No abstract

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.

No abstract

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.

No abstract