The cost, size and availability of electron accelerators are dominated by the achievable accelerating gradient. Conventional high-brightness radio-frequency accelerating structures operate with 30–50 MeV m−1 gradients. Electron accelerators driven with optical or infrared sources have demonstrated accelerating gradients orders of magnitude above that achievable with conventional radio-frequency structures. However, laser-driven wakefield accelerators require intense femtosecond sources and direct laser-driven accelerators suffer from low bunch charge, sub-micron tolerances and sub-femtosecond timing requirements due to the short wavelength of operation. Here we demonstrate linear acceleration of electrons with keV energy gain using optically generated terahertz pulses. Terahertz-driven accelerating structures enable high-gradient electron/proton accelerators with simple accelerating structures, high repetition rates and significant charge per bunch. These ultra-compact terahertz accelerators with extremely short electron bunches hold great potential to have a transformative impact for free electron lasers, linear colliders, ultrafast electron diffraction, X-ray science and medical therapy with X-rays and electron beams.

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The method used to deduce the spectral density distribution of intermolecular and intramolecular (vibrational) degrees of freedom in the liquid state from optical heterodyne detected optical (Raman-induced) Kerr effect (OHD-RIKE) measurements is reexamined within a multimode Brownian oscillator model. The ramifications of nonlinear coupling of the nuclear degrees of freedom to the medium polarizability are explored for discrimination between "homogeneous" and "inhomogeneous" contributions to the vibrational spectral density. Under physically reasonable assumptions, an estimation of the homogeneous contribution to the vibrational line shape can be made from the OHD-RIKE observable (if nonlinear coupling is nonnegligible). The model is developed generally, and calculations are applied specifically to temperature-dependent OHD-RIKE measurements of liquid water. The results indicate that the line broadening in the low-frequency vibrational distribution due to the hydrogen-bonded network structure of liquid water is mostly inhomogeneous, with an effective homogeneous relaxation time of 350 fs at 24°C.