Sebastien M. Popoff

Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media.

We introduce a method to experimentally measure the monochromatic transmission matrix of a complex medium in optics. This method is based on a spatial phase modulator together with a full-field interferometric measurement on a camera. We determine the transmission matrix of a thick random scattering sample. We show that this matrix exhibits statistical properties in good agreement with random matrix theory and allows light focusing and imaging through the random medium. This method might give important insight into the mesoscopic properties of a complex medium.

Image transmission through an opaque material

Optical imaging relies on the ability to illuminate an object, collect and analyse the light it scatters or transmits. Propagation through complex media such as biological tissues was so far believed to degrade the attainable depth, as well as the resolution for imaging, because of multiple scattering. This is why such media are usually considered opaque. Recently, we demonstrated that it is possible to measure the complex mesoscopic optical transmission channels that allow light to traverse through such an opaque medium. Here, we show that we can optimally exploit those channels to coherently transmit and recover an arbitrary image with a high fidelity, independently of the complexity of the propagation.

Controlling light through optical disordered media: transmission matrix approach

We experimentally measure the monochromatic transmission matrix (TM) of an optical multiple scattering medium using a spatial light modulator together with a phase-shifting interferometry measurement method. The TM contains all the information needed to shape the scattered output field at will or to detect an image through the medium. We confront theory and experiment for these applications and study the effect of noise on the reconstruction method. We also extracted from the TM information about the statistical properties of the medium and the light transport within it. In particular, we are able to isolate the contributions of the memory effect and measure its attenuation length.

Imaging With Nature: Compressive Imaging Using a Multiply Scattering Medium

The recent theory of compressive sensing leverages upon the structure of signals to acquire them with much fewer measurements than was previously thought necessary, and certainly well below the traditional Nyquist-Shannon sampling rate. However, most implementations developed to take advantage of this framework revolve around controlling the measurements with carefully engineered material or acquisition sequences. Instead, we use the natural randomness of wave propagation through multiply scattering media as an optimal and instantaneous compressive imaging mechanism. Waves reflected from an object are detected after propagation through a well-characterized complex medium. Each local measurement thus contains global information about the object, yielding a purely analog compressive sensing method. We experimentally demonstrate the effectiveness of the proposed approach for optical imaging by using a 300-micrometer thick layer of white paint as the compressive imaging device. Scattering media are thus promising candidates for designing efficient and compact compressive imagers.

All-fiber spectrometer based on speckle pattern reconstruction.

A standard multimode optical fiber can be used as a general purpose spectrometer after calibrating the wavelength dependent speckle patterns produced by interference between the guided modes of the fiber. A transmission matrix was used to store the calibration data and a robust algorithm was developed to reconstruct an arbitrary input spectrum in the presence of experimental noise. We demonstrate that a 20 meter long fiber can resolve two laser lines separated by only 8 pm. At the other extreme, we show that a 2 centimeter long fiber can measure a broadband continuous spectrum generated from a supercontinuum source. We investigate the effect of the fiber geometry on the spectral resolution and bandwidth, and also discuss the additional limitation on the bandwidth imposed by speckle contrast reduction when measuring dense spectra. Finally, we demonstrate a method to reduce the spectrum reconstruction error and increase the bandwidth by separately imaging the speckle patterns of orthogonal polarizations. The multimode fiber spectrometer is compact, lightweight, low cost, and provides high resolution with low loss.A standard multimode optical fiber can be used as a general purpose spectrometer after calibrating the wavelength dependent speckle patterns produced by interference between the guided modes of the fiber. A transmission matrix was used to store the calibration data and a robust algorithm was developed to reconstruct an arbitrary input spectrum in the presence of experimental noise. We demonstrate that a 20 meter long fiber can resolve two laser lines separated by only 8 pm. At the other extreme, we show that a 2 centimeter long fiber can measure a broadband continuous spectrum generated from a supercontinuum source. We investigate the effect of the fiber geometry on the spectral resolution and bandwidth, and also discuss the additional limitation on the bandwidth imposed by speckle contrast reduction when measuring dense spectra. Finally, we demonstrate a method to reduce the spectrum reconstruction error and increase the bandwidth by separately imaging the speckle patterns of orthogonal polarizations. The multimode fiber spectrometer is compact, lightweight, low cost, and provides high resolution with low loss.

Coherent control of total transmission of light through disordered media.

We used wavefront shaping to enhance/suppress the transmission of coherent light through open highly scattering media. The total transmission was varied by one order of magnitude as a result of mesoscopic correlations of coherent transport.

Exploiting the time-reversal operator for adaptive optics, selective focusing and scattering pattern analysis

We report on the optical measurement of the backscattering matrix in a weakly scattering medium. A decomposition of the time reversal operator allows selective and efficient focusing on individual scatterers, even through an aberrating layer.

Transmission channels for light in absorbing random media: from diffusive to ballistic-like transport

We study numerically the effects of optical absorption on highly transmitting channels in strongly scattering media. We observe that they are robust against weak absorption. Surprisingly, in case of strong absorption diffusive transport becomes ballistic-like.

Broadband subwavelength focusing of light using a passive sink

Optical absorption is usually considered deleterious, something to avoid if at all possible. We propose a broadband nanoabsorber that completely eliminates the diffracting wave, resulting in a subwavelength enhancement of the field. Broadband operation is made possible by engineering the dispersion of the complex dielectric function. The local enhancement can be significantly improved compared to the standard plane wave illumination of a metallic nanoparticle. Our numerical simulation shows that an optical pulse as short as 6 fs can be focused to a 11 nm region. Not only the local field, but also its gradient are greatly enhanced, pointing to applications in ultrafast nonlinear spectroscopy, sensing and communication with deep-subwavelength resolution.

Deterministic control of broadband light through a multiply scattering medium via the multispectral transmission matrix.

We present a method to measure the spectrally-resolved transmission matrix of a multiply scattering medium, thus allowing for the deterministic spatiospectral control of a broadband light source by means of wavefront shaping. As a demonstration, we show how the medium can be used to selectively focus one or many spectral components of a femtosecond pulse, and how it can be turned into a controllable dispersive optical element to spatially separate different spectral components to arbitrary positions.