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Spatiotemporal sculpturing of light pulse with ultimately sophisticated structures represents the holy grail of the human everlasting pursue of ultrafast information transmission and processing as well as ultra-intense energy concentration and extraction. It also holds the key to unlock new extraordinary fundamental physical effects. Traditionally, spatiotemporal light pulses are always treated as spatiotemporally separable wave packet as solution of the Maxwell's equations. In the past decade, however, more generalized forms of spatiotemporally nonseparable solution started to emerge with growing importance for their striking physical effects. This roadmap intends to highlight the recent advances in the creation and control of increasingly complex spatiotemporally sculptured pulses, from spatiotemporally separable to complex nonseparable states, with diverse geometric and topological structures, presenting a bird's eye viewpoint on the zoology of spatiotemporal light fields and the outlook of future trends and open challenges., Comment: This is the version of the article before peer review or editing, as submitted by an author to Journal of Optics. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it

The ability to measure polarisation, spectrum, temporal dynamics, and spatial amplitude and phase of optical beams is essential to study fundamental phenomena in laser dynamics, telecommunications and nonlinear optics. Current characterisation techniques only apply in limited contexts. Non-interferometric methods typically lack access to spatial phase, while phase-sensitive approaches necessitate either an auxiliary reference source or an adequate self-reference, neither of which is universally available. Regardless of the reference, deciphering complex wavefronts of multiple co-propagating incoherent fields remains particularly challenging. Here, we harness the principles of quantum state tomography to circumvent these limitations. A full description of an unknown beam is retrieved by measuring its temporally and spectrally resolved density matrices for both polarisations, using a spatial light modulator to display projective holograms and a single-mode fibre to guide the collected signal to a high-speed photodiode and a spectrometer. Despite no spatial resolution of the detector and the intensity-only character of the collected signal, the method resolves multiple arbitrary spatial fields within a single beam, including their phase and amplitude, as well as their spatial coherence. Leveraging the coherence information unlocks unambiguous determination of the spectral and temporal evolution of mutually incoherent fields, even when these spectrally overlap or have an identical time delay. We demonstrate these hallmark features by characterising the rich spatiotemporal and spectral output of a vertical-cavity surface-emitting laser diode that has so far resisted full analysis using existing techniques., Comment: 11 pages, 5 figures

The complex temporal behavior of an ultrashort pulse of light propagating through a multiply scattering medium can be characterized experimentally through a time-gated transmission matrix. Using a spatial light modulator, we demonstrate here, that injecting singular vectors of this matrix allows us to optimally control energy deposition at any controllable delay time. Our approach provides insights into fundamental aspects of multi-spectral light scattering and could find applications in imaging or coherent control.

Propagation of an ultrashort pulse of light through strongly scattering media generates an intricate spatio-spectral speckle that can be described by means of the multi-spectral transmission matrix (MSTM). In conjunction with a spatial light modulator, the MSTM enables the manipulation of the pulse leaving the medium; in particular focusing it at any desired spatial position and/or time. Here, we demonstrate how to engineer the point-spread-function of the focused beam both spatially and spectrally, from the measured MSTM. It consists in numerically filtering the spatial content at each wavelength of the matrix prior to focusing. We experimentally report on the versatility of the technique through several examples, in particular as an alternative to simultaneous spatial and temporal focusing, with potential applications in multiphoton microscopy., Comment: 7 pages, 5 figures

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.

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 temporal control of the total impulse response integrated over all the spatial and polarization modes propagating through a multimode fiber. We notably demonstrate a global enhancement of light intensity at a chosen arrival time, as well as attenuating light intensity at an arbitrary delay. We also demonstrate the full polarization control of such engineered states and a multiple control at different delay times, which opens interesting perspectives for non-linear imaging through complex systems and high power fiber lasers., Comment: 10 pages including main and supplemental documents. 5 figures in the main manuscript, 4 figures in the supplemental

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 either with spectral or temporal resolution. Thanks to wavefront shaping, temporal and spatial refocusing have been demonstrated. In this work, 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 such fluorescent microbeads located after a thick scattering medium, at a depth where conventional imaging would be impossible because of scattering effects., Comment: 5 pages, 4 figures

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., Comment: 4 pages, 3 figures

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., Comment: 6 pages, 5 figures

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., Comment: 4 pages, 4 figures

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., Comment: revised version, 5 pages, 4 figures, and supplementary materials(including 5 figures