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Terahertz (THz) generation via photomixing on photoconductive antenna using twin delayed chirped pulses provides a long THz pulse with a narrow bandwidth. To generate a long pulse with broad bandwidth, we propose a new method that combines two long optical pulses with opposite chirps. The pulses exhibit temporal distributions of their instantaneous frequencies with opposite slopes. As a result, interaction between the beat frequency evolving over time and a photoconductor produces a broad THz spectrum with temporal variations. In our experimental setup, we generate a 12 ps-long pulse with a 1 THz bandwidth spectrum, featuring a frequency ramp of 90 GHz/ps, resembling a chirped THz pulse. This approach signifies a major advancement toward integrating photomixer technology, particularly in THz ranging applications.

Terahertz microscopy has attracted attention owing to distinctive characteristics of the THz frequency region, particularly non-ionizing photon energy, spectral fingerprint, and transparency to most nonpolar materials. Nevertheless, the well-known Rayleigh diffraction limit imposed on THz waves commonly constrains the resultant imaging resolution to values beyond the millimeter scale, consequently limiting the applicability in numerous emerging applications for chemical sensing and complex media imaging. In this theoretical and numerical work, we address this challenge by introducing a new imaging approach, based on acquiring high-spatial frequencies by adapting the Fourier synthetic aperture approach to the terahertz spectral range, thus surpassing the diffraction-limited resolution. Our methodology combines multi-angle terahertz pulsed illumination with time-resolved field measurements, as enabled by the state-of-the-art time-domain spectroscopy technique. We demonstrate the potential of the approach for hyperspectral terahertz imaging of semi-transparent samples and show that the technique can reconstruct spatial and temporal features of complex inhomogeneous samples with subwavelength resolution., Comment: 15 pages, 5 figures

We present measurements on Fe$_2$O$_3$ amorphization and melt under laser-driven shock compression up to 209(10) GPa via time-resolved in situ x-ray diffraction. At 122(3) GPa, a diffuse signal is observed indicating the presence of a non-crystalline phase. Structure factors have been extracted up to 182(6) GPa showing the presence of two well-defined peaks. A rapid change in the intensity ratio of the two peaks is identified between 145(10) and 151(10) GPa, indicative of a phase change. Present DFT+$U$ calculations of temperatures along Fe$_2$O$_3$ Hugoniot are in agreement with SESAME 7440 and indicate relatively low temperatures, below 2000 K, up to 150 GPa. The non-crystalline diffuse scattering is thus consistent with the - as yet unreported - shock amorphization of Fe$_2$O$_3$ between 122(3) and 145(10) GPa, followed by an amorphous-to-liquid transition above 151(10) GPa. Upon release, a non-crystalline phase is observed alongside crystalline $\alpha$-Fe$_2$O$_3$. The extracted structure factor and pair distribution function of this release phase resemble those reported for Fe$_2$O$_3$ melt at ambient pressure., Comment: 11 pages, 4 figures, under review

We report here the first equation of state measurements of Fe$_2$O$_3$ obtained with laser-driven shock compression. The data are in excellent agreement with previous dynamic and static compression measurements at low pressure, and extend the known Hugoniot up to 700 GPa. We observe a large volume drop of $\sim$10% at 86 GPa, which could be associated, according to static compression observations, with the iron spin transition. Our measurements also suggest a change of the Hugoniot curve between 150 and 250 GPa. Above 250 GPa and within our error bars, we do not observe significant modifications up to the maximum pressure of 700 GPa reached in our experiment., Comment: 8 pages, 3 figures, 2 tables

The validity of the instanton analysis approach is tested numerically in the case of the diffraction-amplification problem $\partial_z\psi -\frac{i}{2m}\partial^2_{x^2} \psi =g\vert S\vert^2\, \psi$ for $\ln U\gg 1$, where $U=\vert\psi(0,L)\vert^2$. Here, $S(x,z)$ is a complex Gaussian random field, $z$ and $x$ respectively are the axial and transverse coordinates, with $0\le z\le L$, and both $m\ne 0$ and $g>0$ are real parameters. We consider a class of $S$, called the `one-max class', for which we devise a specific biased sampling procedure. As an application, $p(U)$, the probability distribution of $U$, is obtained down to values less than $10^{-2270}$ in the far right tail. We find that the agreement of our numerical results with the instanton analysis predictions in Mounaix (2023 {\it J. Phys. A: Math. Theor.} {\bf 56} 305001) is remarkable. Both the predicted algebraic tail of $p(U)$ and concentration of the realizations of $S$ onto the leading instanton are clearly confirmed, which validates the instanton analysis numerically in the large $\ln U$ limit for $S$ in the one-max class., Comment: 23 pages, 9 figures, submitted to J. Phys. A: Math. Theor

