## 4 Results and Discussion  
By adaptively programming phase maps via calibrated gray value maps of symmetric and non-symmetric axicons into the LCoS-SLM, corresponding types of linear light bullets were generated  
Figure 4: Experimental setup for adaptive shaping and detection of paraxial linear few-cycle light bullets (schematically). For collinear autocorrelation, a balanced interferometer generates two identical replica of the pulse. The variable time delay (\(\Delta\tau\)) is induced by the length variation (\(\Delta\)z) of the interferometer arm with a piezo actuator. The SLM shapes the light bullets in finite but extended zones of stable nondiffracting propagation. The combination with second order nonlinear conversion and 2D detection enables to extract spatially resolved pulse duration via image autocorrelation, as well as wavefront curvature, vortex characterization, and highly resolved time delay mapping. and their spatio-temporal features were analyzed. The solitary or multiple light bullets are of radially symmetric and non-symmetric structure belong to the classes of above discussed pulsed needle beams and highly localized wavepackets (HLWs). Figure 5 shows the gray value distributions corresponding to the phase maps of the axicons (left) and the resulting, measured time-integrated intensity maps (right) of a set of simultaneously formed light bullets of different spatial structures (here: disks, rings, lines and stadiums). All of these light bullets have two important properties in common which are the main benchmarks of HLWs: (1) They are non-oscillating in space (_i.e._, they have no side wings), and (2) they preserve the temporal properties during the nondiffracting propagation. The propagation invariance can be well recognized for a stadium-shaped 6-fs light bullet (smaller and larger diameter: 700 \(\upmu\)m and 1500 \(\upmu\)m, respectively) in Figure 6. From an axial distance of 80 mm  
Figure 5: Flexible generation of few-cycle light bullets with the characteristics of spatially oscillation-free, temporally nondiffracting highly localized wavepackets (HLWs): **(a)** gray value distributions corresponding to the phase maps of axicons; **(b)** measured time-integrated intensity maps of a set of simultaneously formed light bullets of different spatial structures in a transversal plane (disks, lines, rings and stadiums). Both the new types of shaping phase elements and the HLWs represent generalizations of the conventional approaches of axicons and nondiffracting beams, respectively. Arrays of programmable HLWs enable to realize time-wavefront sensors with spatially encoded spots and flexible array geometries. Figure 6: Nondiffracting intensity propagation of a stadium-shaped light bullet (time integrated, field of view 2.7 \(\times\) 2.7 mm\({}^{2}\), detected after SHG at 400 nm, initial pulse duration 6.5 fs). to 130 mm, only a slight enhancement of the local cross-section of the light ring is observed. The basic geometrical structure, however, propagates unchanged and the outer dimensions are stable. In Figure 7, the spatially resolved second order autocorrelation function measured by imaging autocorrelation is shown for two planar cuts through the long and short axes of the stadium-shaped bullet. The maxima clearly indicate the few-cycle field oscillation in time. The autocorrelation at three different propagation distances (80 mm, 100 mm and 120 mm) is compared in Figure 8.  
The FWHM width of the autocorrelation function was found to be about 10.1 fs. Assuming a sech\({}^{2}\)-pulse shape, the corresponding final pulse duration is 6.6 fs at an input pulse duration of 6.5 fs. Thus, the results indicate a very stable propagation behavior also in temporal domain within the fluctuations (the estimated error bar was about 0.1 fs).