Sparsity-based super-resolution and phase-retrieval in waveguide arrays.

We present a scheme for recovering the complex input field launched into a waveguide array, from partial measurements of its output intensity, given advance knowledge that the input is sparse. In spite of the fact that in general the inversion problem is ill-conditioned, we demonstrate experimentally and in simulations that the prior knowledge of sparsity helps overcome the loss of information. Our method is based on GESPAR, a recently proposed efficient phase retrieval algorithm. Possible applications include optical interconnects and quantum state tomography, and the ideas are extendable to other multiple input and multiple output (MIMO) communication schemes.

Polarization control of multiply scattered light through random media by wavefront shaping.

We show that the polarization state of coherent light propagating through an optically thick multiple scattering medium can be controlled by wavefront shaping, that is, by controlling only the spatial phase of the incoming field with a spatial light modulator. Any polarization state of light at any spatial position behind the scattering medium can be attained with this technique. Thus, transforming the random medium to an arbitrary optical polarization component becomes possible.

Spatiotemporal focusing through a thin scattering layer.

We analyze the spatiotemporal distortions of an ultrashort pulse focused through a thin scattering surface. We show and experimentally verify that in such a scenario temporal distortions are proportional to the distance from the optical axis and are present only outside the focal point, as result of geometrical path length differences. We use wavefront shaping to correct for the spatiotemporal distortions and to temporally compress chirped input pulses through the scattering medium.

Spectral control of broadband light through random media by wavefront shaping.

A random medium can serve as a controllable arbitrary spectral filter with spectral resolution determined by the inverse of the interaction time of the light in the medium. We use wavefront shaping to implement an arbitrary spectral response at a particular point in the scattered field. We experimentally demonstrate this technique by selecting either a narrow band or dual bands with a width of 5.5 nm each.

Universal correlations in a nonlinear periodic 1D system.

When a periodic 1D system described by a tight-binding model is uniformly initialized with equal amplitudes at all sites, yet with completely random phases, it evolves into a thermal distribution with no spatial correlations. However, when the system is nonlinear, correlations are spontaneously formed. We find that for strong nonlinearities, the intensity histograms approach a narrow Gaussian distributed around their mean and phase correlations are formed between neighboring sites. Sites tend to be out of phase for a positive nonlinearity and in phase for a negative one. Most impressively, the field correlation takes a universal shape independent of parameters. These results are relevant to bosonic gas in 1D optical lattices as well as to nonlinear optical waveguide arrays, which are used to demonstrate experimentally some of the features of this equilibrium state.

Spatio-temporal X-wave.

We introduce an illumination configuration which is a spatiotemporal analog of a non-diffracting X-wave. By interfering multiple ultrashort converging plane waves, we generate a tight central spot at which a transform limited ultrashort pulse is formed. Outside this tight focus a spatiotemporal speckle field with longer duration and reduced peak power is created. We investigate this spatiotemporal X-wave configuration analytically, numerically, and experimentally demonstrate the effect using two photon excitation fluorescence.