The topological features of optical vortices have been opening opportunities for free-space and on-chip photonic technologies,e.g.,for multiplexed optical communications and robust information transport.In a parallel ...The topological features of optical vortices have been opening opportunities for free-space and on-chip photonic technologies,e.g.,for multiplexed optical communications and robust information transport.In a parallel but disjoint effort,polar anisotropic van der Waals nanomaterials supporting hyperbolic phonon polaritons(HP2s)have been leveraged to drastically boost light-matter interactions.So far HP2 studies have been mainly focusing on the control of their amplitude and scale features.Here we report the generation and observation of mid-infrared hyperbolic polariton vortices(HP2Vs)associated with reconfigurable topological charges.Spiral-shaped gold disks coated with a flake of hexagonal boron nitride are exploited to tailor spin-orbit interactions and realise deeply subwavelength HP2Vs.The complex interplay between excitation spin,spiral geometry and HP2 dispersion enables robust reconfigurability of the associated topological charges.Our results reveal unique opportunities to extend the application of HP2s into topological photonics,quantum information processing by integrating these phenomena with single-photon emitters,robust on-chip optical applications,sensing and nanoparticle manipulation.展开更多
While approaching the target body, the deep-space probe is orbiting hyperbolically before the maneuver. We discuss the variation of perturbed hyperbolic orbit using the method similar to that used in elliptic orbit. E...While approaching the target body, the deep-space probe is orbiting hyperbolically before the maneuver. We discuss the variation of perturbed hyperbolic orbit using the method similar to that used in elliptic orbit. Ephemeris calculating and orbit control will benefit from the given analytical solution.展开更多
In this paper, the robustness of the orbit structure is investigated for a partially hyperbolic endomorphism f on a compact manifold M. It is first proved that the dynamical structure of its orbit space （the inverse ...In this paper, the robustness of the orbit structure is investigated for a partially hyperbolic endomorphism f on a compact manifold M. It is first proved that the dynamical structure of its orbit space （the inverse limit space） M^f of f is topologically quasi-stable under C^0-small perturbations in the following sense： For any covering endomorphism g C^0-close to f, there is a continuous map φ from M^9 to Π-∞^∞ M such that for any {yi}i∈z∈φ（M^9）, yi＋1 and f（yi） differ only by a motion along the center direction. It is then proved that f has quasi-shadowing property in the following sense： For any pseudo-orbit {xi}i∈z, there is a sequence of points {yi}i∈z tracing it, in which yi＋1 is obtained from f（yi） by a motion along the center direction.展开更多
A hyperbolic Lindstedt-Poincare method is presented to determine the homoclinic solutions of a kind of nonlinear oscillators, in which critical value of the homoclinic bifurcation parameter can be determined. The gene...A hyperbolic Lindstedt-Poincare method is presented to determine the homoclinic solutions of a kind of nonlinear oscillators, in which critical value of the homoclinic bifurcation parameter can be determined. The generalized Lienard oscillator is studied in detail, and the present method＇s predictions are compared with those of Runge-Kutta method to illustrate its accuracy.展开更多
Let ■ be the linear space of all C<sup>1</sup> vector fields X on a compact n-dimensionalC<sup>∞</sup> Riemann manifold（n≥2）,endowed with the C<sup>1</sup> norm ‖X‖<sub>...Let ■ be the linear space of all C<sup>1</sup> vector fields X on a compact n-dimensionalC<sup>∞</sup> Riemann manifold（n≥2）,endowed with the C<sup>1</sup> norm ‖X‖<sub>1</sub>.Write θ（X）for the numberof contractible periodic orbits of X∈（?）,which may be finite or infinite.Let （?）<sup>*</sup> be the set ofall X∈（?） possessing the property that X has a neighbourhood （?） such that every Y∈（?） hasonly a finite number of singularities and at most a countable number of periodic orbits.Inthis paper,it is shown that any given S∈（?） has a neighbourhood （?） in （?） together with anumber λ=λ（?）】0 such that θ（X）≤λfor all X∈（?）.展开更多
Displaced non-Keplerian orbits above planetary bodies can be achieved by orientating the solar sail normal to the sun line. The dynamical systems techniques are employed to analyze the nonlinear dynamics of a displace...Displaced non-Keplerian orbits above planetary bodies can be achieved by orientating the solar sail normal to the sun line. The dynamical systems techniques are employed to analyze the nonlinear dynamics of a displaced orbit and different topologies of equilibria are yielded from the basic configurations of Hill＇s region, which have a saddlenode bifurcation point at the degenerated case. The solar sail near hyperbolic or degenerated equilibrium is quite unstable. Therefore, a controller preserving Hamiltonian structure is presented to stabilize the solar sail near hyperbolic or degenerated equilibrium, and to generate the stable Lissajous orbits that stay stable inside the stabilizing region of the controller. The main contribution of this paper is that the controller preserving Hamiltonian structure not only changes the instability of the equilibrium, but also makes the modified elliptic equilibrium become unique for the controlled system. The allocation law of the controller on the sail＇s attitude and lightness number is obtained, which verifies that the controller is realizable.展开更多
基金Office of Naval Research(Grant No.N00014-19-1-2011)Vannevar Bush Faculty Fellowship,Air Force Office of Scientific Research MURI program,A*STAR AME Young Individual Research Grant(YIRG,No.A2084c0172)+4 种基金National Research Foundation Singapore(CRP22-2019-0006)Advanced Research and Technology Innovation Centre(No.R-261-518-004-720)National Science Foundation under Grant No.2044281Elemental Strategy Initiative conducted by MEXT,Japan,Grant Number JPMXP0112101001JSPS KAKENHI Grant Number JP20H00354。
文摘The topological features of optical vortices have been opening opportunities for free-space and on-chip photonic technologies,e.g.,for multiplexed optical communications and robust information transport.In a parallel but disjoint effort,polar anisotropic van der Waals nanomaterials supporting hyperbolic phonon polaritons(HP2s)have been leveraged to drastically boost light-matter interactions.So far HP2 studies have been mainly focusing on the control of their amplitude and scale features.Here we report the generation and observation of mid-infrared hyperbolic polariton vortices(HP2Vs)associated with reconfigurable topological charges.Spiral-shaped gold disks coated with a flake of hexagonal boron nitride are exploited to tailor spin-orbit interactions and realise deeply subwavelength HP2Vs.The complex interplay between excitation spin,spiral geometry and HP2 dispersion enables robust reconfigurability of the associated topological charges.Our results reveal unique opportunities to extend the application of HP2s into topological photonics,quantum information processing by integrating these phenomena with single-photon emitters,robust on-chip optical applications,sensing and nanoparticle manipulation.