We study the tail of $p(U)$, the probability distribution of $U=\vert\psi(0,L)\vert^2$, for $\ln U\gg 1$, $\psi(x,z)$ being the solution to $\partial_z\psi -\frac{i}{2m}\nabla_{\perp}^2 \psi =g\vert S\vert^2\, \psi$, where $S(x,z)$ is a complex Gaussian random field, $z$ and $x$ respectively are the axial and transverse coordinates, with $0\le z\le L$, and both $m\ne 0$ and $g>0$ are real parameters. We perform the first instanton analysis of the corresponding Martin-Siggia-Rose action, from which it is found that the realizations of $S$ concentrate onto long filamentary instantons, as $\ln U\to +\infty$. The tail of $p(U)$ is deduced from the statistics of the instantons. The value of $g$ above which $\langle U\rangle$ diverges coincides with the one obtained by the completely different approach developed in Mounaix et al. 2006 {\it Commun. Math. Phys.} {\bf 264}~741. Numerical simulations clearly show a statistical bias of $S$ towards the instanton for the largest sampled values of $\ln U$. The high maxima -- or `hot spots' -- of $\vert S(x,z)\vert^2$ for the biased realizations of $S$ tend to cluster in the instanton region., Comment: 41 pages, 10 figures, submitted to J. Phys. A: Math. Theor

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.

We compute exactly the mean number of records $\langle R_N \rangle$ for a time-series of size $N$ whose entries represent the positions of a discrete time random walker on the line. At each time step, the walker jumps by a length $\eta$ drawn independently from a symmetric and continuous distribution $f(\eta)$ with probability $1-r$ (with $0\leq r < 1$) and with the complementary probability $r$ it resets to its starting point $x=0$. This is an exactly solvable example of a weakly correlated time-series that interpolates between a strongly correlated random walk series (for $r=0$) and an uncorrelated time-series (for $(1-r) \ll 1$). Remarkably, we found that for every fixed $r \in [0,1[$ and any $N$, the mean number of records $\langle R_N \rangle$ is completely universal, i.e., independent of the jump distribution $f(\eta)$. In particular, for large $N$, we show that $\langle R_N \rangle$ grows very slowly with increasing $N$ as $\langle R_N \rangle \approx (1/\sqrt{r})\, \ln N$ for $0

We compute exactly the statistics of the number of records in a discrete-time random walk model on a line where the walker stays at a given position with a nonzero probability $0\leq p \leq 1$, while with the complementary probability $1-p$, it jumps to a new position with a jump length drawn from a continuous and symmetric distribution $f_0(\eta)$. We have shown that, for arbitrary $p$, the statistics of records up to step $N$ is completely universal, i.e., independent of $f_0(\eta)$ for any $N$. We also compute the connected two-time correlation function $C_p(m_1, m_2)$ of the record-breaking events at times $m_1$ and $m_2$ and show it is also universal for all $p$. Moreover, we demonstrate that $C_p(m_1, m_2)< C_0(m_1, m_2)$ for all $p>0$, indicating that a nonzero $p$ induces additional anti-correlations between record events. We further show that these anti-correlations lead to a drastic reduction in the fluctuations of the record numbers with increasing $p$. This is manifest in the Fano factor, i.e. the ratio of the variance and the mean of the record number, which we compute explicitly. We also show that an interesting scaling limit emerges when $p \to 1$, $N \to \infty$ with the product $t = (1-p)\, N$ fixed. We compute exactly the associated universal scaling functions for the mean, variance and the Fano factor of the number of records in this scaling limit. ., Comment: 30 pages, 9 figures. Revised (and published) version. To appear in J. Phys. A

