It is shown that when an few-cycle, relativistically intense, p-polarized laser pulse is obliquely incident on overdense plasma, the surface electrons may form ultra-thin, highly compressed layers, with a width of a few nanometers. These electron "nanobunches" emit synchrotron radiation coherently. We calculate the one-dimensional synchrotron spectrum analytically and obtain a slowly decaying power-law with an exponent of 4/3 or 6/5. This is much flatter than the 8/3 power of the BGP (Baeva-Gordienko-Pukhov) spectrum, produced by a relativistically oscillating bulk skin layer. The synchrotron spectrum cut-off frequency is defined either by the electron relativistic $γ$-factor, or by the thickness of the emitting layer. In the numerically demonstrated, locally optimal case, the radiation is emitted in the form of a single attosecond pulse, which contains almost the entire energy of the full optical cycle.
With the high-order harmonic generation (HHG) from plasma sur- faces it is possible to turn a laser pulse into a train of attosecond or even zeptosecond pulses in the backward radiation. These attosecond pulses may have amplitude several orders of magnitude higher than that of the laser pulse under appropriate conditions. We study this process in detail, especially the nanobunching of the plasma electron density. We derive an analytical expression that describes the electron density pro- file and obtain a good agreement with particle-in-cell simulation results. We investigate the most efficien…
With the generation of high order harmonics (HHG) on the plasma surface it is possible to turn the laser pulse into a train of attosecond or even zeptosecond pulses in the back radiation. These attosecond pulses may have amplitude several orders of magnitude larger than that of the laser pulse under appropriate conditions. We study this process in detail, especially the nanobunching of the plasma electron density. We derive the analytical expression that describes the electron density profile and obtain a good agreement with particle-in-cell simulations. We investigate the most efficient case …
Experiments on the excitation of propagating surface plasmons (SPs) by ultrashort, high intensity laser interaction with "grating" targets are reviewed. At intensities exceeding $10^{19}~\mbox{W cm}^{-2}$ on target, i.e. in the strongly relativistic regime of electron dynamics, multi-MeV electrons are accelerated by the SP field as dense bunches collimated in a near-tangent direction. By the use of a suitable blazed grating, the bunch charge can be increased up to $\simeq $660 picoCoulomb. Intense XUV high harmonics (HH) diffracted by the grating are observed when a plasma with sub-micrometer …
We introduce two-color counterrotating circularly polarized laser fields as a new way to spectrally control high harmonic generation (HHG) from relativistic plasma mirrors. Through particle-in-cell simulations, we show that only a selected group of harmonic orders can appear owing to the symmetry of the laser fields and the related conservation laws. By adjusting the intensity ratio of the two driving field components, we demonstrate the overall HHG efficiency, the relative intensity of allowed neighboring harmonic orders, and the polarization state of the harmonic source can be tuned. The HHG…
The role of relativistic surface plasmons (SPs) in high order harmonic emission from laser-irradiated grating targets has been investigated by means of particle-in-cell simulations. SP excitation drives a strong enhancement of the intensity of harmonics, particularly in the direction close to the surface tangent. The SP-driven enhancement overlaps with the angular separation of harmonics generated by the grating, which is beneficial for applications requiring monochromatic XUV pulses.
