## All-fiber wavefront shaping by transmission matrix engineering [highlight]

[S. Resisi et al., Arxiv (2019)]

In the past 10 years, many applications were successfully demonstrated for wavefront shaping in multimode fibers, from endoscopic to telecommunications through optical tweezers. However, these techniques require to modulate the incident field using free space modulators. In the present paper, S. Resisi and co-authors introduce a new approach that relies on modulating the transmission matrix itself by applying changes that modify its boundary conditions. Using an all-fiber apparatus, focusing light at the distal end of the fiber and conversion between fiber modes is demonstrated. Since in this approach the number of degrees of control can be larger than the number of fiber modes, it allows simultaneous control over multiple inputs and multiple wavelengths.

$$\def\ket#1{{\left|{#1}\right\rangle}} \def\bra#1{{\left\langle{#1}\right|}} \def\braket#1#2{{\left\langle{#1}|{#2}\right\rangle}}$$

## The Speckle-Correlation Transmission Matrix [highlight]

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

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

[L. Gong, Q. Zhao, H. Zhang, X.-Y. Hu, K. Huang, J.-M. Yang and Y.-M. Li, Light Sci. Appl., 8 (2019)]

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.

$$\def\ket#1{{\left|{#1}\right\rangle}} \def\bra#1{{\left\langle{#1}\right|}} \def\braket#1#2{{\left\langle{#1}|{#2}\right\rangle}}$$

## Wavefront shaping in complex media for analog computation [highlight]

[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.

# [highligth] A microwave spatial modulator to improve in-home WiFi

[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.

## [highlight] From diffusive to ballistic-like transport in absorbing media

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.

## Imaging with nature: Using a scattering medium as a universal scrambler for imaging by compressed sensing [highlight]

[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.