Fig. 1. Schematic overview of the experimental setup. The pulse propagates from right to left. The distance along the capillary is and downstream the capillary is . Optical lenses have the following focal lengths: L, –10 cm; L, 40 cm; L, 150 cm; L, 100 cm; L, 60 cm.

Fig. 2. Examples of experimentally measured transverse pulse intensity distributions: left, at vacuum focus; center, at the capillary exit plane when the pulse propagated in the 40 cm long capillary #4; right, at the capillary exit plane when the pulse propagated in vacuum. Blue lines show the horizontal and vertical projections of the camera images. Red dotted lines show the results of Gaussian fits of the projections. The left and middle plots are on the same linear color scale; the color scale of the right plot is enhanced by a factor of 10.

Fig. 3. Reconstructed radial plasma electron density profile. (a) Measurements of the centroid position of the guided pulse at the capillary exit as a function of the parallel capillary offset with respect to the laser propagation axis (green markers). Error bars (standard deviation of the individual measurements) are not visible because they are smaller than the marker size. The blue line shows a linear fit to the data; it is solid over the measurement range and dashed outside (assuming the continuation of a parabolic channel outside the measurement range). (b) Calculated relative change of the radial plasma electron density (green markers) compared with one-dimensional NPINCH simulation results (gray line). The blue line corresponds to the result of the fit shown in panel (a).

Fig. 4. (a) Pulse centroid position variations , where is the measured pulse center and the average value of all measurements; (b) spot size deviations , where is the rms pulse size and the average value of all measurements. The figure shows the running average of 100 measurements (solid line) as well as their standard deviation (error-band) for capillary #1. Measurements for the incoming pulse at the capillary entrance are shown in blue and those for the guided pulse at the capillary exit in orange. (c) Correlation between and the timing jitter between the discharge and the probe pulse () for an initial neutral gas density of atoms/cm for capillary #2. The green dashed line shows the result of a linear fit.

Fig. 5. Reconstructed radial plasma electron density profile. (a) Measurements of the centroid position of the guided pulse at the capillary exit (green markers) as a function of the parallel capillary offset with respect to the laser propagation axis . Error bars (standard deviation of the individual measurements) are not visible as they are smaller than the marker size. The blue and red solid (within the measurement range) and dashed (outside the measurement range) lines show the calculated centroid oscillation scan result corresponding to the density profiles of the same color on the right. (b) Calculated relative change of the plasma electron density as a function of radial position for a parabolic channel (blue line), a channel with an component (red line) compared with the result from NPINCH simulations (gray line).

Fig. 6. Waterfall plot of the simulated pulse intensity evolution downstream the capillary exit . The red dashed line shows the rms spot size from Gaussian fits to the intensity distribution from the simulations for a parabolic channel using   (red). The green line shows the measured evolution of the rms size of the pulse after guiding. The blue line shows the pulse evolution downstream the vacuum focus.

Fig. 7. (a) Simulation result of the laser pulse intensity evolution along the capillary #3 in a plasma telescope configuration, using the channel profile according to Figure 5 as input. (b) Simulated pulse intensity evolution downstream the capillary exit . Orange markers show the second moment of the pulse obtained from experimental measurements. The gray vertical dashed line indicates the location of the measured intensity distributions shown in (c)–(f). (c) The experimentally measured intensity profile, (d) the corresponding simulation result when using the Gerchberg–Sexton algorithm to reconstruct the input pulse modes, (e) when using a perfect Gaussian pulse as simulation input, and (f) when using a Gaussian pulse that was matched to the channel with   .