We demonstrate coherent hard electromagnetic radiation generation from reflection by the electron density singularity formed at the relativistic bow wave in laser plasma via particle-in-cell simulations. Wake and bow waves driven by an intense laser pulse form an electron density singularity at the laser pulse front where they join. A counter-propagating laser pulse is reflected at the electron density modulations moving with relativistic velocity. The reflected electromagnetic pulse is compressed and its frequency is upshifted. Its frequency spectrum contains relativistic harmonics of the dri…
Ultrafast extreme ultraviolet (XUV) sources with a controllable polarization state are powerful tools for investigating the structural and electronic as well as the magnetic properties of materials. However, such light sources are still limited to only a few free-electron laser facilities and, very recently, to high-order harmonic generation from noble gases. Here we propose and numerically demonstrate a laser-plasma scheme to generate bright XUV pulses with fully controlled polarization. In this scheme, an elliptically-polarized laser pulse is obliquely incident on a plasma surface, and the r…
We report evidence for the first generation of XUV spectra from relativistic surface high-harmonic generation (SHHG) on plasma mirrors at a kilohertz repetition rate, emitted simultaneously with energetic electrons. SHHG spectra and electron angular distributions are measured as a function of the experimentally controlled plasma density gradient scale length $L_\mathrm{g}$ for three increasingly short and intense driving pulses: 24~fs and $a_0=1.1$, 8~fs and $a_0=1.6$, and finally 4~fs and $a_0\approx2.1$, where $a_0$ is the peak vector potential normalized by $m_\mathrm{e} c/e$ with the eleme…
We present measurements of high-order harmonics and relativistic electrons emitted into the vacuum from a plasma mirror driven by temporally-shaped ultra-intense laser waveforms, produced by collinearly combining the main laser field with its second harmonic. We experimentally show how these observables are influenced by the phase delay between these two frequencies at the attosecond timescale, and relate these observations to the underlying physics through an advanced analysis of 1D/2D Particle-In-Cell simulations. These results demonstrate that sub-cycle shaping of the driving laser field pr…
In this letter we report on an experimental study of high harmonic radiation generated in nanometer-scale foil targets irradiated under normal incidence. The experiments constitute the first unambiguous observation of odd-numbered relativistic harmonics generated by the $\vec{v}\times\vec{B}$ component of the Lorentz force verifying a long predicted property of solid target harmonics. Simultaneously the observed harmonic spectra allow in-situ extraction of the target density in an experimental scenario which is of utmost interest for applications such as ion acceleration by the radiation press…
The reflection and transmission of a few-cycle Ti:Sa laser pulse iminging on a thin plasma layer have been analysed on the basis of classical electrodynamics. An approximate analytic solution has been given for the coupled Maxwell-Lorentz equations describing the dynamics of the surface current and the composite radiation field. The nonlinearities stemming from the relativistics kinematics of free electrons lead to the appearance of higher-harmonics in the scattered spectra. In our analysis particular attention has been paid to the effect of the carrier-envelope phase difference of the incomin…
We propose and demonstrate that relativistic harmonics with a slowly decaying power law are generated from a femtosecond lase pulse incident parallel to a micro-scale overdense plasma. It is shown that due to the excitation of a strong surface wave, dense electron nanobunches are continuously accelerated forward while oscillating in the transverse laser field. Even around the stationary phase point, relativistic gamma factors of the nanobunches increase considerably, leading to a much stronger attosecond burst, compared to the case with constant gamma. Our two-dimensional particle-in-cell simu…
We report the enhancement of individual harmonics generated at a relativistic ultra-steep plasma vacuum interface. Simulations show the harmonic emission to be due to the coupled action of two high velocity oscillations -- at the fundamental $ω_L$ and at the plasma frequency $ω_P$ of the bulk plasma. The synthesis of the enhanced harmonics can be described by the reflection of the incident laser pulse at a relativistic mirror oscillating at $ω_L$ and $ω_P$.
