We report broadband characterization of the propagation of light through a multiply scattering medium by means of its Multi-Spectral Transmission Matrix. Using a single spatial light modulator, our approach enables the full control of both spatial and spectral properties of an ultrashort pulse transmitted through the medium. We demonstrate spatiotemporal focusing of the pulse at any arbitrary position and time with any desired spectral shape. Our approach opens new perspectives for fundamental studies of light-matter interaction in disordered media, and has potential applications in sensing, coherent control and imaging.Propagation of coherent light through a scattering medium produces a speckle pattern at the output [1], due to light scrambling by multiple scattering events [2]. The phase and amplitude information of the light are spatially mixed, thus limiting resolution, depth and contrast of most optical imaging techniques. Ultrashort pulses, generated by broadband modelocked lasers, are very useful for multiphotonic imaging and non-linear physics [3][4][5]. In the temporal domain, an ultrashort pulse is temporally broadened during propagation in a scattering medium, due to the long dwell time within it [6,7], which therefore limits its range of applications.However, this scattering process is linear and deterministic. Therefore, one can control the input wavefront to design the output field. In this respect, spatial light modulators (SLMs) offer more than a million degrees of freedom to control the propagation of coherent light. These systems have played an important role in the development of wavefront shaping techniques to manipulate light in complex media. Iterative optimization algorithm [8][9][10] and phase conjugation methods [11,12] have been proposed to focus light at a given output position, an essential ingredient for imaging. An alternative method for light control is the optical transmission matrix (TM). The TM is a linear operator that links the input field (SLM) to the output field (CCD camera) [1,13]. The measurement of the TM allows imaging through [15] or inside a scattering medium [16], and potentially access mesoscopic properties of the system [17].The possibility of shaping the pulse in time is also essential for coherent control [18]. Temporally, photons exit a scattering medium at different times, giving rise to a broadened pulse at its output [7,19]. Temporal spreading of the original pulse is characterized by a confinement time τ m [20] related to the Thouless time [21]. Equivalently, from a spectral point of view, the scattering medium responds differently for distinct spectral components of an ultrashort pulse, with a spectral correlation bandwidth ∆ω m ∝ 1/τ m , giving rise to a very complex spatio-temporal speckle pattern [22][23][24][25]. With a single SLM, one can manipulate spatial degrees of freedom to adjust the delay between different optical paths. Therefore spatial and temporal distortions can be both compensated using wavefront shaping techniques. This approach allows th...

Electromechanical resonators have emerged as a versatile platform in which detectors with unprecedented sensitivities and quantum mechanics in a macroscopic context can be developed. These schemes invariably utilise a single resonator but increasingly the concept of an array of electromechanical resonators is promising a wealth of new possibilities. In spite of this, experimental realisations of such arrays have remained scarce due to the formidable challenges involved in their fabrication. In a variation to this approach, we identify 75 harmonic vibration modes in a single electromechanical resonator of which 7 can also be parametrically excited. The parametrically resonating modes exhibit vibrations with only 2 oscillation phases which are used to build a binary information array. We exploit this array to execute a mechanical byte memory, a shift-register and a controlled-NOT gate thus vividly illustrating the availability and functionality of an electromechanical resonator array by simply utilising higher order vibration modes.

We report a method to characterize the propagation of an ultrashort pulse of light through a multiple scattering medium by measuring its time-resolved transmission matrix. This method is based on the use of a spatial light modulator together with a coherent time-gated detection of the transmitted speckle field. Using this matrix, we demonstrate the focusing of the scattered pulse at any arbitrary position in space and time after the medium. Our approach opens new perspectives for both fundamental studies and applications in imaging and coherent control in disordered media .

Lossless linear wave propagation is symmetric in time, a principle which can be used to create time reversed waves. Such waves are special “pre-scattered” spatiotemporal fields, which propagate through a complex medium as if observing a scattering process in reverse, entering the medium as a complicated spatiotemporal field and arriving after propagation as a desired target field, such as a spatiotemporal focus. Time reversed waves have previously been demonstrated for relatively low frequency phenomena such as acoustics, water waves and microwaves. Many attempts have been made to extend these techniques into optics. However, the much higher frequencies of optics make for very different requirements. A fully time reversed wave is a volumetric field with arbitrary amplitude, phase and polarisation at every point in space and time. The creation of such fields has not previously been possible in optics. We demonstrate time reversed optical waves with a device capable of independently controlling all of light’s classical degrees of freedom simultaneously. Such a class of ultrafast wavefront shaper is capable of generating a sequence of arbitrary 2D spatial/polarisation wavefronts at a bandwidth limited rate of 4.4 THz. This ability to manipulate the full field of an optical beam could be used to control both linear and nonlinear optical phenomena.

