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[K. Lee and Y. Park, Nat. Commun, 7 (2016)]

[Y. Baek, K. Lee and Y. Park, Phys. Rev. Appl., 7 (2016)]

Measuring the optical phase is an ubiquitous challenge in optique. Through a linear scattering medium, one can always links the output optical field to the input one using the transmission matrix. However, one still has to measure the phase of the complex output field. In [K. Lee and Y. Park, Nat. Commun, 7 (2016)] the authors introduce a technique to reconstruct a complex optical field using a thin diffuser. Once the matrix is calibrated, only an intensity measurement is required to reconstruct the amplitude and the phase of the complex optical field.

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\def\ket#1{{\left|{#1}\right\rangle}}

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[M. W. Matthès et al., Optica, 6 (2019)]

Performing linear operations using optical devices is a crucial building block in many fields ranging from telecommunications to optical analogue computation and machine learning. For many of these applications, key requirements are robustness to fabrication inaccuracies, reconfigurability and scalability. Traditionally, the conformation or the structure of the medium is optimized in order to perform a given desired operation. Since the advent of wavefront shaping, we know that the complexity of a given operation can be shifted toward the engineering of the wavefront, allowing, for example, to use any random medium as a lens.

In [M. W. Matthès et al., Optica, 6 (2019)], we propose to use this approach to use complex optical media such as multimode fibers or scattering media as a computational platform driven by wavefront shaping to perform analogue linear operations. Given a large random transmission matrix representing the light propagation in such a medium, we can extract any desired smaller linear operator by finding suitable input and output projectors. We demonstrate this concept by finding input wavefronts using a Spatial Light Modulator that cause the complex medium to act as a desired complex-valued linear operator on the optical field.

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[N. Kaina et al., Sci. Rep. (2014)]

Wavefront shaping is not limited to optical waves. Similar techniques can be used for any kind of wave for which one can control dynamically the phase over a large number of independent elements. In [N. Kaina et al., Sci. Rep. (2014)], the authors demonstrate the use of their Spatial Microwave Modulator (SMM) to control the propagation of radio frequency waves inside a room to improve the WiFi signal at any chosen position. The system is passive as there is no energy transfer from the modulator to the WiFi signal, it only controls the local phase of the waves reflected of the modulator. The device is thin and has the typical size of small poster, it can be conveniently placed on the wall of a typical room without any loss of space.

]]>Intuitively, absorption of light is detrimental for imaging as it reduces the intensity of the image we see. On the other hand, scattering is also an known obstacle for imaging as it mixes light sending it in all the dirrections. In the present paper, S.F. Liew and his collaborators from Yale University (CT, USA) and the University of Twente (The Netherlands) show that, contrary to appearances, absorption can in fact help light to follow a direct path through disordered media.

Without absorption, spatial information of an object transmitted through an opaque material is totally mixed and difficult to recover. The reason is that the photons are multiply scattered, hence their propagation directions are randomized at every scattering event. In their recent numerical calculation study, the authors noticed that when absorption becomes strong, the transport of light occurs via much straighter paths.

]]>[A. Liutkus et al., *arXiv*, 1309.0425, (2013)]

The idea of compressive sensing is to acquire an image with fewer measurement that dictated by the Shannon-Nyquist theorem. In other words, an image divided in "pixels" can usually be reconstructed using less measurements than the total number of pixels. To do so, one need a way to mix the information, so that any measurement contain at least a bit of information on any input element. Previous implementation of compressive sensing consisted in artificially designing a hardware and a sampling procedure to generate randomness. In the present paper, the authors shows that one can use a random scattering medium as a universal image scrambler. The light reflected from an image propagates through a layer of white paint and the field is measured on different receptors on the other side of the sample. By previously measuring the transmission matrix, the authors shows that sparse images can be successfully reconstructed using compressed sensing techniques taking advantage of the randomness generated by multiple scattering.

]]>[N. Bachelard et al., *Phys. Rev. Lett.*, 109, (2012)]

[M. Leonetti et al., *Appl. Phys. Lett.*, 102, (2013)]

[N. Bachelard et al., *arXiv*, 1303.1398, (2013)]

[T. Hirsch et al., *Phys. Rev. Lett.*, 111, (2013)]

While conventional lasers use mirrors to confine light in a cavity with gain to achieve spontaneous emission, random lasers take advantage of multiple scattering to trap light in a disordered medium [1]. Such lasers do not require to carefully tune the geometry of the cavity, which greatly simplify their design. They are potentially cheaper and more robust in presence of perturbations (temperature, vibration). The resulting emission spectrums and radiation patterns are broad but mainly uncontrolled. In recent studies [2-5] different groups demonstrated numerically and experimentally the modulation of the spatial profile of the pump to control the spectrum [2-4] or the emission pattern [5].

