1. Observation of the relativistic cross-phase modulation in a high intensity laser plasma interaction Shouyuan Chen, Matt Rever, Ping Zhang, Wolfgang Theobald, Ned Saleh, Anatoly Maksimchuk, Donald Umstadter Department of Physics and Astronomy Lincoln, Nebraska, 68512, Experimental Setup Spectrum in the forward direction shows Raman satellite Raman spectrum broadens asymmetrically with increasing laser power Comparison of the laser spectrum before and after RXPM A novel nonlinear optical phenomenon, relativistic cross- phase modulation, is reported. A relativistically intense light beam (I = 1.3  10 18 Wcm -2, =1.05  m) is experimentally observed to cause phase modulation of a lower intensity, copropagating light beam in a plasma. The latter beam is generated when the former undergoes the stimulated Raman forward scattering instability. The bandwidth of a Raman satellite is found to be broadened from 3.8 nm to 100 nm when the pump laser power is increased from 0.45 TW to 2.4 TW. A signature of relativistic cross-phase modulation, namely, asymmetric spectral broadening of the Raman signal, is observed at a pump power of 2.4 TW. The experimental cross-phase modulated spectra compared well with theoretical calculations. Applications to high-power attosecond duration light-pulse generation are also discussed. This work was supported by the Chemical Sciences, Geosciences, and Biosciences Divisions of the Office of Science, U.S. Department of Energy and the National Science Foundation. Abstract and Acknowledgment Self-phase modulation Frequency Chirp Self-phase modulation Red shift Pulse Intensity Time Blue Shift Self phase modulation XPM happens when two optical pulses copropagate in a nonlinear medium Normal Group velocity dispersion dn/d  >0 Asymmetric spectral broadening Anomalous Group velocity dispersion dn/d  >0 For two optical pulse with different frequency For I 1 >>I 2, one pulse is modulated by another pulse (XPM) SPMXPM Raman generation, harmonic generation, pump probe. Refractive Index of Plasma where  is relativistic factor of the electron in a laser field For a linear polarized laser Where is the normalized vector potential Further simplification of n where Nonlinear-index coefficient n 2 in the relativistic plasma Analysis of Relativistic XPM Ignore the transverse spatial variance of the laser pulse along Z direction Nonlinear Schrödinger Equation Self-focusing The second derivative in the coupled equation can be neglected Analytical solution can be achieved for our particular experimental parameters Comparison shows qualitative agreement between analytical and experimental results FIG. 3: The comparison of experimental data (top) and analysis results (bottom) shows good agreement. (a) The RXPM Raman spectrum at 2.0 TW. The propagation distance is 400  m as measured from the top view image. (b) The RXPM Raman spectrum at 2.4 TW. The laser intensity used in the analysis is 1.9× 10 18 Wcm -2 instead of 1.3  10 18 Wcm -2 from the calculation. The propagation distance is 1000  m. The relatively higher intensity required in the analysis is due to the effect of self-focusing, which increased the laser intensity. The pedestal in the experimental data is due to the strong coupling, which is not included in the model. Pulse compression Generation of high power, single cycle laser pulses Advantages of this method: Variable pulse energy Uniform modulation (probe pulse diameter can be smaller than pump beam) Plasma diagnostics laser intensity laser pulse duration plasma density delay time between pump and probe pulse Numerous applications of RXPM Generation of 15-TW single-cycle laser pulse Experimental parameters: Electron density 1  10 18 cm -3 Pump pulse 20 TW 100 fs 2J 800 nm Probe pulse 2 TW 30 fs 60 mJ 650 nm Interaction distance 5 cm Initial delay 5 fs RXPM induced chirp with respect to the laser pulse intensity Comparison of the duration of the laser pulse before and after compression