Simulation of Laser Beam Propagation With a Paraxial Model in a Tilted Frame

We study the Schr\"odinger equation which comes from the paraxial approximation of the Helmholtz equation in the case where the direction of propagation is tilted with respect to the boundary of the domain. In a first part, a mathematical analysis is made which leads to an analytical formula of the solution in the simple case where the refraction index and the absorption coefficients are constant. Afterwards, we propose a numerical method for solving the initial problem which uses the previous analytical expression. Numerical results are presented. We also sketch an extension to a time dependant model which is relevant for laser plasma interaction

Boundary Value Problem for an Oblique Paraxial Model of Light Propagation

We study the Schr\"odinger equation which comes from the paraxial approximation of the Helmholtz equation in the case where the direction of propagation is tilted with respect to the boundary of the domain. This model has been proposed in (Doumic, Golse, Sentis, CRAS, 2003). Our primary interest here is in the boundary conditions successively in a half-plane, then in a quadrant of R2. The half-plane problem has been used in (Doumic, Duboc, Golse, Sentis, JCP, to appear) to build a numerical method, which has been introduced in the HERA plateform of CEA

Simulation of Laser Propagation in a Plasma with a Frequency Wave Equation

The aim of this work is to perform numerical simulations of the propagation of a laser in a plasma. At each time step, one has to solve a Helmholtz equation in a domain which consists in some hundreds of millions of cells. To solve this huge linear system, one uses a iterative Krylov method with a preconditioning by a separable matrix. The corresponding linear system is solved with a block cyclic reduction method. Some enlightments on the parallel implementation are also given. Lastly, numerical results are presented including some features concerning the scalability of the numerical method on a parallel architecture

Higher dimensional quantum communication in a curved spacetime: an efficient simulation of the propagation of the wavefront of a photon

A photon with a modulated wavefront can produce a quantum communication channel in a larger Hilbert space. For example, higher dimensional quantum key distribution (HD-QKD) can encode information in the transverse linear momentum (LM) or orbital angular momentum (OAM) modes of a photon. This is markedly different than using the intrinsic polarization of a photon. HD-QKD has advantages for free space QKD since it can increase the communication channel\~Os tolerance to bit error rate (BER) while maintaining or increasing the channels bandwidth. We describe an efficient numerical simulation of the propagation photon with an arbitrary complex wavefront in a material with an isotropic but inhomogeneous index of refraction. We simulate the waveform propagation of an optical vortex in a volume holographic element in the paraxial approximation using an operator splitting method. We use this code to analyze an OAM volume-holographic sorter. Furthermore, there are analogue models of the evolution of a wavefront in the curved spacetime environs of the Earth that can be constructed using an optical medium with a given index of refraction. This can lead to a work-bench realization of a satellite HD-QKD system.Comment: 20 pages, 7 figure

Quantum Hall Physics with Cold Atoms in Cylindrical Optical Lattices

We propose and study various realizations of a Hofstadter-Hubbard model on a cylinder geometry with fermionic cold atoms in optical lattices. The cylindrical optical lattice is created by copropagating Laguerre-Gauss beams, i.e.~light beams carrying orbital angular momentum. By strong focusing of the light beams we create a real space optical lattice in the form of rings, which are offset in energy. A second set of Laguerre-Gauss beams then induces a Raman-hopping between these rings, imprinting phases corresponding to a synthetic magnetic field (artificial gauge field). In addition, by rotating the lattice potential, we achieve a slowly varying flux through the hole of the cylinder, which allows us to probe the Hall response of the system as a realization of Laughlin's thought experiment. We study how in the presence of interactions fractional quantum Hall physics could be observed in this setup.Comment: 10 pages, 9 figure

Laser and electron deflection from transverse asymmetries in laser-plasma accelerators.

We report on the deflection of laser pulses and accelerated electrons in a laser-plasma accelerator (LPA) by the effects of laser pulse front tilt and transverse density gradients. Asymmetry in the plasma index of refraction leads to laser steering, which can be due to a density gradient or spatiotemporal coupling of the laser pulse. The transverse forces from the skewed plasma wave can also lead to electron deflection relative to the laser. Quantitative models are proposed for both the laser and electron steering, which are confirmed by particle-in-cell simulations. Experiments with the BELLA Petawatt Laser are presented which show controllable 0.1-1 mrad laser and electron beam deflection from laser pulse front tilt. This has potential applications for electron beam pointing control, which is of paramount importance for LPA applications