Author Correction: Demonstration of sub-luminal propagation of single-cycle terahertz pulses for particle acceleration.

The original version of this Article contained an error in the abstract, referring to "multi-megawatt-per-metre" instead of "multi-megavolt-per-metre". This has now been corrected in both the PDF and HTML versions of the Article.

Demonstration of sub-luminal propagation of single-cycle terahertz pulses for particle acceleration.

The sub-luminal phase velocity of electromagnetic waves in free space is generally unobtainable, being closely linked to forbidden faster than light group velocities. The requirement of sub-luminal phase-velocity in laser-driven particle acceleration schemes imposes a limit on the total acceleration achievable in free space, and necessitates the use of dispersive structures or waveguides for extending the field-particle interaction. We demonstrate a travelling source approach that overcomes the sub-luminal propagation limits. The approach exploits ultrafast optical sources with slow group velocity propagation, and a group-to-phase front conversion through nonlinear optical interaction. The concept is demonstrated with two terahertz generation processes, nonlinear optical rectification and current-surge rectification. We report measurements of longitudinally polarised single-cycle electric fields with phase and group velocity between 0.77c and 1.75c. The ability to scale to multi-megavolt-per-metre field strengths is demonstrated. Our approach paves the way towards the realisation of cheap and compact particle accelerators with femtosecond scale control of particles.Controlled generation of terahertz radiation with subluminal phase velocities is a key issue in laser-driven particle acceleration. Here, the authors demonstrate a travelling-source approach utilizing the group-to-phase front conversion to overcome the sub-luminal propagation limit.

Revealing carrier-envelope phase through frequency mixing and interference in frequency resolved optical gating.

We demonstrate that full temporal characterisation of few-cycle electromagnetic pulses, including retrieval of the carrier envelope phase (CEP), can be directly obtained from Frequency Resolved Optical Gating (FROG) techniques in which the interference between non-linear frequency mixing processes is resolved. We derive a framework for this scheme, defined Real Domain FROG (ReD-FROG), for the cases of interference between sum and difference frequency components and between fundamental and sum / difference frequency components. A successful numerical demonstration of ReD-FROG as applied to the case of a self-referenced measurement is provided. A proof-of-principle experiment is performed in which the CEP of a single-cycle THz pulse is accurately obtained and demonstrates the possibility for THz detection beyond optical probe duration limitations inherent to electro-optic sampling.

Role of misalignment-induced angular chirp in the electro-optic detection of THz waves.

A general description of electro-optic detection including non-collinear phase matching and finite transverse beam profiles is presented. It is shown theoretically and experimentally that non-collinear phase matching in ZnTe (and similar materials) produces an angular chirp in the χ(2)-generated optical signal. Due to this, in non-collinear THz and probe arrangements such as single-shot THz measurements or through accidental misalignment, measurement of an undistorted THz signal is critically dependent on having sufficient angular acceptance in the optical probe path. The associated spatial walk-off can also preclude the phase retardation approximation used in THz-TDS. The rate of misalignment-induced chirping in commonly used ZnTe and GaP schemes is tabulated, allowing ready analysis of a detection system.

Electron bunch length measurements from laser-accelerated electrons using single-shot THz time-domain interferometry.

Laser-plasma wakefield-based electron accelerators are expected to deliver ultrashort electron bunches with unprecedented peak currents. However, their actual pulse duration has never been directly measured in a single-shot experiment. We present measurements of the ultrashort duration of such electron bunches by means of THz time-domain interferometry. With data obtained using a 0.5 J, 45 fs, 800 nm laser and a ZnTe-based electro-optical setup, we demonstrate the duration of laser-accelerated, quasimonoenergetic electron bunches [best fit of 32 fs (FWHM) with a 90% upper confidence level of 38 fs] to be shorter than the drive laser pulse, but similar to the plasma period.

Benchmarking of electro-optic monitors for femtosecond electron bunches.

The longitudinal profiles of ultrashort relativistic electron bunches at the soft x-ray free-electron laser FLASH have been investigated using two single-shot detection schemes: an electro-optic (EO) detector measuring the Coulomb field of the bunch and a radio-frequency structure transforming the charge distribution into a transverse streak. A comparison permits an absolute calibration of the EO technique. EO signals as short as 60 fs (rms) have been observed, which is a new record in the EO detection of single electron bunches and close to the limit given by the EO material properties.

Temporally resolved electro-optic effect.

The electro-optic effect between an ultrafast optical probe pulse and an ultrashort terahertz pulse is shown to depend on the time derivatives of the product of the probe and terahertz electric fields. Application of this theory to temporally resolved single-shot terahertz detection techniques, where the electro-optic effect is temporally localized within an optical probe pulse, shows that the description presented here differs fundamentally and verifiably from that commonly used in literature.

Generation of quasimonoenergetic electron bunches with 80-fs laser pulses.

Highly collimated, quasimonoenergetic multi-MeV electron bunches were generated by the interaction of tightly focused, 80-fs laser pulses in a high-pressure gas jet. These monoenergetic bunches are characteristic of wakefield acceleration in the highly nonlinear wave breaking regime, which was previously thought to be accessible only by much shorter laser pulses in thinner plasmas. In our experiment, the initially long laser pulse was modified in underdense plasma to match the necessary conditions. This picture is confirmed by semianalytical scaling laws and 3D particle-in-cell simulations. Our results show that laser-plasma interaction can drive itself towards this type of laser wakefield acceleration even if the initial laser and plasma parameters are outside the required regime.

Radiation sources based on laser-plasma interactions.

Plasma waves excited by intense laser beams can be harnessed to produce femtosecond duration bunches of electrons with relativistic energies. The very large electrostatic forces of plasma density wakes trailing behind an intense laser pulse provide field potentials capable of accelerating charged particles to high energies over very short distances, as high as 1GeV in a few millimetres. The short length scale of plasma waves provides a means of developing very compact high-energy accelerators, which could form the basis of compact next-generation light sources with unique properties. Tuneable X-ray radiation and particle pulses with durations of the order of or less than 5fs should be possible and would be useful for probing matter on unprecedented time and spatial scales. If developed to fruition this revolutionary technology could reduce the size and cost of light sources by three orders of magnitude and, therefore, provide powerful new tools to a large scientific community. We will discuss how a laser-driven plasma wakefield accelerator can be used to produce radiation with unique characteristics over a very large spectral range.

Electro-optic technique with improved time resolution for real-time, nondestructive, single-shot measurements of femtosecond electron bunch profiles.

Electro-optic detection of the Coulomb field of a relativistic electron bunch combined with single-shot cross correlation of optical pulses is used to enable single-shot measurements of the shape and length of femtosecond electron bunches. This method overcomes a fundamental time-resolution limit of previous single-shot electro-optic measurements, which arises from the inseparability of time and frequency properties of the probing optical pulse. Using this new technique we have made real-time measurements of a 50 MeV electron bunch, observing the profile of 650 fs FWHM ( approximately 275 fs rms) long bunches.