High harmonic generation due to the interaction of a short ultra relativistic laser pulse with overdense plasma is studied analytically and numerically. On the basis of the ultra relativistic similarity theory we show that the high harmonic spectrum is universal, i.e. it does not depend on the interaction details. The spectrum includes the power law part $I_n\propto n^{-8/3}$ for $n<\sqrt{8α}γ_{\max}^3$, followed by exponential decay. Here $γ_{\max}$ is the largest relativistic $γ$-factor of the plasma surface and $α$ is the second derivative of the surface velocity at this moment. The high ha…
The influence of laser frequency on laser-driven ion acceleration is investigated by means of two-dimensional particle-in-cell simulations. When ultrashort intense laser pulse at higher harmonic frequency irradiates a thin solid foil, the target may become relativistically transparent for significantly lower laser pulse intensity compared to irradiation at fundamental laser frequency. The relativistically induced transparency results in an enhanced heating of hot electrons as well as increased maximum energies of accelerated ions and their numbers. Our simulation results have shown the increas…
Visible or near infra-red light can be manipulated to produce bursts of coherent extreme ultraviolet (XUV) or X-rays via the relativistic high-order harmonic generation process when a laser irradiates a solid plasma target. The intensity of the spectral components of the reflected signal decays with increase of harmonic order and the efficiency of this non-linear process largely hinges on how prompt this decay is. This is governed by the conditions of the laser-plasma interaction for which various models have been proposed. At relativistic intensities, a spectrum exhibiting a power-law decay w…
In this work using three-dimensional particle-in-cell simulations and analytical considerations we demonstrate intense high-order plasma surface harmonics carrying a time-varying orbital angular momentum (OAM) -- the self-torque. We show that by using two laser beams with different OAMs $l_1$ and $l_2$ and a certain delay between each other and shooting them obliquely on an overdense plasma target, one can generate harmonics with OAM spanning $nl_1$ to $nl_2$, where $n$ is the order of the harmonic. Such intense self-torqued harmonics can offer new possibilities in ultrafast spectroscopy.
Vector beam, with a spatial nonuniform polarization distribution, is important for many applications due to its unique field characteristics and novel effects when interacting with matter. Here through three-dimensional particle-in-cell simulations, we demonstrate that intense vector beams in the extreme-ultraviolet to x-ray spectral region can be generated by means of high harmonic generation (HHG) in the relativistic regime. The vector features of the fundamental laser beam can be transferred to the higher frequency emission coherently during the extreme nonlinear HHG dynamics from relativis…
When a high power laser beam irradiates a small aperture on a solid foil target, the strong laser field drives surface plasma oscillation at the periphery of this aperture, which acts as a "relativistic oscillating window". The diffracted light that travels though such an aperture contains high-harmonics of the fundamental laser frequency. When the driving laser beam is circularly polarised, the high-harmonic generation (HHG) process facilitates a conversion of the spin angular momentum of the fundamental light into the intrinsic orbital angular momentum of the harmonics. By means of theoretic…
Energy coupling during relativistically intense laser-matter interactions is encoded in the attosecond motion of strongly driven electrons at the pre-formed plasma-vacuum boundary. Studying and controlling this motion can reveal details about the microscopic processes that govern a vast array of light-matter interaction physics and applications. These include research areas right at the forefront of extreme laser-plasma science such as laser-driven ion acceleration1, bright attosecond pulse generation2,3 and efficient energy coupling for the generation and study of warm dense matter4. Here we …
When a relativistically intense linearly polarized laser pulse is incident on an overdense plasma, a dense electron layer is formed on the plasma edge which relativistic motion results in high harmonic generation, ion acceleration and incoherent synchrotron emission of gamma-photons. Here we present a self-consistent analytical model that describes the edge motion and apply it to the problem of incoherent synchrotron emission by ultrarelativistic plasma electrons. The model takes into account both coherent radiation reaction from high harmonics and incoherent radiation reaction in the Landau-L…
Relativistic surface high harmonics have been considered a unique source for the generation of intense isolated attosecond pulses in the extreme ultra-violet (XUV) and X-ray spectral range. However, its experimental realization is still a challenging task requiring identification of the optimum conditions for the generation of isolated attosecond pulses as well as their temporal characterization. Here, we demonstrate measurements in both directions. Particularly, we have made a first step towards the temporal characterization of the emitted XUV radiation by adapting the attosecond streak camer…
