Time-space Modulation Research Articles

Sub-Nyquist SAR Imaging and Error Correction Via an Optimization-Based Algorithm.

Sub-Nyquist synthetic aperture radar (SAR) based on pseudo-random time-space modulation has been proposed to increase the swath width while preserving the azimuthal resolution. Due to the sub-Nyquist sampling, the scene can be recovered by an optimization-based algorithm. However, these methods suffer from some issues, e.g., manually tuning difficulty and the pre-definition of optimization parameters, and a low signal-noise ratio (SNR) resistance. To address these issues, a reweighted optimization algorithm, named pseudo-ℒ0-norm optimization algorithm, is proposed for the sub-Nyquist SAR system in this paper. A modified regularization model is first built by applying the scene prior information to nearly acquire the number of nonzero elements based on Bayesian estimation, and then this model is solved by the Cauchy-Newton method. Additionally, an error correction method combined with our proposed pseudo-ℒ0-norm optimization algorithm is also present to eliminate defocusing in the motion-induced model. Finally, experiments with simulated signals and strip-map TerraSAR-X images are carried out to demonstrate the effectiveness and superiority of our proposed algorithm.

Nonreciprocal wave propagation in a time-space modulated metasurface using the modified plane wave expansion method

The present work focuses on the impact of including the time-space modulation features on the band structure. This study introduces a modified plane wave expansion method for dealing with the out-of-plane wave propagation in a two-dimensional periodic metasurface. The proposed method, which is applied to structures with modulated properties, tackles the constraints of the conventional plane wave method. The characteristics of uncommon systems with space-time-variant properties are explored by analyzing the produced dispersion curves by modified plane wave method. This approach can also resolve the inconsistencies and drawbacks of other similar approaches. Three scenarios are employed to extract the patterns of bandgap regions and discover the impact of time-traveling material features on the creation of bandgap in periodic metasurfaces. The integrity of the introduced method has been established by comparison with data obtained from COMSOL finite element software as well as the reported results in the literature. The secondary objective of this study is to manipulate the location of the bandgap to achieve complete control over the propagation of waves. The effectiveness of the proposed approach becomes more apparent when applied to metamaterials that incorporate piezoelectric materials with discrete structures. This relates primarily to enhanced precision and speed, particularly in higher modes and sheds light on a potential application of extending this scenario to the more complex structures.

On-chip optical isolator based on unidirectional wavelength-mode conversion waveguide

Breaking Lorentz reciprocity is one necessary condition of optical isolator design. Unidirectional wavelength-mode conversion will be realized in a time-dependent system through a short operating range. Based on plasma dispersion effect, generate space-asymmetric periodical time-space modulation on silicon waveguide, and non-reciprocal propagation is realized in the waveguide. The designed unidirectional wavelength-mode conversion waveguide demonstrated that in the forward direction, input 1.55 [Formula: see text]m fundamental mode light signal and then output 1.5492 [Formula: see text]m is of 1st-order mode, while in the backward direction, input 1.5492 [Formula: see text]m is of 1st-order mode light signal and then output 1.5484 [Formula: see text]m is of fundamental mode. Based on this non-reciprocal structure, mode conversion waveguide and two-ring resonance filters were designed then, to accomplish on-chip optical isolation. The scale of the designed isolator is 160 [Formula: see text]m × 60 [Formula: see text]m, and the isolation is 21 dB, revealing perfect application potential.

Localized nonlinear waves and dynamical stability in spinor Bose–Einstein condensates with time–space modulation

Nonlinearity is one of the most remarkable characteristics of Bose–Einstein condensates (BECs). Much work has been done on one- and two-component BECs with time- or space-modulated nonlinearities, while there is little work on spinor BECs with space–time-modulated nonlinearities. In the present paper we investigate localized nonlinear waves and dynamical stability in spinor Bose–Einstein condensates with nonlinearities dependent on time and space. We solve the three coupled Gross–Pitaevskii equations by similarity transformation and obtain two families of exact matter wave solutions in terms of Jacobi elliptic functions and the Mathieu equation. The localized states of the spinor matter wave describe the dynamics of vector breathing solitons, moving breathing solitons, quasi-breathing solitons and resonant solitons. The results show that one-order vector breathing solitons, quasi-breathing solitons, resonant solitons and the moving breathing solitons ψ±1 are all stable, but the moving breathing soliton ψ0 is unstable. We also present the experimental parameters to realize these phenomena in future experiments.

