Search results for "Linear system"
showing 10 items of 1558 documents
Lieb polariton topological insulators
2018
We predict that the interplay between the spin-orbit coupling, stemming from the TE-TM energy splitting, and the Zeeman effect in semiconductor microcavities supporting exci- ton-polariton quasi-particles results in the appearance of unidirectional linear topological edge states when the top microcavity mirror is patterned to form a truncated dislocated Lieb lattice of cylindrical pillars. Periodic nonlinear edge states are found to emerge from the linear ones. They are strongly localized across the interface and they are remarkably robust in comparison to their counterparts in hexagonal lattices. Such robustness makes possible the existence of nested unidirectional dark solitons that move …
Directional Second Harmonic Generation Controlled by Sub-wavelength Facets of an Organic Mesowire
2018
Directional harmonic generation is an important property characterizing the ability of nonlinear optical antennas to diffuse the signal in well-defined region of space. Herein, we show how sub-wavelength facets of an organic molecular mesowire crystal can be utilized to systematically vary the directionality of second harmonic generation (SHG) in the forward scattering geometry. We demonstrate this capability on crystalline diamonoanthraquinone (DAAQ) mesowires with subwavelength facets. We observed that the radial angles of the SHG emission can be tuned over a range of 130 degrees. This angular variation arises due to spatially distributed nonlinear dipoles in the focal volume of the excit…
Small-time bilinear control of Schrödinger equations with application to rotating linear molecules
2023
In [14] Duca and Nersesyan proved a small-time controllability property of nonlinear Schrödinger equations on a d-dimensional torus $\mathbb{T}^d$. In this paper we study a similar property, in the linear setting, starting from a closed Riemannian manifold. We then focus on the 2-dimensional sphere $S^2$, which models the bilinear control of a rotating linear top: as a corollary, we obtain the approximate controllability in arbitrarily small times among particular eigenfunctions of the Laplacian of $S^2$.
Diffusion front capturing schemes for a class of Fokker–Planck equations: Application to the relativistic heat equation
2010
In this research work we introduce and analyze an explicit conservative finite difference scheme to approximate the solution of initial-boundary value problems for a class of limited diffusion Fokker-Planck equations under homogeneous Neumann boundary conditions. We show stability and positivity preserving property under a Courant-Friedrichs-Lewy parabolic time step restriction. We focus on the relativistic heat equation as a model problem of the mentioned limited diffusion Fokker-Planck equations. We analyze its dynamics and observe the presence of a singular flux and an implicit combination of nonlinear effects that include anisotropic diffusion and hyperbolic transport. We present numeri…
Nonlinear Characterisation of an AsSe Chalcogenide Holey Fiber
2009
oral session TuA " Highly Nonlinear Fibers " [TuA1]; International audience; We report the nonlinear characterization of a chalcogenide holey fiber, based on the AsSe glass composition. A nonlinear coefficient as high as 15 000 W-1 km-1 has been measured.
Optical Amplification in Hollow-Core Negative-Curvature Fibers Doped with Perovskite CsPbBr3 Nanocrystals
2019
| openaire: EC/H2020/820423/EU//S2QUIP We report a hollow-core negative-curvature fiber (HC-NCF) optical signal amplifier fabricated by the filling of the air microchannels of the fiber with all-inorganic CsPbBr3 perovskite nanocrystals (PNCs). The optimum fabrication conditions were found to enhance the optical gain, up to +3 dB in the best device. Experimental results were approximately reproduced by a gain assisted mechanism based on the nonlinear optical properties of the PNCs, indicating that signal regeneration can be achieved under low pump powers, much below the threshold of stimulated emission. The results can pave the road of new functionalities of the HC-NCF with PNCs, such as op…
Feedback Classification and Optimal Control with Applications to the Controlled Lotka-Volterra Model
2023
Let M be a σ-compact C^∞ manifold of dimension n ≥ 2 and consider a single-input control system: ẋ(t) = X (x(t)) + u(t) Y (x(t)), where X , Y are C^∞ vector fields on M. We prove that there exist an open set of pairs (X , Y ) for the C^∞ –Whitney topology such that they admit singular abnormal rays so that the spectrum of the projective singular Hamiltonian dynamics is feedback invariant. It is applied to controlled Lotka–Volterra dynamics where such rays are related to shifted equilibria of the free dynamics.
Avoiding strange attractors in efficient parametric families of iterative methods for solving nonlinear problems
2019
[EN] Searching zeros of nonlinear functions often employs iterative procedures. In this paper, we construct several families of iterative methods with memory from one without memory, that is, we have increased the order of convergence without adding new functional evaluations. The main aim of this manuscript yields in the advantage that the use of real multidimensional dynamics gives us to decide among the different classes designed and, afterwards, to select its most stable members. Moreover, we have found some elements of the family whose behavior includes strange attractors of different kinds that must be avoided in practice. In this sense, Feigenbaum diagrams have resulted an extremely …
320GHz, 640GHz and 1THz femtosecond pulse sources based on multiple four wave mixing in highly non linear optical fibers
2006
Ultra-high repetition rate, transform-limited femtosecond pulse trains have been generated around 1555 nm at 320 GHz, 640 GHz and 1 THz through the compression of a dual frequency beat-signal in a highly nonlinear optical fiber.
Impact of initial pulse shape on the nonlinear spectral compression in optical fibre
2018
International audience; We theoretically study the effects of the temporal intensity profile of the initial pulse on the nonlinear spectral compression process arising from nonlinear propagation in an optical fibre. Various linearly chirped input pulse profiles are considered, and their dynamics is explained with the aid of time-frequency representations. While initially parabolic-shaped pulses show enhanced spectral compression compared to Gaussian pulses, no significant spectral narrowing occurs when initially super-Gaussian pulses are used. Triangular pulses lead to a spectral interference phenomenon similar to the Fresnel bi-prism experiment.