Harmonic generation in the limit of ultra-steep density gradients is studied experimentally. Observations demonstrate that while the efficient generation of high order harmonics from relativistic surfaces requires steep plasma density scale-lengths ($L_p/λ< 1$) the absolute efficiency of the harmonics declines for the steepest plasma density scale-length $L_p \to 0$, thus demonstrating that near-steplike density gradients can be achieved for interactions using high-contrast high-intensity laser pulses. Absolute photon yields are obtained using a calibrated detection system. The efficiency of h…
A highly intense femtosecond laser pulse incident on a plasma target of supercritical density, gives rise to reflected high-order harmonics of the laser frequency. The radiation model adopted here considers Brunel electrons -those reinjected into the plasma after performing a vacuum excursion-perturbed by a localized turbulent region of an electrostatic field that is generated during the interaction, and characterized by a soliton-like structure. The observed power spectrum is characterized by a power-law decay scaled as P_m ~ m^{-p}, here m denotes the harmonic order. In this work an appeal i…
We demonstrate a new high-order harmonic generation mechanism reaching the `water window' spectral region in experiments with multi-terawatt femtosecond lasers irradiating gas jets. A few hundred harmonic orders are resolved, giving uJ/sr pulses. Harmonics are collectively emitted by an oscillating electron spike formed at the joint of the boundaries of a cavity and bow wave created by a relativistically self-focusing laser in underdense plasma. The spike sharpness and stability are explained by catastrophe theory. The mechanism is corroborated by particle-in-cell simulations.
High harmonic generation by relativistically intense laser pulses from overdense plasma layers is surveyed. High harmonics are generated in form of (sub-)attosecond pulses when the plasma surface rebounds towards the observer with relativistic velocity. Different cases are considered. The "relativistically oscillating mirror" (ROM) model, describing the most typical case, is analyzed in detail. The resulting harmonic spectrum is usually a power law with the exponent -8/3 [baeva2006relativistic], but possible exceptions due to "higher order γ-spikes" are considered. It is shown that under certa…
An ultra-bright high-intensity X- and gamma-radiation source is proposed. A high-density thin plasma slab, accelerating in the radiation pressure dominant regime by a co-propagating ultra-intense electromagnetic wave, reflects a counter-propagating relativistically strong electromagnetic wave, producing strongly time-compressed and intensified radiation due to the double Doppler effect. The reflected light contains relativistic harmonics generated at the plasma slab, all upshifted with the same factor as the fundamental mode of the incident light.
Formation of femtosecond sawtooth pulses by high harmonic generation from relativistic oscillating mirrors is studied. For oblique incidence of $p$-polarized laser pulse, one can efficiently control the intensity of the first few harmonics by modifying the plasma density gradient at the plasma-vacuum interface. With appropriate choice of the laser amplitude and incidence angle, the generated harmonics can form a millijoule femtosecond sawtooth pulse. The scheme does not rely on phase manipulation and/or pulse synchronization as in the state-of-art methods. It is also shown that such a sawtooth…
Quantum-optical spectrometry is a recently developed shot-to-shot photon correlation-based method, namely using a quantum spectrometer (QS), that has been used to reveal the quantum optical nature of intense laser-matter interactions and connect the research domains of quantum optics (QO) and strong laser-field physics (SLFP). The method provides the probability of absorbing photons from a driving laser field towards the generation of a strong laser-field interaction product, such as high-order harmonics. In this case, the harmonic spectrum is reflected in the photon number distribution of the…
X-ray devices are far superior to optical ones for providing nanometre spatial and attosecond temporal resolutions. Such resolution is indispensable in biology, medicine, physics, material sciences, and their applications. A bright ultrafast coherent X-ray source is highly desirable, for example, for the diffractive imaging of individual large molecules, viruses, or cells. Here we demonstrate experimentally a new compact X-ray source involving high-order harmonics produced by a relativistic-irradiance femtosecond laser in a gas target. In our first implementation using a 9 Terawatt laser, cohe…
In this letter, cutting-edge 3D Particle-In-Cell simulations are used to demonstrate that so-called relativistic plasma mirrors irradiated by PetaWatt (PW) lasers and naturally curved by laser radiation pressure can be used to tightly focus Doppler-generated harmonics to extreme intensities between $10^{25}-10^{26}W.cm^{-2}$. Those simulations are then employed to develop and validate a general 3D model of harmonic focusing by a curved relativistic plasma mirror. Finally, the insight gained from this model is used to propose novel all-optical techniques that would further increase the plasma m…
A propagation of an ultra-intense short laser pulse in a fiber is investigated with two dimensional Particle-in-Cell simulations. The fiber is a narrow hollow channel with walls consisting of overdense plasma. In the nonlinear interaction of the laser pulse with fiber walls high order harmonics are generated. Sufficiently high harmonics, for which the fiber walls are transparent, propagate outwards at certain angle. This is a scheme of a generator of ultra-short pulses of coherent light with a very short wavelength.