Nonlinear Waves on Localized and Periodic Backgrounds with Time-Space Modulation**Supported by the National Natural Science Foundation of China under Grant Nos. 11475135 and 11547302

We present one family of general analytical solutions for the generalized nonlinear Schrödinger equation with time-space modulation via the method of a combination of the Darboux transformation and similarity transformation. Nonlinear waves on different localized and periodic backgrounds depending on the corresponding nonlinearity modulations are obtained. In particular, we demonstrate the existence and property of localized modes on a double-periodic background under a special designed optical lattice potential. Our results may raise the possibility of related experiments and potential applications in nonlinear optics and Bose–Einstein condensates.

Nonautonomous rogue wave solutions and numerical simulations for a three-dimensional nonlinear Schrödinger equation

We consider nonautonomous rogue wave solutions of a \((3+1)\)-dimensional (3D) nonlinear Schrodinger equation (NLSE) with time–space modulation terms, the dispersion and the nonlinear coefficients engendering temporal dependency. Similarity transformation is used to convert the nonautonomous equation into autonomous NLSE; we obtain the multi-rogue wave solutions employing the generalized Darboux transformation. Particularly, the rogue wave solutions possess several free parameters. Then, the first-order and second-order nonautonomous rogue wave solutions are considered for the 3D NLSE with variable coefficients. At last, the numerical simulations on the evolution and collision of rogue wave solutions are performed to verify the prediction of the analytical formulations. The obtained nonautonomous rogue wave solutions can be used to describe the dynamics waves in the nonlinear optical fibers and Bose–Einstein condensates, respectively.

Novel exact solutions of coupled nonlinear Schrödinger equations with time—space modulation

We construct various novel exact solutions of two coupled dynamical nonlinear Schrödinger equations. Based on the similarity transformation, we reduce the coupled nonlinear Schrödinger equations with time- and space-dependent potentials, nonlinearities, and gain or loss to the coupled dynamical nonlinear Schrödinger equations. Some special types of non-travelling wave solutions, such as periodic, resonant, and quasiperiodically oscillating solitons, are used to exhibit the wave propagations by choosing some arbitrary functions. Our results show that the number of the localized wave of one component is always twice that of the other one. In addition, the stability analysis of the solutions is discussed numerically.

Dynamics of Matter-Wave Solitons for Three-Dimensional Bose—Einstein Condensates with Time-Space Modulation

By two direct assumption methods and symbolic computation, we present two families of one-soliton solutions and a family of two-soliton solutions with some arbitrary functions for the three-dimensional Gross—Pitaevskii equation with time-space modulation. Then we investigate the dynamics of these matter-wave solitons in three-dimensional Bose—Einstein condensates. We can see that the intensities of both one-solitons and two-solitons first increase rapidly to the condensation peak value, then decay very slowly to the background value. Thus these matter-wave solitons in three-dimensional Bose—Einstein condensates can remain for a sufficiently long time to be fully observed and modulated for real applications in today's experiments.

Three-Dimensional Bright–Dark Soliton, Bright Soliton Pairs, and Rogue Wave of Coupled Nonlinear Schr¨odinger Equation with Time–Space Modulation

We systematically provide a similarity transformation reducing the (3+1)-dimensional inhomogeneous coupled nonlinear Schrodinger (CNLS) equation with variable coefficients and parabolic potential to the (1+1)-dimensional coupled nonlinear Schrodinger equation with constant coefficients. Based on the similarity transformation, we discuss the dynamics of the propagation of the three-dimensional bright-dark soliton, the interaction between two bright solitons, and the feature of the three-dimensional rogue wave with different parameters. The obtained results may raise the possibility of relative experiments and potential applications.

Exact analytical solutions of three-dimensional Gross—Pitaevskii equation with time—space modulation

By the generalized sub-equation expansion method and symbolic computation, this paper investigates the (3 + 1)-dimensional Gross—Pitaevskii equation with time- and space-dependent potential, time-dependent nonlinearity, and gain or loss. As a result, rich exact analytical solutions are obtained, which include bright and dark solitons, Jacobi elliptic function solutions and Weierstrass elliptic function solutions. With computer simulation, the main evolution features of some of these solutions are shown by some figures. Nonlinear dynamics of a soliton pulse is also investigated under the different regimes of soliton management.

Analytical three-dimensional bright solitons and soliton pairs in Bose-Einstein condensates with time-space modulation

We provide analytical three-dimensional bright multisoliton solutions to the $(3+1)$-dimensional Gross-Pitaevskii equation with time- and space-dependent potential, time-dependent nonlinearity, and gain or loss. The zigzag propagation trace and the breathing behavior of solitons are observed. Different shapes of bright solitons and fascinating interactions between two solitons can be achieved with different parameters. The obtained results may raise the possibility of relative experiments and potential applications.