]]>[T. Chaigne et al., *arXiv*, 1305.6246, (2013)]

Optical wavefront shaping allows imaging or focusing of light in strongly scattering media at depth where usual microscopy techniques fails. However, wavefront shaping techniques usually require captors (like a CCD array) or probes (like fluorescent entities) to guide the focusing of light or to characterize the system for imaging purposes. Recently, [X. Xu, H. Liu and L.V. Wang, *Nat. Photon.*, 5, 154, (2011)] and [X. Xu, H. Liu and L.V. Wang, *Nat. Photon.*, 7, 300, (2013)] (see Retrieving an optical scale resolution with light focusing guided by ultrasound) have shown how to use ultrasound to noninvasively guide light focusing in a scattering medium. This methods use an iterative optimization schemes for focusing on each target. This limits the applications for imaging due to the time requirements. In this paper, the authors use the photo-acoustic effect to measure the transmission matrix that links the optical field on the surface of a spatial light modulator (SLM) modulating the input light to the optical field on different points inside a scattering medium. This knowledge of this matrix allows selective focusing on multiple points and detection of targets buried in the medium.

[J. H. Park et al., *Nat. Photon.*, (2013)]

After the first experiment of light focusing through a scattering medium using wavefront shaping (see A pioneer experiment), the same group demonstrated in [I. M. Vellekoop et al., *Nat. Photon.*, 4, 320, (2010)] that a random medium can improve the sharpness of the focus. The scattering in a medium behind a lens randomizes the direction of the light. The speckle pattern shows high spatial frequencies not allowed by the lens alone because of its finite numerical aperture. After optimization of the input wavefront, the focus spot obtained is sharper than the resolution limit of the lens. In these experiments, the intensity profile was always measured in the far field, *i.e.* at least several wavelengths away from the surface, where only the propagating waves contribute to the optical field. In the present paper, J. H. Park and his colleagues optimize the input wavefront impinging on turbid media to increase the intensity measured in the near field at a given position. Subwavelength focusing is achieved thanks to the contributions of the evanescent waves.

[A. Goetschy and A. D. Stone, *Phys. Rev. Lett.*, 1304.5562, (2013)]

Almost thirty years ago, theoreticians predicted that the distribution of the transmission values of a multiple scattering sample should follow a 'bimodal distribution'. Physically, that means that, in the diffusive regime, there is a large number of strongly reflected channels - the closed channels - and a small number of channels of transmission close to one - the open channels. The existence of these open channels regardless of the thickness of the medium is of big interest for researchers, especially for imaging or communication applications. Nevertheless, such channels have not yet been directly observed. A investigation on those channels requires a measurement of the entire transmission matrix of a lossless scattering medium. For practical reasons (open geometry, limited numerical aperture, noise...) one usually has access to a subpart of the total transmission matrix. In recent experimental measures of the transmission matrix in optics [S.M. Popoff et al., *Phys. Rev. Lett.*, 104, 100601, (2010)] the distribution of the transmission values follows a 'quarter circle law', characteristic of totally uncorrelated systems. This means that the fraction of the transmission matrix measured shows no effect of the correlations at the origin of the bimodal distribution due to the loss of information. In this paper, A. Goetschy and D. Stone theoretically study the effect of the loss of information or the imperfect control on the statistics of the transmission matrix of a scattering system.

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[B. Judkewitz et al., *Nat. Photon.*, 7, 300, (2013)]

To focus light in or through a scattering medium using wavefront shaping techniques, one need a way to probe the intensity or the field at the target position. To avoid having to insert a probe in the medium, Xu et al. proposed in 2011 the use of an ultrasonic focused beam to select a target area by photo-acoustic effect [X. Xu, H. Liu and L.V. Wang, *Nat. Photon.*, 5, 154, (2011)]. This technique allows to focus light on a spot of the size of the ultrasound focused beam, which is typically at least one order of magnitude larger than the optical wavelength. In this new study, B. Judkewitz and co-authors used an innovative method to be able to focus light on a much smaller scale.