase of soliton power and form a supercritical type bifurcation for self-focusing saturable nonlinearity; the branches of asymmetric solitons bifurcates from the branches of unstable antisymmetric solitons for self-defocusing saturable nonlinearity, featuring a convex shape of the bifurcation loops: an antisymmetric soliton loses its stability via a supercritical bifurcation, which is followed by a reverse bifurcation that restores the stability of the symmetric soliton. Furthermore, we found a scheme of restoration or destruction the symmetry of the antisymmetric solitons by controlling the fractional diffraction in the case of self-defocusing saturable nonlinearity.

Molecular insights into the dispersion stability of graphene oxide in mixed solvents: Theoretical simulations and experimental verification.

HYPOTHESIS: Improving the dispersion stability of graphene oxide (GO) suspensions is of great importance in many potential applications of GO, such as GO-based laminated membranes used for separation, printable electronics, and aqueous liquid crystals. EXPERIMENTS: Molecular dynamics (MD) simulations and quantum chemistry (QC) calculations along with complementary experiments were performed to study the dispersion stability of GO in the mixtures of water and polar organic solvents (dimethyl sulfoxide (DMSO), ethanol, and acetone). FINDINGS: GO exhibits better dispersion stability in a solvent mixture than in pure water. The MD simulations uncover the underlying mechanism that mixed solvent layers are formed steadily on the surface of GO sheets and screen the interactions between them. QC calculations reveal that both DMSO and water form hydrogen bonds with the oxidized regions of GO. X-ray diffraction experiments confirm that the GO sheets are intercalated by DMSO and water molecules. Furthermore, the optimal ratio of the organic solvent to water is determined to achieve the best dispersion stability of GO through MD simulations. And such ratio is also verified by ultraviolet absorption spectral experiments. Thus, our findings provide a facile method to prepare GO suspensions with high dispersion stability.

Symmetric and asymmetric solitons supported by a 𝒫𝒯-symmetric potential with saturable nonlinearity: bifurcation, stability and dynamics.

The symmetry breaking bifurcation of solitons in an optical waveguide with focusing saturable nonlinearity and parity-time (𝒫𝒯)-symmetric complex-valued external potentials is investigated. As the soliton power increases, it is found that the branches of asymmetric solitons split off from the base branches of 𝒫𝒯-symmetric fundamental soliton. The bifurcation diagrams, consisting essentially of the propagation constants of optical solitons, indicate that symmetric fundamental and multipole solitons, as well as asymmetric solitons can exist. The stabilities and the dynamics characteristics of solitons are comprehensively investigated. We find the different instability scenarios of the symmetric solitons, but the symmetry breaking bifurcation is caused only by the onset of instability of the symmetric fundamental solitons. This result is further confirmed by the numerical examples with the different saturable nonlinearity parameters. In particular, we find that the soliton power and the stability of soliton at the bifurcation points are significantly changed by varying the strength of the saturable nonlinearities. These results provide additional way to control symmetry breaking bifurcations in 𝒫𝒯-symmetric optical waveguide.

Vectorial effect of hybrid polarization states on the collapse dynamics of a structured optical field.

The collapse dynamics of a structured optical field with a distribution of spatially-variant states of polarization (SoP) and a spiral phase in the field cross section is studied using the two-dimensional coupled nonlinear SchrÓ§dinger equations. The self-focusing of a structured optical field with an inhomogeneous SoP distribution can give rise to new phenomena of collapse dynamics that is completely different from a scalar field. The collapse patterns are closely related to the topological charges of the vortexas well as the polarization, the initial power, and the SoP distribution in the field cross section. A single on-axis collapse or multiple off-axis partial collapses may occur due to the self-focusing effects of linearly, elliptically and circularly polarized components located at different positions of the field cross-section. The polarization in the core of the collapsing beam is always linearly polarized. The structured collapsing beams, which are driven by the vortex, propagate along a spiral trajectory in a saturated medium.

Effects on lipid bilayer and nitrogen distribution induced by lateral pressure.

The lateral pressure exerted on cell membrane is of great importance to signal transduction. Here, we perform molecular dynamics simulation to explore how lateral pressure affects the biophysical properties of lipid bilayer as well as nitrogen distribution in the membrane. Our results show that both physical properties of cell membrane and nitrogen distribution are highly sensitive to the lateral pressure. With the increasing lateral pressure, area per lipid drops and thickness of membrane increases obviously, while nitrogen molecules are more congested in the center of lipid bilayer than those under lower lateral pressure. These results suggest that the mechanism of nitrogen narcosis may be related to the lateral pressure.