Doppler harmonic generation of a high-power laser on a relativistic plasma mirror is a promising path to produce bright attosecond light bursts. Yet, a major challenge has been to find a way to generate isolated attosecond pulses, better suited to timed-resolved experiments, rather than trains of pulses. A promising technique is the attosecond lighthouse effect, which consists in imprinting different propagation directions to successive attosecond pulses of the train, and then spatially filtering one pulse in the far field. However, in the relativistic regime, plasma mirrors get curved by the …
To describe the high harmonic generation at plasma surfaces in the relativistic regime, we introduce the concept of {\it apparent reflection point} (ARP). It appears to an external observer that the radiation electric field is zero at the ARP. The relativistic dynamics of the ARP completely defines the generation of high harmonics and attosecond pulses. The ARP velocity is a smooth function of time. The corresponding $γ$-factor, however, has sharp spikes at the times when the tangential vector potential vanishes and the surface velocity becomes close to the speed of light. We show that managin…
We report on a numerical observation of the train of zeptosecond pulses produced by reflection of a relativistically intense femtosecond laser pulse from the oscillating boundary of an overdense plasma because of the Doppler effect. These pulses promise to become a unique experimental and technological tool since their length is of the order of the Bohr radius and the intensity is extremely high $\propto 10^{19}$ W/cm$^2$. We present the physical mechanism, analytical theory, and direct particle-in-cell simulations. We show that the harmonic spectrum is universal: the intensity of $n$th harmon…
Anomalous Relativistic Emission from Self-Modulated Plasma Mirrors
ELI Beamlines Facility, The Extreme Light Infrastructure ERIC（ELI光束线设施，极端光基础设施ERIC）；Faculty of Mathematics and Physics, Charles University（查理大学数学物理学院）；Institute of Laser Engineering, Osaka University（大阪大学激光工程研究所）；Faculty of Nuclear Science and Physical Engineering, Czech Technical University in Prague（捷克布拉格工业大学核科学与物理工程学院）；Kansai Photon Science Institute, National Institutes for Quantum and Radiological Science and Technology（量子与放射科学研究所关西光子科学研究所）
The advent of Petawatt-class laser systems allows generating electro-magnetic fields of unprecedented strength in a controlled environment, driving increasingly more efforts to probe yet unobserved processes through their interaction with the quantum vacuum. Still, the lowest intensity scale governing these effects lies orders of magnitude beyond foreseen capabilities, so that such endeavor is expected to remain extremely challenging. In recent years, however, plasma mirrors have emerged as a promising bridge across this gap, by enabling the conversion of intense infrared laser pulses into coh…
The laser interaction with an electron-positron-ion mixed plasma is studied, from the perspective of the associated high-order harmonic generation. For an idealized mixed plasma which is assumed with a sharp plasma-vacuum interface and uniform density distribution, when it is irradiated by a weakly relativistic laser pulse, well-defined signals at harmonics of the plasma frequency in the harmonic spectrum are observed. These characteristic signals are attributed to the inverse two-plasmon decay of the counterpropagating monochromatic plasma waves which are excited by the energetic electrons an…
