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We produce families of two-dimensional gap solitons (GSs) maintained by moir\'{e} lattices (MLs) composed of linear and nonlinear sublattices, with the defocusing sign of the nonlinearity. Depending on the angle between the sublattices, the ML may be quasiperiodic or periodic, composed of mutually incommensurate or commensurate sublattices, respectively (in the latter case, the inter-lattice angle corresponds to Pythagorean triples). The GSs include fundamental, quadrupole, and octupole solitons, as well as quadrupoles and octupoles carrying unitary vorticity. Stability segments of the GS families are identified by means of the linearized equation for small perturbations, and confirmed by direct simulations of perturbed evolution., Comment: 4 figures, to be published in Optics Letters (2024)

Atomic time scale imaging, opening a new era for studying dynamics in microcosmos, is presently attracting immense research interesting on the global level due to its powerful ability. On the atom level, physics, chemistry, and biology are identical for researching atom motion and atomic state change. The light possesses twoness, the information carrier and the research resource. The most fundamental principle of this imaging is that light records the event modulated light field by itself, so called all optical imaging. This paper can answer what is the essential standard to develop and evaluate atomic time scale imaging, what is the optimal imaging system, and what are the typical techniques to implement this imaging, up to now. At present, the best record in the experiment, made by multistage optical parametric amplification (MOPA), is realizing 50 fs resolved optical imaging with a spatial resolution of ~83 lp/mm at an effective framing rate of 10^13 fps for recording an ultrafast optical lattice with its rotating speed up to 10^13 rad/s.

We introduce a system combining the quadratic self-attractive or composite quadratic-cubic nonlinearity, acting in the combination with the fractional diffraction, which is characterized by its L\'{e}vy index $\alpha $. The model applies to a gas of quantum particles moving by L\'{e}vy flights, with the quadratic term representing the Lee-Huang-Yang correction to the mean-field interactions. A family of fundamental solitons is constructed in a numerical form, while the dependence of its norm on the chemical potential characteristic is obtained in an exact analytical form. The family of \textit{quasi-Townes solitons}, appearing in the limit case of $\alpha =1/2$, is investigated by means of a variational approximation. A nonlinear lattice, represented by spatially periodical modulation of the quadratic term, is briefly addressed too. The consideration of the interplay of competing quadratic (attractive) and cubic (repulsive) terms with a lattice potential reveals families of single-, double-, and triple-peak gap solitons (GSs) in two finite bandgaps. The competing nonlinearity gives rise to alternating regions of stability and instability of the GS, the stability intervals shrinking with the increase of the number of peaks in the GS., Comment: to be published in Chaos, Solitons and Fractals

We present a framing integration ultrafast photography (FIP), which integrates the framing structure, codes a dynamic event by an inversed 4f system (I4F) and decodes regionally with high spatial resolution. In the experiment about laser-induced plasma, FIP achieved a framing rate of 5.3*1012 frames per second (fps) and an intrinsic spatial resolution of 110.4 lp/mm. It has an excellent spatio-temporal resolution and a compact and flexible structure. Hence, it can probe unrepeatable ultrafast intra- and inter-atomic/molecular dynamics, different in size and duration with high-quality. Besides, FIP can lay a foundation for integrating and simplifying ultrafast photography instruments. Here the minimum framing time (temporal resolution) is limited by only the laser pulse duration; be sure, attosecond laser technology may further increase framing rates by several orders of magnitude.

We consider one- and two-dimensional (1D and 2D) optical or matter-wave media with a maximum of the local self-repulsion strength at the center, and a minimum at periphery. If the central area is broad enough, it supports ground states in the form of flat-floor \textquotedblleft bubbles", and topological excitations, in the form of dark solitons in 1D and vortices with winding number $m$ in 2D. Unlike bright solitons, delocalized bubbles and dark modes were not previously considered in this setting. The ground and excited states are accurately approximated by the Thomas-Fermi expressions. The 1D and 2D bubbles, as well as vortices with $m=1$, are completely stable, while the dark solitons and vortices with $m=2$ have nontrivial stability boundaries in their existence areas. Unstable dark solitons are expelled to the periphery, while unstable double vortices split in rotating pairs of unitary ones. Displaced stable vortices precess around the central point., Comment: to be published in Nonlinear Dynamics