Ammonia is predicted to be one of the major components in the depths of the ice giant planets Uranus and Neptune. Their dynamics, evolution, and interior structure are insufficiently understood and models rely imperatively on data for equation of state and transport properties. Despite its great significance, the experimentally accessed region of the ammonia phase diagram today is still very limited in pressure and temperature. Here we push the probed regime to unprecedented conditions, up to $\sim$350 GPa and $\sim$40000 K. Along the Hugoniot, the temperature measured as a function of pressure shows a subtle change in slope at $\sim$7000 K and $\sim$90 GPa, in agreement with ab initio simulations we have performed. This feature coincides with the gradual transition from a molecular liquid to a plasma state. Additionally, we performed reflectivity measurements, providing the first experimental evidence of electronic conduction in high-pressure ammonia. Shock reflectance continuously rises with pressure above 50 GPa and reaches saturation values above 120 GPa. Corresponding electrical conductivity values are up to 1 order of magnitude higher than in water in the 100 GPa regime, with possible significant contributions of the predicted ammonia-rich layers to the generation of magnetic dynamos in ice giant interiors., Comment: Please visit publisher's website for supplementary information

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

We study the statistics of the number of records $R_n$ for a symmetric, $n$-step, discrete jump process on a $1D$ lattice. At a given step, the walker can jump by arbitrary lattice units drawn from a given symmetric probability distribution. This process includes, as a special case, the standard nearest neighbor lattice random walk. We derive explicitly the generating function of the distribution $P(R_n)$ of the number of records, valid for arbitrary discrete jump distributions. As a byproduct, we provide a relatively simple proof of the generalized Sparre Andersen theorem for the survival probability of a random walk on a line, with discrete or continuous jump distributions. For the discrete jump process, we then derive the asymptotic large $n$ behavior of $P(R_n)$ as well as of the average number of records $E(R_n)$. We show that unlike the case of random walks with symmetric and continuous jump distributions where the record statistics is strongly universal (i.e., independent of the jump distribution for all $n$), the record statistics for lattice walks depends on the jump distribution for any fixed $n$. However, in the large $n$ limit, we show that the distribution of the scaled record number $R_n/E(R_n)$ approaches a universal, half-Gaussian form for any discrete jump process. The dependence on the jump distribution enters only through the scale factor $E(R_n)$, which we also compute in the large $n$ limit for arbitrary jump distributions. We present explicit results for a few examples and provide numerical checks of our analytical predictions., Comment: 34 pages, 6 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.

We consider non-interacting particles (or lions) performing one-dimensional random walks or L\'evy flights (with L\'evy index $1 < \mu \leq 2$) in the presence of a constant drift $c$. Initially these random walkers are uniformly distributed over the positive real line $z\geq 0$ with a density $\rho_0$. At the origin $z=0$ there is an immobile absorbing trap (or a lamb), such that when a particle crosses the origin, it gets absorbed there. Our main focus is on (i) the flux of particles $\Phi_c(n)$ out of the system (the "Smoluchowski problem") and (ii) the survival probability $S_c(n)$ of the trap or lamb (the "lamb-lion problem") until step $n$. We show that both observables can be expressed in terms of the average maximum $\mathbb{E}[M_c(n)]$ of a single random walk or L\'evy flight after $n$ steps. This allows us to obtain the precise asymptotic behavior of both $\Phi_c(n)$ and $S_c(n)$ analytically for large $n$ in the two problems, for any value of $1<\mu\leq 2$ and $c \in {\mathbb{R}}$. In particular, for $c>0$, we show the rather counterintuitive result that for $1< \mu < 2$, $S_{c>0}(n \to \infty)$ vanishes as $S_{c>0}(n \to \infty) \approx \exp\left(-\lambda \, n^{2-\mu}\right)$, where $\lambda$ is a $\mu$-dependent positive constant, while for standard random walks (i.e., with $\mu = 2$), $S_{c>0}(n \to \infty) \to K_{RW} > 0$, as expected. Our analytical results are confirmed by numerical simulations., Comment: 28 pages, 4 figures

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

Characterising materials at pressures of several megabar and temperatures of a few thousand Kelvin is critical for the understanding of the Warm Dense Matter regime and to improve planetary models as these conditions are typical of planets' interiors. Today, laser-driven shock compression is the only technique to achieve multimegabar pressures, but the associated temperatures are too high to be representative of planetary states. Double-shock compression represents an alternative to explore lower temperatures. Here we present a method to create well-controlled double-shocked states and measure their thermodynamic state and optical reflectivity using standard optical diagnostics (Doppler velocimetry and optical pyrometry) in a laser-driven shock experiment. This method, which does not require the support of hydrodynamical simulations, is based on the application of generalised Rankine-Hugoniot relations together with a self impedance mismatch technique. A validation experiment has been performed at the LULI2000 facility (\'Ecole Polytechnique, France) on a sample of $\alpha$-quartz. A temperature $60 \%$ lower than along the principal Hugoniot has been obtained at 7.5 Mbar., Comment: 10 pages, 7 figures

