Much of our knowledge of molecular geometry and interaction dynamics comes from indirect measurements of the molecular fragments following breakup. This technique-Coulomb-explosion imaging (CEI), i.e., determining the initial molecular configuration of a system from the momenta of the resulting fragments using knowledge of the particle interactions-is one of the fundamental tools of molecular physics. Moreover, CEI has been a staple of molecular studies for decades. Here we show that one often cannot assign a unique initial configuration to the few-body breakup of a polyatomic molecule given the measurement of the resulting fragments' momenta. Specifically, multiple initial configurations can result in identical momenta for a molecule breaking into three or more parts. Further, the nonunique and nonuniform mapping from the initial configuration to the measured momenta also significantly complicates the determination of molecular alignment at the time of breakup.

High order harmonic generation from relativistic laser-solid interactions (focused intensity of $$>10^{18}~$$ Wcm $$^{-2}$$ ) has the potential to serve as a source of bright attosecond radiation. One key mechanism that can generate such radiation is the Relativistically Oscillating Mirror (ROM) where the overdense plasma surface oscillates at relativistic velocities leading to a Doppler upshift of the reflected laser radiation. A major obstacle to the application of such a harmonic source is that the radiation is emitted as a periodic pulse train with the frequency of the driving laser. One route to limiting this emission to a single pulse is to exploit the ellipticity dependence of these mechanisms by forming a pulse whose polarisation varies from circular to linear to circular—a technique known as polarization gating. At small angles of incidence it is expected that the efficiency of the ROM mechanism drops dramatically for circular polarization. Here we present a novel method of implementing this technique for high power laser pulses along with proof of principle experimental results.

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 demonstrate attosecond control over the trajectories of relativistic electron bunches formed during such interactions by studying the emission of extreme ultraviolet (XUV) harmonic radiation. We describe how the precise addition of a second laser beam operating at the second harmonic of the driving laser pulse can significantly transform the interaction by modifying the accelerating potential provided by the fundamental frequency to drive strong coherent emission. Numerical particle-in-cell code simulations and experimental observations demonstrate that this modification is extremely sensitive to the relative phase of the two beams and can lead to significant enhancements in the resulting harmonic yield. This work also reveals that the ability to control these extreme interactions with attosecond precision is an essential requirement for generation of ultra-bright, high temporal contrast attosecond radiation for atomic and molecular pump-probe experiments5,6.

Experimental data supported by simulations indicate that the trajectories of relativistic electron bunches can be controlled at the attosecond timescale by precise adjustment of the relative phase in a two-colour field scheme. An enhancement in the harmonic yield is also reported. 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 phenomena, including those 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 experimentally demonstrate that by precisely adjusting the relative phase of an additional laser beam operating at the second harmonic of the driving laser it is possible to control the trajectories of relativistic electron bunches formed during the interaction with a solid target at the attosecond scale. We observe significant enhancements in the resulting high-harmonic yield, suggesting potential applications for sources of ultra-bright, extreme ultraviolet attosecond radiation to be used in atomic and molecular pump–probe experiments5,6.

High order harmonics generated at relativistic intensities have long been recognized as a route to the most powerful extreme ultraviolet pulses. Reliably generating isolated attosecond pulses requires gating to only a single dominant optical cycle, but techniques developed for lower power lasers have not been readily transferable. We present a novel method to temporally gate attosecond pulse trains by combining noncollinear and polarization gating. This scheme uses a split beam configuration which allows pulse gating to be implemented at the high beam fluence typical of multi-TW to PW class laser systems. Scalings for the gate width demonstrate that isolated attosecond pulses are possible even for modest pulse durations achievable for existing and planned future ultrashort high-power laser systems. Experimental results demonstrating the spectral effects of temporal gating on harmonic spectra generated by a relativistic laser plasma interaction are shown.

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 $\omega_L$ and at the plasma frequency $\omega_P$ 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 $\omega_L$ and $\omega_P$.

Waveform shaping and frequency synthesis based on waveform modulation is ubiquitous in electronics, telecommunication technology, and optics. For optical waveforms, the carrier frequency is on the order of several hundred THz, while the modulation frequencies used in conventional devices like electro- or acousto-optical modulators are orders of magnitude lower. As a consequence, any new frequencies are typically very close to the fundamental. The synthesis of new frequencies in the extreme ultraviolet (XUV), e.g. by using relativistic oscillating mirrors, requires modulation frequencies in the optical regime or even in the extreme ultraviolet. The latter has not been proven possible to date. Here we demonstrate that individual strong harmonics can indeed be generated by reflecting light off a plasma surface that oscillates at XUV frequencies. The strong harmonics are explained by nonlinear frequency mixing of near-infrared light and a laser-driven plasma oscillation in the extreme ultra-violet mediated by a relativistic non-linearity.

We report on the unequal spacing attosecond pulse trains from relativistic surface plasmas. The surface high harmonics efficiency is determined and could be enhanced using an optimized plasma scale length and density.

Harmonic generation in the limit of ultrasteep density gradients is studied experimentally. Observations reveal 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)→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 harmonics reflected from the laser driven plasma surface via the relativistic oscillating mirror was estimated to be in the range of 10(-4)-10(-6) of the laser pulse energy for photon energies ranging from 20-40 eV, with the best results being obtained for an intermediate density scale length.