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J. Eur. Opt. Society-Rapid Publ. 21, 14( 2025)
Fig. 3. The first line shows the oscillograms, the second line presents the corresponding Poincaré maps of the peak intensities of Q-switched pulses I n + 1 = f( I n), and the third line presents histograms used for calculating the peak entropy( embedded dimension m = 4 and 5). Tree different operation regimes are presented: 1st column( a) corresponds to a stable Q-switched regime, 2nd column:( b) corresponds to an intermittency regime, 3th column( c) corresponds to a chaotic regime.
First, the part of the theoretical curve outside the map is contracted over the x-axis and stretched over the y-axis. The contracting and stretching coefficients are difficult to calculate and we obtained estimations from the experimental data.
Second, the obtained modified curve is then folded under the bisector line. The expected peak power is then under the bisector line which explains the characteristic“ drop” of the intermittence.
Figure 4b, shows the experiment points and the theoretical points for two consecutive laminar phases. To consider theoretically the intermittency, a baker transformation has to be introduced. We consider that, if the normalized I n + 1 is above 1, then the intermittency occurs and the next point is found using the baker transformation on the folded and stretched part of the fitting curve. Since the normalization is not obvious, one must consider the experimental data. One important point to consider here concerns the start and the end of the laminar phase to appropriately evaluate, first, its length and second, concerning the baker’ s transformation, to also have a good estimation of when to cut the fitting curve before the stretching and the folding of the dough. In our case, since the intermittency occurs quickly after the minimum distance, the baker’ s transformation involves a large stretching of the dough in the vertical direction [ 21 ] before being folded under the bisector line. The contraction ratio([ 20 ], p, 254) is around b = 0.03which implies a folding of the“ fitting curve” almost linear and quasi vertical. In Figure 4b, we found a good accuracy for a very strong asymmetric stretching of the dough considering the first points of the intermittencies.
Observing the Poincaré maps, one can notice that the density of points is more important when the laminar phase