In this paper, we study the large $n$ asymptotics of the expected maximum of an $n$-step random walk/L\'evy flight (characterized by a L\'evy index $1<\mu\leq 2$) on a line, in the presence of a constant drift $c$. For $0<\mu\leq 1$, the expected maximum is infinite, even for finite values of $n$. For $1<\mu\leq 2$, we obtain all the non-vanishing terms in the asymptotic expansion of the expected maximum for large $n$. For $c<0$ and $\mu =2$, the expected maximum approaches a non-trivial constant as $n$ gets large, while for $1<\mu < 2$, it grows as a power law $\sim n^{2-\mu}$. For $c>0$, the asymptotic expansion of the expected maximum is simply related to the one for $c<0$ by adding to the latter the linear drift term $cn$, making the leading term grow linearly for large $n$, as expected. Finally, we derive a scaling form interpolating smoothly between the cases $c=0$ and $c\ne 0$. These results are borne out by numerical simulations in excellent agreement with our analytical predictions., Comment: 42 pages, 7 figures

Water, ethanol, and ammonia are the key components of the mantles of Uranus and Neptune. To improve structure and evolution models and give an explanation of the magnetic fields and luminosities of the icy giants, those components need to be characterised at planetary conditions (some Mbar and a few $10^3$ K). Those conditions are typical of the Warm Dense Matter regime, which exhibits a rich phase diagram, with the coexistence of many states of matter and a large variety of chemical processes. H$_2$O, C:H:O, and C:H:N:O mixtures have been compressed up to 2.8 Mbar along the principal Hugoniot using laser-driven decaying shocks. The experiments were performed at the GEKKO XII and LULI 2000 laser facilities using standard optical diagnostics (Doppler velocimetry and pyrometry) to characterise equation of state and optical reflectivity of the shocked states. The results show that H$_2$O and the C:H:N:O mixture share the same equation of state with a density scaling, while the reflectivity behaves differently by what concerns both the onset pressures and the saturation values. The reflectivity measurement at two frequencies allows to estimate the conductivity and the complex refractive index using a Drude model.

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

We investigate the realizations of a random Gaussian field on a finite domain of ${\mathbb R}^d$ in the limit where a given linear functional of the field is large. We prove that if its variance is bounded, the field converges uniformly and almost surely to a non random profile depending only on the covariance and the considered linear functional of the field. This is a significant improvement of the weaker $L^2$-convergence in probability previously obtained in the case of conditioning on a large quadratic functional., Comment: 7 pages, LaTeX + AMS + elsarticle (included), submitted to Statist. Probab. Lett

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 consider a one-dimensional random walk (RW) with a continuous and symmetric jump distribution, $f(\eta)$, characterized by a L\'evy index $\mu \in (0,2]$, which includes standard random walks ($\mu=2$) and L\'evy flights ($0<\mu<2$). We study the survival probability, $q(x_0,n)$, representing the probability that the RW stays non-negative up to step $n$, starting initially at $x_0 \geq 0$. Our main focus is on the $x_0$-dependence of $q(x_0,n)$ for large $n$. We show that $q(x_0,n)$ displays two distinct regimes as $x_0$ varies: (i) for $x_0= O(1)$ ("quantum regime"), the discreteness of the jump process significantly alters the standard scaling behavior of $q(x_0,n)$ and (ii) for $x_0 = O(n^{1/\mu})$ ("classical regime") the discrete-time nature of the process is irrelevant and one recovers the standard scaling behavior (for $\mu =2$ this corresponds to the standard Brownian scaling limit). The purpose of this paper is to study how precisely the crossover in $q(x_0,n)$ occurs between the quantum and the classical regime as one increases $x_0$., Comment: 20 pages, 3 figures, revised and accepted version

