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100 GW [4]. It is important to note that this has been achieved without any dispersion compensation or pressure gradients. However, Skupin et al.’s theoretical analysis has revealed that this compression scheme is only optimum up to about five times the critical power [7].
Alternatively, a Japanese research group has used an argon-filled hollow fiber with a pressure gradient to produce sub- pulses with an energy as high as 5 mJ [8]. Moreover, Nurhuda et al. have proposed a highly efficient compression scheme (conversion ratio: 88%) using , pulses in a helium-filled ( 1 Torr) multi-pass cell (length: 6 m, mirror radii: each 3.1 m) [9].
In 2006, Painter et al. have measured the spatial evolution of a , pulse in a helium-filled ( 80 Torr) gas cell [10]. The authors concluded the “direct observation of laser filamentation in high-order harmonic generation”. However, the input power of 160 GW was well below the critical power 2.4 TW for a helium pressure of inferred from the literature value of the nonlinear refractive index [11]. Thus, it has been suggested that the Kerr nonlinearity of helium should be re-examined. However, later it has been conceded by the same authors that their results could also be interpreted using the above value [12] and [13].
Therefore, it is important to carry out a direct measurement of the critical power of helium. In this work, we have experimentally measured the critical power of helium using the moving focus method [14]. Also, the critical power has been obtained from the electron densities, based on the intensity clamping process, which have been measured as a function of energy and pressure.
2. Experiment
The experiments were performed using 42 fs pulses (repetition rate: 10 Hz) with a center wavelength of about 800 nm. The pulses were focused ( ) into a gas chamber filled with pure helium gas whose pressure could be varied from 50 Torr to 1 atm. The energy could be varied in the range of 1–63 mJ. The pulses created a plasma filament inside the chamber. The fluorescence was collected from the side by imaging the length of the filament onto the entrance slit of a spectrometer (Acton Research Corp., Spectra Pro-500i). The images of the filament were recorded in the spectrometer’s imaging mode (accumulations: 20) by using the zero-order grating reflection with the slit widely opened. The presence of a single filament was verified. The spectra were taken with the 1200 grooves/mm grating. The spectral resolution of this grating was about 0.4 nm (slit width: 100 μm) [15]. The dispersed fluorescence was detected with a gated intensified CCD (ICCD, Princeton Instruments Pi-Max 512). The ICCD gate width was set to 20 ns. The detection window was opened with zero delay after the laser-plasma interaction. The instrumental response was calibrated in the range of 250–800 nm using a tungsten lamp.
3. Results and discussion毕业论文
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http://www.youerw.com/Fig. 1 shows a log-linear plot of the peak position of the fluorescence signal as a function of energy in the range of 3–45 mJ. The pressure was fixed at 1 atm. The peak positions were retrieved from Gaussian fittings of the on-axis fluorescence distributions versus distance in units of ICCD chip pixels [14]. Note that smaller pixel values correspond to distances closer to the focussing lens. It can be seen in Fig. 1 that the peak position moves closer towards the focussing lens as the energy is increased. This behaviour has been explained before [14] as a consequence of the power dependence of the self-focussing distance above the critical power [16].
Fig. 1. Critical power of helium. The peak position of the fluorescence signal is plotted versus energy in a log-linear scale. The vertical axis is in units of ICCD chip pixels. Smaller pixel values correspond to distances closer to the focussing lens. The pressure is fixed at 1 atm. The critical energy is determined from the crossing point of two linear fits (red lines) through the data (black squares). The value of 11.25 mJ corresponds to a critical power of (pulse duration: 42 fs).
The plasma effect that shifts the center of gravity of the plasma in the linear focal region is known in long pulse laser-induced breakdown (see, e.g. [17]). This latter shift is due to the high density plasma created in the linear focal region that partially blocks the transmission of the laser pulse through the plasma. This is true in both the long pulse regime where the plasma is generated principally through collisional ionization and the short pulse regime (current case) where the plasma is due to pure tunnel ionization. Note that the plasma density in this case is very high, more than (see below).
The critical energy is determined from the crossing point of two linear fits (Fig. 1, red lines1) through the data (Fig. 1, black squares) [14]. The value of 11.25 mJ (Fig. 1) corresponds to a critical power of (1 atm) 268 GW (pulse duration: 42 fs). The relative errors in the measured energy ( 18%) and pulse
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