Research Shorter, Intenser, Faster!
The most intense laser pulses, of multi-terawatt and even petawatt power, are produced nowadays using the chirped-pulse-amplification (CPA) technique. The high power is achieved due to the very short pulse duration.However, for technology reasons, the lower limit for the pulse duration is located somewhere around 30 fs, when the CPA is employed and laser pulses of at least terawatt power have to be produced. The physical reason for this limitation is the finite bandwidth of the active medium amplifiers used in the lasers. The newly proposed OP-CPA (optical parametric chirped pulse amplification), where broadband nonlinear crystals are used for parametric amplification, may result in even shorter powerful laser pulses. Presently, however, the generation of sub-10 fs laser pulses is based on the self-phase modulation of a laser pulse propagating through a gaseous medium with a Kerr-like nonlinearity. This technology allows to produce routinely sub-10 fs pulses of sub-terawatt level.
Recently, several concepts have been suggested for pulse compression in plasma. We mention here super-radiant amplification of colliding laser pulses due to Compton scattering [G. Shvets, N. J. Fisch, A. Pukhov and J. Meyer-ter-Vehn Superradiant Amplification of an Ultrashort Laser Pulse in a Plasma by a Counterpropagating Pump Phys. Rev. Lett.81, 004879 (1998)] , Raman scattering and pulse reflection from a counter-propagating nonlinear plasma wave. The most important advantage of plasma as an ``active'' medium for pulse compression is that it sustains extremely high intensities.The nonlinearities become significant only close to the relativistic threshold and thus high powers can be achieved. All the mentioned schemes require at least two counter-propagating laser pulses, which must intersect in space and time. This fact makes the practical realization of these schemes difficult.
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In the work [Shorokhov O, Pukhov A, Kostyukov Self-compression of laser pulses in plasma PHYSICAL REVIEW LETTERS 91, 265002, (2003)] we have shown that a weakly relativistic laser pulse can be successfully self-compressed in slightly underdense plasma. The laser pulse dynamics in underdense plasma can be approximated by the non-linear Schroedinger equation, whose properties are well-known. It has a self-similar solution in the solitonic form. The soliton runs through the plasma with nearly light velocity maintaining its shape. The plasma dispersion is compensated by the relativistic non-linearity. It is also well-known in the soliton theory, that if one starts with a pulse slightly different from the soliton shape (e.g., with a wider pulse), then the pulse width oscillates around the equilibrium value. This effect can be exploited to compress an initially wide laser pulse to a shorter one.
Another way of pulse compression is the self-shortening in the Bubble regime [A. Pukhov and J. Meyer-ter-Vehn, Laser wake field acceleration: The highly non-linear broken-wave regime, Appl. Phys. B 74, 355 (2002)] ].
In our 3D PIC simulations, we have observed as the laser intensity, initially 10 cycles long, underwent self-modulation and developed a steep front with a peak intensity much larger than the incident one. This is due to group velocity dispersion, causing high-intensity parts to travel faster and to form an optical shock. It compresses electrons in front of it into a layer with 20 times the unperturbed plasma density. Between this layer and the stem electrons, there is a void. The longitudinal electric field, jumps sharply at the compressed cavity front and then falls smoothly inside the cavity. The relativistic stem is also highly compressed, up to 18 times the background density. Yet, the corresponding space charge causes no jump in the longitudinal electric field Ez. This is due to the relativistic reduction of Ez for fast moving charges. The transverse field, however, is large and only partially compensated by the pinching effect
of the magnetic field of the stem. This radial E-field delays background electrons to flow in radially and to close the cavity. Apparently, beam loading of the cavity occurs by radial inflow of electrons. In the present 3D simulation, the beam loading is transverse.
In the experiment done by the experimental group of Dr. Victor Malka at LOA, Palaiseau, France, the temporal shortening of an ultraintense laser pulse was measured after its interaction with underdense plasma. When interacting with strongly nonlinear plasma waves, the laser pulse is shortened from 38 2 fs to the 10–14 fs level, with a 20% energy efficiency. The laser ponderomotive force excites a wakefield, which, along with relativistic self-phase modulation, broadens the laser spectrum and subsequently compresses the pulse. This mechanism is confirmed by 3D particle in cell simulations.
See [ J. Faure, Y. Glinec, J. J. Santos, F. Ewald, J.-P. Rousseau, S. Kiselev, A. Pukhov, T. Hosokai, and V. Malka Observation of Laser-Pulse Shortening in Nonlinear Plasma Waves Phys. Rev. Lett. 95, 205003 (2005) ]
Raman amplification in plasma has been suggested as a method to allow the creation of ultra-short, ultra-intense laser pulses \cite{raman-shvets-compton}, which could be used either instead of, or in conjunction with, CPA. Plasma has no damage threshold in the conventional sense, removing the limitation of peak fluence in the amplifying medium. Various instabilities, such as self-modulation, may compete with the Raman amplification process, but these are only expected to become significant at intensities above 1017 W/cm2 , a factor of 108 higher than that which may be achieved in conventional amplifying media.
The Raman process is a three-wave interaction, in which two laser pulses of different frequencies are coupled by an excited Langmuir wave, allowing energy to be transferred from a pump pulse to a lower frequency probe pulse. A counter-propagating geometry allows a short probe to interact with a long pump, allowing significant amplification. The process may readily be understood by considering the two laser pulses giving rise to a beat wave, which drives a plasma wave through the ponderomotive force; the resulting density perturbation acts as a moving Bragg grating, scattering the pump pulse into the probe, amplifying the latter.
In linear regimes, the amplification bandwidth is small, due to the narrow resonance of the plasma wave, giving rise to gain narrowing. However, several regimes exist in which superradiant amplification may be attained, in which the probe amplitude increases linearly with propagation distance, while its duration scales inversely with propagation distance. The most important of these regimes are the Compton regime and the pump depletion regime. In the Compton regime, named after the analogous regime in free electron lasers, the intensities of the laser pulses are sufficiently high that the electrostatic force of the plasma wave becomes negligible, allowing broad bandwidth amplification. In the pump depletion regime, sufficient energy is transferred from pump to probe that amplification to the rear of the probe is suppressed, leading to the compression.
Numerical simulations of Raman amplification in plasmas require appropriate numerical methods. The simulation must be three dimensional as the major problem in the plasma-based amplification schemes is the relativistic self-pinching of laser pulses. The conventional particle-in-cell methods although might provide insight into the process, are hardly appropriate as they have intrinsically high noise level. This vastly overestimates the plasma pre-heating by the pump pulse. We plan developing a reduced particle-in-cell model that can efficiently simulate laser pulse amplification based on stimulated scattering.