High Harmonics Generation
Generation of high-order harmonics from solids
In contrast to the attosecond sources from gas targets based on rescattering physics, Ultra-high intensity (>1018 W/cm2) relativistic laser interactions with solid targets have the potential of generating significantly brighter, higher energy x-rays with sub-attosecond (zeptosecond) duration. This approach could be the enabling technology needed to dramatically change the scope of attosecond applications beyond current capabilities.
As an ultra-intense laser pulse interacts with a plasma having a density scale-length less than the laser wavelength, high harmonics are generated. Under these conditions the laser's electric field can efficiently couple to the critical density surface causing the electrons to oscillate in phase, effectively constituting a relativistic oscillating mirror. As shown in the Figure below, the position of this mirror surface is a temporal function of the incident optical laser cycle, thus the phase of the reflected light wave is modulated such that it is no longer purely sinusoidal.
The two main driving terms are the electric field of the laser (at the laser frequency) and the ponderomotive force or light pressure (at twice the laser frequency), leading to the production of both odd- and even-order harmonics. The coherent oscillation of the plasma surface results in a well defined reflection plane that locks the phase of the entire harmonic spectrum and theoretically should produce a train of attosecond/zeptosecond x-ray pulses in a small reflected cone Furthermore, the large nonlinearity allows efficient coupling into the harmonic comb. Our recent experiments have demonstrated harmonic emission extending into the x-ray region with the largest conversion efficiencies (approaching 10-2) reported to date. The complementary characteristics of our high intensity, ultra-fast laser sources (Hercules and λ3) provide an unprecedented ability for exploring both x-ray and attosecond generation using this technique.
Figure: Very intense lasers (i.e. > 1018 Wµm2cm-2) make the critical surface oscillate as a "moving mirror". The reflected light no longer has a sinusoidal waveform and consequently contains harmonics
In recent experiments we have measured the production of sub-nanometer, x-ray harmonic radiation (extending to 3.3 Å [3.8 keV]) from a high energy (> 200 J) Petawatt class laser-solid (CH-film) interaction (see Figure). This corresponds to the most extreme non-linear optical process observed in the laboratory to date (harmonic order n > 3200). The coherent nature of the generated harmonics was verified by the highly directional beam emission, which for photon energy hν > 1 keV was emitted into a cone angle < 4°, significantly less than that of the incident laser cone (20°). Such observations are only possible using a very high contrast laser pulse which is already available using HERCULES configured to operate with a double "plasma mirror". The harmonic yield in these previous experiments was measured to have an n-(2.5−3) power law decay up to the 2500th-order, indicative of harmonic emission in the relativistic limit. Such measurements imply that the potential exists for producing attosecond pulses with conversion efficiencies as high as ~10-2 (hν > 20eV) and ~10-5 (hν > 1 keV). Contrasting this with the best efficiencies reported for an optimized gas harmonic source of ~10-4 (hν > 20eV) and ~10-7 (hν > 100 eV), clearly indicates that the realization of such intense attosecond sources could revolutionize the breadth of attosecond science and potentially provide the extreme intensities needed to probe nonlinear QED.
Figure: Relativistic high harmonic spectrum. The harmonic orders beyond 1000 are so closely spaced than the emission appears continuous.
We have also made measurements of ultra-high magnetic fields produced during intense laser interaction experiments with solids. We have shown that polarization measurements of high-order VUV laser harmonics generated during the interaction (up to the 25th order) suggest the existence of magnetic field strengths of 0.7 GGauss in the overdense plasma. This technique may be useful for laboratory studies of exotic highly magnetized astrophysical objects such as neutron stars.
Figure: High order laser harmonic data. The harmonics range from 7th to 25th order (right to left). By comparing the top set of harmonics (s-polarized) to the bottom set (p-polarized) the magnetic field in the plasma can be determined.
