Eran Small

Focusing and compression of ultrashort pulses through scattering media

Scientists show that spatiotemporal focusing and compression of non-Fourier-limited pulses through scattering media can be achieved by manipulating only the spatial degrees of freedom of the incident wavefront. This technique is potentially attractive for optical manipulation and nonlinear imaging in scattering media.

Noninvasive nonlinear focusing and imaging through strongly scattering turbid layers

Diffraction-limited imaging through complex scattering media is a long-sought-after goal with important applications in biomedical research. In recent years, high-resolution wavefront shaping has emerged as a powerful approach to generate a sharp focus through highly scattering, visually opaque samples. However, it requires a localized feedback signal from the target point of interest, which necessitates an invasive procedure in all-optical techniques. Here, we show that by exploiting optical nonlinearities, a diffraction-limited focus can be formed inside or through a complex sample, even when the feedback signal is not localized. We prove our approach theoretically and numerically, and experimentally demonstrate it with a two-photon fluorescence signal through highly scattering biological samples. We use the formed focus to perform two-photon microscopy through highly scattering, visually opaque layers.

Real-time wavefront shaping through scattering media by all-optical feedback

The self-organization of many laser modes in phase and frequency realized by minimizing radiation losses in a cavity enables the complex wavefront required to focus light scattered by turbid samples to be generated on sub-microsecond timescales without employing electronic feedback, spatial light modulators or phase-conjugation crystals.

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.

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.

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.

Phasematching in semiconductor nonlinear optics by linear long-period gratings

We experimentally demonstrate a phasematching technique for frequency conversion in nonlinear semiconductor structures by employing linear long-period gratings. We designed a specific semiconductor photonic device for second harmonic generation using coupled-mode equations with parameters extracted from beam propagation method simulations. Optical frequency converters were fabricated according to the design with the main feature; linear long-period weak gratings imprinted on semiconductor waveguides, providing the required photon momentum difference for matching the phases of the different-wavelength photons. The measured nonlinear conversion efficiency and its spectrum comply with our theoretical predictions.

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.

Nonlinear propagation of an optical speckle field

We provide a theoretical explanation of the results on the intensity distributions and correlation functions obtained from a random-beam speckle field in nonlinear bulk waveguides reported in the recent publication by Bromberg et al. [Nat. Photonics 4, 721 (2010) ].. We study both the focusing and defocusing cases and in the limit of small speckle size (short-correlated disordered beam) provide analytical asymptotes for the intensity probability distributions at the output facet. Additionally we provide a simple relation between the speckle sizes at the input and output of a focusing nonlinear waveguide. The results are of practical significance for nonlinear Hanbury Brown and Twiss interferometry in both optical waveguides and Bose-Einstein condensates.