Three-dimensional structures of the spatiotemporal nonlinear Schrödinger equation with power-law nonlinearity in PT-symmetric potentials.

The spatiotemporal nonlinear Schrödinger equation with power-law nonlinearity in PT-symmetric potentials is investigated, and two families of analytical three-dimensional spatiotemporal structure solutions are obtained. The stability of these solutions is tested by the linear stability analysis and the direct numerical simulation. Results indicate that solutions are stable below some thresholds for the imaginary part of PT-symmetric potentials in the self-focusing medium, while they are always unstable for all parameters in the self-defocusing medium. Moreover, some dynamical properties of these solutions are discussed, such as the phase switch, power and transverse power-flow density. The span of phase switch gradually enlarges with the decrease of the competing parameter k in PT-symmetric potentials. The power and power-flow density are all positive, which implies that the power flow and exchange from the gain toward the loss domains in the PT cell.

Discussion and a new attack of the optical asymmetric cryptosystem based on phase-truncated Fourier transform.

A discussion and a cryptanalysis of the optical phase-truncated Fourier-transform-based cryptosystem are presented in this paper. The concept of an optical asymmetric cryptosystem, which was introduced into the optical image encryption scheme based on phase-truncated Fourier transforms in 2010, is suggested to be retained in optical encryption. A new method of attack is also proposed to simultaneously obtain the main information of the original image, the two decryption keys from its cyphertext, and the public keys based on the modified amplitude-phase retrieval algorithm. The numerical results illustrate that the computing efficiency of the algorithm is improved and the number of iterations is much less than that by the specific attack, which has two iteration loops.

Controllable Akhmediev breather and Kuznetsov-Ma soliton trains in PT-symmetric coupled waveguides.

The PT-symmetric and PT-antisymmetric Akhmediev breather (AB) and Kuznetsov-Ma (KM) soliton train solutions of a (2+1)-dimensional variable-coefficient coupled nonlinear Schrödinger equation in PT-symmetric coupled waveguides with gain and loss are derived via the Darboux transformation method. From these analytical solutions, we investigate the controllable behaviors of AB and KM soliton trains in a diffraction decreasing system with exponential profile. By adjusting the relation between the maximum Zm of effective propagation distance and the peak locations Zi of AB and KM soliton trains, we can control the restraint, maintenance and postpone excitations of AB and KM soliton trains.

Controllable optical rogue waves in the femtosecond regime.

We derive analytical rogue wave solutions of variable-coefficient higher-order nonlinear Schrödinger equations describing the femtosecond pulse propagation via a transformation connected with the constant-coefficient Hirota equation. Then we discuss the propagation behaviors of controllable rogue waves, including recurrence, annihilation, and sustainment in a periodic distributed fiber system and an exponential dispersion decreasing fiber. Finally, we investigate nonlinear tunneling effects for rogue waves.

Wigner distribution function of an Airy beam.

We study the Wigner distribution function (WDF) of an Airy beam. The analytical expression of the WDF of an Airy beam is obtained. Numerical and graphical results of the WDF of an Airy beam provide an intuitive picture to explain the intriguing features of an Airy beam, such as weak diffraction, curved propagation, and self-healing. Our results confirm that these novel properties of an Airy beam are attributed to the continuum of sideways contributions to the field.

Exact spatial similaritons and rogons in 2D graded-index waveguides.

We analytically obtain both bright and dark spatial similaritons on the background wave and rogons in two-dimensional (2D) graded-index waveguides.

Nonlinear similariton tunneling effect in the birefringent fiber.

We derive analytical bright and dark similaritons of the generalized coupled nonlinear Schrodinger equations with distributed coefficients. An exact balance condition between the dispersion, nonlinearity and the gain/loss has been obtained. Under this condition, we discuss the nonlinear similariton tunneling effect.

Analytical spatiotemporal localizations for the generalized (3+1)-dimensional nonlinear Schrödinger equation.

We derive analytical 3D spatiotemporal similaritons and solitons of the generalized (3+1)-dimensional nonlinear Schrödinger equation with distributed coefficients.