Phase-sensitive characterization of short scale-length plasmas

By irradiation of solid targets with intense femtosecond pulses it is possible to create microplasmas of very small gradient scale length. Useful information on the early evolution of these plasmas on a picosecond or even subpicosecond time scale can be obtained via optical detection. For instance, subpicosecond time-resolved Schlieren measurements can determine the location of the critical density layer. However diffraction effects limit the accuracy to a value of the order of the incident wavelength. From time-resolved measurements of the absolute reflectivity of a short probe pulse as a function of angle and polarisation one can extract information on the plasma density gradient. This method requires series of independent measurements and yields information on the expansion of the plasma only indirectly. A more direct method relies on the spectral analysis of the reflected probe beam at different delays. Expansion velocities can be then inferred from Doppler shifts. However, the large Fourier spectrum Δω ≈ 1/Δt of short pulses makes it difficult to estimate frequency shifts much less than Δω. Furthermore, this method is sensitive to the detrimental shot-to-shot frequency and spatial fluctuations of the lasers. We have implemented a method with greatly improved sensitivity. In the experiments, the moving plasma target is probed with two successive identical femtosecond probe pulses separated in time by an external Michelson interferometer. It is well known that the power spectrum of a double pulse sequence is modulated with a fringe period inversely proportional to the pulse separation. Any phase shift due the motion of the plasma critical layer occurring between the two pulses can be therefore detected directly in the reflected spectrum as a fringe displacement. The improvement of this method over single pulse spectrum analysis is manifold. First, the sharpness of fringes allows high precision measurements of small frequency shifts. Second, the inherent multiplexing of the information in all observed fringes for each laser shot further improves the signal to noise ratio. Finally, the method is largely insensitive to shot-to-shot frequency fluctuations. Indeed, besides phase shifts due to the signal, only phase fluctuations occurring inside the external interferometer during the time interval between both probe pulses affect the fringe position. We have tested our method in two different regimes. In the first regime, the plasma-inducing strong pump pulse lies between both probe pulses. This type regime is well adapted to the absolute measurement of the location of the reflective plasma layer at a given delay. In the second regime the pump pulse precedes both probe pulses. This regime yields with high accuracy the relative location of the critical layer at two different times and is therefore well suited for the precise measurement of the plasma axial expansion velocity. An example of both regimes, obtained in a hot dense laser-induced plasma formed in SiO₂ is shown in Figs. 1 and 2.