Dark solitons and localized defect modes against periodic backgrounds are considered in arrays of waveguides with defocusing Kerr nonlinearity constituting a nonlinear lattice. Bright defect modes are supported by local increase of the nonlinearity, while dark defect modes are supported by a local decrease of the nonlinearity. Dark solitons exist for both types of the defect, although in the case of weak nonlinearity they feature side bright humps making the total energy propagating through the system larger than the energy transferred by the constant background. All considered defect modes are found stable. Dark solitons are characterized by relatively narrow windows of stability. Interactions of unstable dark solitons with bright and dark modes are described., Comment: published in Optics Letters

Families of coupled solitons of $\mathcal{PT}$-symmetric physical models with gain and loss in fractional dimension and in settings with and without cross-interactions modulation (CIM), are reported. Profiles, powers, stability areas, and propagation dynamics of the obtained $\mathcal{PT}$-symmetric coupled solitons are investigated. By comparing the results of the models with and without CIM, we find that the stability area of the model with CIM is much broader than the one without CIM. Remarkably, oscillating $\mathcal{PT}$-symmetric coupled solitons can also exist in the model of CIM with the same coefficients of the self- and cross-interactions modulations. In addition, the period of these oscillating coupled solitons can be controlled by the linear coupling coefficient., Comment: Published in Nonlinear Dynamics, 103(2), 1831-1840 (2021)

We construct families of fundamental, dipole, and tripole solitons in the fractional Schr\"{o}dinger equation (FSE)\ incorporating self-focusing cubic and defocusing quintic terms modulated by factors $\cos ^{2}x$ and $\sin^{2}x$, respectively. While the fundamental solitons are similar to those in the model with the uniform nonlinearity, the multipole complexes exist only in the presence of the nonlinear lattice. The shapes and stability of all the solitons strongly depend on the L\'{e}vy index (LI)\ that determines the FSE fractionality. Stability areas are identified in the plane of LI and propagation constant by means of numerical methods, and some results are explained with the help of an analytical approximation. The stability areas are broadest for the fundamental solitons and narrowest for the tripoles., Comment: Publised in Chaos, Solitons and Fractals, 144, 110589 (2021)

We demonstrate that, with the help of a Gaussian potential barrier, dark modes in the form of a local depression ("bubbles") can be supported by the repulsive Kerr nonlinearity in combination with fractional dimension. Similarly, W-shaped modes are supported by a double potential barrier. Families of the modes are constructed in a numerical form, and also by means of the Thomas-Fermi and variational approximations. All these modes are stable, which is predicted by computation of eigenvalues for small perturbations and confirmed by direct numerical simulations., Comment: to be published in Nonlinear Dynamics

The discovery and understanding of many ultrafast dynamical processes are often invaluable. This paper is the first report to apply optical parametric amplification to implement single-shot ultrafast imaging with high space and time resolutions. Our setup breaks the constraints usually occurring among the time resolution, frame number, frame interval and spatial resolution in existing single-shot femtosecond imagers, so its performance can be greatly improved by using laser pulses with higher power and shorter time durations. Our setup has provided the highest experimental record of the frame rate and spatial resolution with the temporal resolution of 50 fs simultaneously. It is very powerful for accurate temporal and spatial observations of the ultrafast transient events with a lifetime down to the femtosecond scale, such as atomic or molecular dynamics in photonic material, plasma physics, living cells, and neural activity., Comment: arXiv admin note: substantial text overlap with arXiv:1807.00685

Ultrafast imaging is a powerful tool for studying space-time dynamics in photonic material, plasma physics, living cells, and neural activity. Pushing the imaging speed to the quantum limit could reveal extraordinary scenes about the questionable quantization of life and intelligence, or the wave-particle duality of light. However, previous designs of ultrafast photography are intrinsically limited by framing speed. Here, we introduce a new technique based on a multiple non-collinear optical parametric amplifier principle (MOPA), which readily push the frame rate into the area of ten trillion frames per second with higher spatial resolution than 30 line pairs per millimeter. The MOPA imaging is applied to record the femtosecond early evolution of laser-induced plasma grating in air for the first time. Our approach avoids the intrinsic limitations of previous methods, thus can be potentially optimized for higher speed and resolution, opening the way of approaching quantum limits to test the fundamentals.