4. ANÁLISIS DE RESULTADOS
4.2. Encuesta aplicada a los empleados de la COAC “PACÍFICO” Ltda
Based on a simplified description of the high harmonic dipole response, our numerical simulation can qualitatively reproduce several important features of the experimental data. At the same time, it is interesting to compare our experimental and simulation re- sults to a more advanced numerical simulation, which may also allow a more quantitative understanding of NCHHG.
We thus started a collaboration with Carlos Hern´andez-Garc´ıa from the group of Luis Plaja at the University of Salamanca who adapted his numerical code to simulate non-collinear HHG in Xe. Details of the numerical approach are described in reference [258]. In brief, the single atom response is calculated using an extended version of the commonly used strong field approximation (see Section 3.2.3) that has been termed SFA+ [203]. The far field emission pattern is then obtained within the so-called discrete dipole approximation, i.e. the target volume is discretized into cells of macroscopic size that are subsequently treated as point-like dipoles for which analytical solutions of Maxwell’s equations exist.
On the following pages, first results of ongoing systematic investigations of NCHHG for varying parameters are shown to exemplify general dependences. Unless stated oth- erwise, all results have been obtained for two Gaussian driving beams and sin2 pulse envelopes7 with a FWHM duration of 16 fs. The beams are non-collinearly focused at an angle ofθ = 30 mrad to a common focus ofw0 = 60 nm in a Xe target with a Gaussian gas distribution (Lmed = 140µm). The single beam peak intensity is 2.2×1013W/cm2, and both ionization and neutral dispersion are taken into account. Compared to the experiment, shorter pulses and lower intensities were used for our first investigations to reduce computational time and to avoid potential inaccuracies due to the implemented ionization model (ADK) near the barrier suppression regime of Xe (cf. Section 3.2.1), respectively.
7Using a pulse envelope of this form is computationally easier than both Gaussian and hyberbolic
(a) 15th (b) 17th (c) 19th
Figure 4.22: Simulated far field profiles for the (a) 15th, (b) 17th, and (c) 19th harmonic order for different single beam driving intensities of, from top to bottom, 2.2×1013W/cm2,
3.2×1013W/cm2, and 4.3×1013W/cm2 at a phase delay of ∆φ = 0. Note that individual color scales corresponding to the respective intensities in atomic units are used in each plot.
4.7.1 Dependence on driving intensity
Figure 4.22 shows the simulated far field profiles of the strongest harmonic orders ob- served in our experiment (15th, 17th, and 19th) for a phase delay of ∆φ = 0 and three different (single beam) driving intensities, namely 2.2×1013W/cm2, 3.2×1013W/cm2, and 4.3×1013W/cm2.
In agreement with our experimental results, the profiles of the 15th and 17th harmonic orders show two groups of fringes at each of the simulated intensities. However, the relative strengths of the fringes are seen to change with intensity so that it is no longer unambiguous to use the differentiation into “primary” and “secondary” fringes. This is particularly obvious for the 19th harmonic, where on-axis emission and only one group of fringes are observed at the lowest intensity. In contrast, a second group of fringes appears quite prominently at the two other intensities and only weak and spectrally shifted on-axis emission can be observed. A similar spectral offset was also visible in our experiments (cf. Figure 4.13). As a first conclusion, we note that the non-collinear emission profile is very sensitive to the intensity of the driving beams.
(a)15th (b) 17th (c) 19th
Figure 4.23: Simulated far field profiles at a phase delay of∆φ= 0for (a) 15th, (b) 17th, and (c) 19th harmonic order for different waists of, from top to bottom,55µm,60µm,65µm, and
70µm. Note that individual color scales corresponding to the respective intensities in atomic units are used in each plot.
4.7.2 Dependence on waist
Figure 4.23 shows the simulated far field profiles of the 15th, 17th, and 19th harmonic for a phase delay of ∆φ= 0 and four different waists, from top to bottom, 55µm, 60µm, 65µm, and 70µm.
The simulation results indicate that the size of the waist is a crucial parameter for the observation of high harmonic emission along the bisector of the driving beams. While strong on-axis emission is present at the smallest waist for the 17th and the 19th harmonic, the on-axis contribution continuously decreases with increasing waist. The 15th harmonic profile does not vary strongly for the simulated waists and does only show very weak emission along the bisectrix.
As a conclusion, we note that the simulated profiles are extremely sensitive to com- parably small variations of the driving beam waist. The latter should thus be precisely measured and controlled in an experiment.
Figure 4.24: Simulated non-collinear spectrum for a phase delay of ∆φ= 0. The logarithmic color scale represents the intensity in atomic units.
4.7.3 Non-collinear spectrum
Figure 4.24 shows the simulated non-collinear spectrum for a phase delay of ∆φ = 0. In agreement with the measured spectrum shown in Figure 4.10, different harmonic orders exhibit a different fringe spacing so that the spectral content of the observed high harmonic radiation varies with the angle of emission. Since the divergence of the harmonic radiation decreases with order, the highest orders can only be detected close to the bisector of the driving beams. These aspects are further exemplified inFigure 4.25, which compares the emission angles 0 mrad and 1 mrad with regard to their spectral content, the corresponding temporal domain description (i.e. the generated attosecond pulse trains), and a time-frequency (wavelet) analysis.
(a)
(b)
Figure 4.25: Spectrum (top panel), corresponding temporal domain description (center panel), and time-frequency analysis (bottom panel) for emission angles of (a)0 mrad and (b)1 mrad. All data shown in atomic units. Compare Figure 4.24.