We have demonstrated nonlinear cross-phase modulation in electro-optic crystals using intense, single-cycle terahertz (THz) radiation. Individual THz pulses, generated by coherent transition radiation emitted by subpicosecond electron bunches, have peak energies of up to 100 microJ per pulse. The time-dependent electric field of the intense THz pulses induces cross-phase modulation in electro-optic crystals through the Pockels effect, leading to spectral shifting, broadening, and modulation of copropagating laser pulses. The observed THz-induced cross-phase modulation agrees well with a time-dependent phase-shift model.

We show that by using polarization coherent antiS tokes Raman spectroscopy, th.e detection sensitivity. of weak Raman modes is greatly enhanced. The spectra of the real part, the imaginary part, and the absolute magnitude of the resonant nonlinear susceptibility can be separately measured. Raman

We report the experimental demonstration of femtosecond electron diffraction using high-brightness MeV electron beams. High-quality, single-shot electron diffraction patterns for both polycrystalline aluminum and single-crystal 1T-TaS 2 are obtained utilizing a 5 fC (∼3 × 10 4 electrons) pulse of electrons at 2.8 MeV. The high quality of the electron diffraction patterns confirms that electron beam has a normalized emittance of ∼50 nm rad. The transverse and longitudinal coherence length is ∼11 and ∼2.5 nm, respectively. The timing jitter between the pump laser and probe electron beam was found to be ∼100 fs (rms). The temporal resolution is demonstrated by observing the evolution of Bragg and superlattice peaks of 1T-TaS 2 following an 800 nm optical pump and was found to be 130 fs. Our results demonstrate the advantages of MeV electrons, including large elastic differential scattering cross-section and access to high-order reflections, and the feasibility of ultimately realizing below 10 fs time-resolved electron diffraction. X-ray free electron laser (FEL) sources and ultrafast electron diffraction (UED) are two of the most powerful tools for exploring the ultrasmall and ultrafast world [1,2]. The large electron scattering cross section and compactness of electron facilities make UED a particularly attractive option for exploring ultrafast processes and the technique has been used for studying strongly correlated electron systems and revealing transient intermediates in gas phase chemical reactions [1][2][3][4]. However, to date, the time resolution of such experiments has been limited by pulse broadening from repulsive space-charge effects (SCE) and the limited acceleration field [5].To reduce such effects, MeV electron beams generated by a photocathode RF gun have been proposed for UED applications [6][7][8][9]. In such schemes, a laser is used to illuminate a photocathode, producing a highbrightness electron beam, and to control the initial spatial and temporal distributions of that beam. An RF cavity then rapidly accelerates the electrons to a few MeV. The RF field also compresses the electron beam as it is accelerated in the time-dependent acceleration field [6]. For electron pulses at MeV energies, the magnetic field induced by the moving electron beam, together with relativistic effects, greatly reduce the SCE. Specifically, the transverse and longitudinal SCE scale as 1/β 2 γ 3 and 1/β 2 γ 5 , respectively [10], where β and γ are the relativistic velocity and energy, respectively. Thus, increasing the electron energy has the potential to compress more electrons into a shorter electron bunch. Another important advantage of relativistic beams is that they eliminate the velocity mismatch between the pump laser and the electron beam. This mismatch often limits the time resolution of ultrafast dynamics study for gas samples [11,12]. In addition to the higher temporal resolution, MeV electrons can penetrate thicker samples and have much less dynamic scattering effects. Finally, the higher electron beam energ...

Watanabe et al. Reply: After carefully evaluating the preceding Comment by Bonafacio et al. [1] on our Letter [2], we concluded that those comments do not affect our experimental results, nor alter our analysis and the conclusions presented in our Letter. The following is the detailed response to the comments. In the following the detailed response to the comments are given in the order of remark (2), (3), and (1), followed by our conclusion.In our single-pass high-gain free-electron laser (FEL) amplifier experiments, the seed pulse is first amplified in the exponential gain regime where the pulse lengthens; after saturation of the exponential gain regime the FEL transitions into the superradiant regime. Superradiance in a FEL amplifier manifests itself in several ways in addition to the radiation power scaling as I 2 . In the superradiant regime the FEL amplifier pulse length shrinks, the spectral bandwidth increases, and the FEL pulse energy continues to grow (without the use of any undulator tapering) (Refs. [8, 11, 13, 18] of [2]). In our Letter the continuous growth of the FEL energy in the nonlinear regime (Fig. 2), the FEL pulse shortening by roughly 50% (Fig. 3), and the resulting spectral broadening (Fig. 3) were all observed and the results were consistent with the numerical simulations (Fig. 4). These simultaneous observations provide compelling proof of superradiance in our FEL amplifier experiments.The measurement of the power scaling as I 2 as suggested in remark (2) is very challenging for our experimental setup, as a change in the beam charge would affect the electron beam emittance, energy spread, bunch length, and the bunch current distribution, especially in the photoinjector and in the compressor. This means that the FEL saturated power and the distance where the FEL radiation evolves as a superradiant pulse are changed accordingly. For the above reasons, in our experimental conditions a simple scaling as P / I 2 is not expected. Note that measuring the FEL energy as a function of the undulator length has been widely used to characterize single-pass high-gain FELs [2 -5, 23].In [18] it is shown that after saturation the pulse propagates at a constant velocity approximately equal to c and scaling laws are derived in the variable z, defined as the bunch coordinate along the undulator. In response to remark (3) we show that it is straightforward to demonstrate under this assumption the equivalence with the scaling laws derived in Refs. [8, 12]. Here we indicate with (z l ; t l ) the time and position coordinates in the laboratory. In [18] the equations are expressed in a coordinate system (; z) moving at the constant velocity z c in the longitudinal direction.