基金the National Natural Science Foundation of China(Grant No.2000028416).
文摘While approaching the target body, the deep-space probe is orbiting hyperbolically before the maneuver. We discuss the variation of perturbed hyperbolic orbit using the method similar to that used in elliptic orbit. Ephemeris calculating and orbit control will benefit from the given analytical solution.
基金supported by the National Natural Science Foundation of China(No.11371120)the High-level Personnel for Institutions of Higher Learning in Hebei Province(No.GCC2014052)the Natural Science Foundation of Hebei Province(No.A2013205148)
文摘In this paper, the robustness of the orbit structure is investigated for a partially hyperbolic endomorphism f on a compact manifold M. It is first proved that the dynamical structure of its orbit space （the inverse limit space） M^f of f is topologically quasi-stable under C^0-small perturbations in the following sense： For any covering endomorphism g C^0-close to f, there is a continuous map φ from M^9 to Π-∞^∞ M such that for any {yi}i∈z∈φ（M^9）, yi＋1 and f（yi） differ only by a motion along the center direction. It is then proved that f has quasi-shadowing property in the following sense： For any pseudo-orbit {xi}i∈z, there is a sequence of points {yi}i∈z tracing it, in which yi＋1 is obtained from f（yi） by a motion along the center direction.
基金supported by the National Natural Science Foundation of China (10672193)Sun Yat-sen University (Fu Lan Scholarship)the University of Hong Kong (CRGC grant).
文摘A hyperbolic Lindstedt-Poincare method is presented to determine the homoclinic solutions of a kind of nonlinear oscillators, in which critical value of the homoclinic bifurcation parameter can be determined. The generalized Lienard oscillator is studied in detail, and the present method＇s predictions are compared with those of Runge-Kutta method to illustrate its accuracy.
基金Supported by National Natural Science Foundation of China
文摘Let ■ be the linear space of all C<sup>1</sup> vector fields X on a compact n-dimensionalC<sup>∞</sup> Riemann manifold（n≥2）,endowed with the C<sup>1</sup> norm ‖X‖<sub>1</sub>.Write θ（X）for the numberof contractible periodic orbits of X∈（?）,which may be finite or infinite.Let （?）<sup>*</sup> be the set ofall X∈（?） possessing the property that X has a neighbourhood （?） such that every Y∈（?） hasonly a finite number of singularities and at most a countable number of periodic orbits.Inthis paper,it is shown that any given S∈（?） has a neighbourhood （?） in （?） together with anumber λ=λ（?）】0 such that θ（X）≤λfor all X∈（?）.
基金supported by the National Natural Science Foundation of China (11172020)the "Vision" Foundation for Talent Assistant Professor from Ministry of Industry and Information Technologythe "Blue-Sky" Foundation for Talent Assistant Professor from Beihang University
文摘Displaced non-Keplerian orbits above planetary bodies can be achieved by orientating the solar sail normal to the sun line. The dynamical systems techniques are employed to analyze the nonlinear dynamics of a displaced orbit and different topologies of equilibria are yielded from the basic configurations of Hill＇s region, which have a saddlenode bifurcation point at the degenerated case. The solar sail near hyperbolic or degenerated equilibrium is quite unstable. Therefore, a controller preserving Hamiltonian structure is presented to stabilize the solar sail near hyperbolic or degenerated equilibrium, and to generate the stable Lissajous orbits that stay stable inside the stabilizing region of the controller. The main contribution of this paper is that the controller preserving Hamiltonian structure not only changes the instability of the equilibrium, but also makes the modified elliptic equilibrium become unique for the controlled system. The allocation law of the controller on the sail＇s attitude and lightness number is obtained, which verifies that the controller is realizable.