We report a method to design at will the spatial profile of transmitted coherent light after propagation through a scattering sample. We compute an operator based on the experimentally measured transmission matrix, obtained by numerically adding an arbitrary mask in the Fourier domain prior to focusing. We demonstrate the strength of the technique through several examples: propagating Bessel beams, thus generating foci smaller than the diffraction limited speckle grain, donut beams, and helical beams. We characterize the 3D profile of the achieved foci and analyze the fundamental limitations of the technique. Our approach generalizes Fourier optics concepts for random media, and opens in particular interesting perspectives for super-resolution imaging through turbid media.

The transmission matrix is a unique tool to control light through a scattering medium. A monochromatic transmission matrix does not allow temporal control of broadband light. Conversely, measuring multiple transmission matrices with spectral resolution allows fine temporal control when a pulse is temporally broadened upon multiple scattering, but requires very long measurement time. Here, we show that a single linear operator, measured for a broadband pulse with a co-propagating reference, naturally allows for spatial focusing, and interestingly generates a two-fold temporal recompression at the focus, compared with the natural temporal broadening. This is particularly relevant for non-linear imaging techniques in biological tissues.When monochromatic coherent light propagates in a medium with high refractive index inhomogeneities, it quickly develops into a speckle. Despite the complex structure of speckle patterns, each speckle grain has a deterministic relation to the input fields [1]. Over the last decade, wavefront shaping has turned to be an efficient tool to control monochromatic light through highly scattering systems [2], notably by exploiting the transmission matrix [3].Under illumination with a source of large bandwidth, each spectral component can generate a different speckle pattern [4]. Therefore one needs to adjust these additional spectral/temporal degrees of freedom to temporally control the output pulse [5]. This can be achieved using methods such as nonlinear optical processes [6,7], time-gating [8,9], and frequency-resolved measurements [10,11]. However, these methods underly either low signal-to-noise measurements (non-linear processes), or stability issues as they require lengthy acquisition procedures [12] and the need of external reference.An alternative approach is to use self-referencing signals, at the expense of lacking control on spectral degrees of freedom. Recently, "broadband wavefront shaping" experiments reported outcomes disparate from what is expected from monochromatic wavefront shaping, such as a decrease in the independent spectral degrees of freedom [13,14], and recovery of pure polarization states [15]. Notably, these results could have an impact on biomedical imaging [16]. Nonetheless, the exact temporal properties of the obtained output pulse via broadband wavefront shaping remain elusive. In this letter, we report the first characterization of the so-called broadband transmission matrix of a scattering medium. We exploit it for focusing purposes, and we analyze and interpret its temporal behavior. Unexpectedly, the characterized average pulse length is shorter than the pulse propagating without shaping. Figure 1a illustrates and summarizes propagation of broadband light (ultrashort pulse of duration δt, spectral width ∆λ) through an optically thick scattering medium. Transmitted light results in a speckle intensity pattern with low contrast C 0 < 1. This low contrast results from the incoherent summation of various uncorrelated speckles corresponding to different spect...

Control of the spatial and temporal properties of light propagating in disordered media have been demonstrated over the last decade using spatial light modulators. Most of the previous studies demonstrated spatial focusing to the speckle grain size, and manipulation of the temporal properties of the achieved focus. In this work, we demonstrate an approach to control the total temporal impulse response, not only at a single speckle grain but over all spatial degrees of freedom (spatial and polarization modes) at any arbitrary delay time through a multimode fiber. Global enhancement or suppression of the total light intensity exiting a multimode fibre is shown for arbitrary delays and polarization states. This work could benefit to applications that require pulse delivery in disordered media.

Several matrix approaches were developed to control light propagation through multiple scattering media under illumination of ultrashort pulses of light. These matrices can be recorded with either spectral or temporal resolution. Thanks to wavefront shaping, temporal and spatial refocusing has been demonstrated. In this Letter, we study how these different methods can be exploited to enhance a two-photon excitation fluorescence process. We first compare the different techniques on micrometer-size isolated fluorescent beads. We then demonstrate point-scanning imaging of these fluorescent microbeads located after a thick scattering medium at a depth where conventional imaging would be impossible because of scattering effects.