We study one-dimensional discrete as well as continuous time random walks, either with a fixed number of steps (for discrete time) $n$ or on a fixed time interval $T$ (for continuous time). In both cases, we focus on symmetric probability distribution functions (PDF) of jumps with a finite support $[-g_{max}, g_{max}]$. For continuous time random walks (CTRWs), the waiting time $\tau$ between two consecutive jumps is a random variable whose probability distribution (PDF) has a power law tail $\Psi(\tau) \propto \tau^{-1-\gamma}$, with $0<\gamma<1$. We obtain exact results for the joint statistics of the gap between the first two maximal positions of the random walk and the time elapsed between them. We show that for large $n$ (or large time $T$ for CTRW), this joint PDF reaches a stationary joint distribution which exhibits an interesting concentration effect in the sense that a gap close to its maximum possible value, $g\approx g_{max}$, is much more likely to be achieved by two successive jumps rather than by a long walk between the first two maxima. Our numerical simulations confirm this concentration effect., Comment: 19 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 an experimental study of the phase diagrams of periclase (MgO), enstatite (MgSiO3) and forsterite (Mg2SiO4) at high pressures. We investigated with laser driven decaying shocks the pressure/temperature curves of MgO, MgSiO3 and Mg2SiO4 between 0.2-1.2 TPa, 0.12-0.5 TPa and 0.2-0.85 TPa respectively. A melting signature has been observed in MgO at 0.47 TPa and 9860 K, while no phase changes were observed neither in MgSiO3 nor in Mg2SiO4. An increasing of reflectivity of MgO, MgSiO3 and Mg2SiO4 liquids have been detected at 0.55 TPa -12 760 K, 0.15 TPa - 7540 K, 0.2 TPa - 5800 K, respectively. In contrast to SiO2, melting and metallization of these compounds do not coincide implying the presence of poor electrically conducting liquids close to the melting lines. This has important implications for the generation of dynamos in Super-earths mantles.

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

We consider a one-dimensional continuous time random walk (CTRW) on a fixed time interval $T$ where at each time step the walker waits a random time $\tau$, before performing a jump drawn from a symmetric continuous probability distribution function (PDF) $f(\eta)$, of L\'evy index $0 < \mu \leq 2$. Our study includes the case where the waiting time PDF $\Psi(\tau)$ has a power law tail, $\Psi(\tau) \propto \tau^{-1 - \gamma}$, with $0< \gamma < 1$, such that the average time between two consecutive jumps is infinite. The random motion is sub-diffusive if $\gamma < \mu/2$ (and super-diffusive if $\gamma > \mu/2$). We investigate the joint PDF of the gap $g$ between the first two highest positions of the CTRW and the time $t$ separating these two maxima. We show that this PDF reaches a stationary limiting joint distribution $p(g,t)$ in the limit of long CTRW, $T \to \infty$. Our exact analytical results show a very rich behavior of this joint PDF in the $(\gamma, \mu)$ plane, which we study in great detail. Our main results are verified by numerical simulations. This work provides a non trivial extension to CTRWs of the recent study in the discrete time setting by Majumdar et al. (J. Stat. Mech. P09013, 2014)., Comment: 36 pages, 10 figures. arXiv admin note: text overlap with arXiv:1405.1222

Several important geophysical features such as heat flux at the Core-Mantle Boundary or geodynamo production are intimately related with the temperature profile in the Earth's core. However, measuring the melting curve of iron at conditions corresponding to the Earth inner core boundary under pressure of 330 GPa has eluded scientists for several decades. Significant discrepancies in previously reported iron melting temperatures at high pressure have called into question the validity of dynamic measurements. We report measurements made with a novel approach using X-ray absorption spectroscopy using an X-ray free electron laser source coupled to a laser shock experiment. We determine the state of iron along the shock Hugoniot up to 420 GPa (+/- 50) and 10800 K (+/- 1390) and find an upper boundary for the melting curve of iron by detecting solid iron at 130 GPa and molten at 260, 380 and 420 GPa along the shock Hugoniot. Our result establishes unambiguous agreement between dynamic measurement and recent extrapolations from static data thus resolving the long-standing controversy over the reliability of using dynamic compression to study the melting of iron at conditions close to the Earth's inner core boundary and beyond., Comment: 9 pages 3 figures

The physical state and properties of silicates at conditions encountered in the cores of gas giants, ice giants and of Earth like exoplanets now discovered with masses up to several times the mass of the Earth remains mostly unknown. Here, we report on theoretical predictions of the properties of silica, SiO$_2$, up to 4 TPa and about 20,000K using first principle molecular dynamics simulations based on density functional theory. For conditions found in the Super-Earths and in ice giants, we show that silica remains a poor electrical conductor up to 10 Mbar due to an increase in the Si-O coordination with pressure. For Jupiter and Saturn cores, we find that MgSiO$_3$ silicate has not only dissociated into MgO and SiO$_2$, as shown in previous studies, but that these two phases have likely differentiated to lead to a core made of liquid SiO$_2$ and solid (Mg,Fe)O., Comment: 5 pages, 4 figures