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We consider the nonlinear tunneling of a plane wave through a small barrier potential in a medium with self-defocusing, or repulsive, interactions. We show that nonlinearity can either suppress or enhance transmission rates, determined by whether the initial kinetic energy is above or below the barrier height. Associated with this threshold is the appearance of two distinct hysteresis loops, going clockwise or counterclockwise, respectively. Spatial dynamics upon reflection and transmission reveals the formation of dispersive shock waves (dark soliton trains) due to phase jumps at the interfaces and wave steepening during propagation. The results are demonstrated experimentally for optical wave tunneling through a refractive index defect but will hold for any Schrödinger system that contains a nonlinear junction.

We augment layered three-dimensional (3D) displays using a lens placed in front of or between attenuation layers. The lens, or similar optical element, improves the angular resolution of the system and enables translation of the displayed scene from a near-field image to a far-field projection. We analyze the relation between angular resolution (scene depth) and the number of layers and characterize the phase-space trade-offs between spatial and angular frequency components. We also introduce an algorithm for determining the layers of the display, which significantly reduces the computational requirements. The method is demonstrated on a standard 4D light field scene.

By combining a high-resolution image from a standard camera with a low-resolution wavefront measurement from a Shack-Hartmann sensor, we numerically reconstruct a highresolution light field. We experimentally demonstrate the method with a commercially available microscope.

We analyze the tunneling of vortex states from elliptically shaped traps. Using the hydrodynamic representation of the Gross-Pitaevskii (Nonlinear Schrdinger) equation, we derive analytically and demonstrate numerically a novel type of quantum fluid flow: a jet-like singularity formed by the interaction between the vortex and the nonhomogenous field. For strongly elongated traps, the ellipticity overwhelms the circular rotation, resulting in the ejection of field in narrow, well-defined directions. These jets can also be understood as a formation of caustics since they correspond to a convergence of trajectories starting from the top of the potential barrier and meeting at a certain point on the exit line. They will appear in any coherent wave system with angular momentum and non-circular symmetry, such as superfluids, Bose-Einstein condensates, and light.PACS numbers: 74.25. Wx, 42.65.Hw,03.75.Lm Topological charges, such as vortices, are fundamental to the dynamics of coherent fields 1,2 . They appear in laser systems, carry charge in superconductors, characterize turbulence in quantum fluids, and hold potential for quantum memory 3 . To date, the main focus in vortex dynamics has been on transport, so that the charges could move and interact. (see e.g. Ref. 4) However, it is often desirable, and sometimes necessary, to confine and trap vortex structures. This is a basic problem in trapping theory, yet it has received very little attention. Here, we consider the dynamics of vortex decay in a potential and show that asymmetry in the potential can lead to the development of jets during wave tunneling. These formations concentrate wave density in the form of caustics and represent a new type of coherent structure for wave transport.The emphasis on vorticity implies that phase dynamics will be important to the tunneling process. Even in the context of simple wavefunctions, without angular momentum, phase can have profound effects. Examples include the recent prediction of "blips" in the outgoing matter through a trap 5-8 and the development of dispersive shock waves 9-12 , e.g. when tunneling through a barrier. 13 These latter structures are traveling waves with oscillating phase that are finding increasing importance in fluids 14,15 , optics 2,11 , and Bose-Einstein condensates 16,17 . In spatially inhomogeneous potentials, such as the elliptical wells typical of BEC experiments 18 , both shock waves and blips can go unstable and generate vortices. Here, we consider the simplest case of a circular vortex trapped in an elliptical well and examine the competition of symmetry during wavefunction tunneling.Tunneling problems are usually discussed within the framework of the WKB approximation, which looks for a solution of the Schrödinger equation (Nonlinear 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 1111111111111 1111111111111 1111111111111 1111111111111 111111...