Observation of the relativistic cross-phase modulation in a high intensity laser plasma interaction

1. Pulse Intensity For I1>>I2 , onepulse is modulated by another pulse (XPM) Blue Shift SPM XPM Time • For a linear polarized laser Nonlinear Schrödinger Equation Where is the normalized vector potential • Further simplification of n where XPM happens when two optical pulses copropagate in a nonlinear medium For two optical pulse with different frequency Raman generation, harmonic generation, pump probe. Asymmetric spectral broadening Normal Group velocity dispersion dn/d>0 Anomalous Group velocity dispersion dn/d>0 Nonlinear-index coefficient n2 in the relativistic plasma • Refractive Index of Plasma  is relativistic factor of the electron in a laser field where The second derivative in the coupled equation can be neglected Red shift Observation of the relativistic cross-phase modulation in a high intensity laser plasma interaction Raman spectrum broadens asymmetrically with increasing laser power Abstract and Acknowledgment Comparison shows qualitative agreement between analytical and experimental results 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1018 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. Analysis of Relativistic XPM 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 1.9×1018 Wcm-2 instead of 1.3 1018 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. Self phase modulation RXPM induced chirp with respect to the laser pulse intensity Self-focusing Experimental Setup Self-phase modulation Shouyuan Chen, Matt Rever, Ping Zhang, Wolfgang Theobald,Ned Saleh, Anatoly Maksimchuk, Donald Umstadter Department of Physics and Astronomy Lincoln, Nebraska, 68512, Frequency Chirp Ignore the transverse spatial variance of the laser pulse along Z direction Numerous applications of RXPM • 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 Self-phase modulation Comparison of the duration of the laser pulse before and after compression Analytical solution can be achieved for our particular experimental parameters Spectrum in the forward direction shows Raman satellite Generation of 15-TW single-cycle laser pulse Experimental parameters: Electron density 11018 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