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In this paper, the emergence of multistable behavior through the use of fractional-order-derivatives in a Piece-Wise Linear (PWL) multi-scroll generator is presented. Using the integration-order as a bifurcation parameter, the stability in the system is modified in such a form that produces a basin of attraction segmentation, creating many stable states as scrolls are generated in the integer-order system. The results here presented reproduce the same phenomenon reported in systems with integer-order derivatives, where the multistable regimen is obtained through a parameter variation. The multistable behavior reported is also validated through electronic simulation. The presented results are not only applicable in engineering fields, but they also enrich the analysis and the understanding of the implications of using fractional integration orders, boosting the development of further and better studies.

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Powerful visible luminescence in a Gadolinium Gallium Garnet (GGG) crystal, co-activated with Yb3+ (~15 at.%) and Ho3+ (~0.1 at.%) ions, is investigated under CW laser diode pumping (lambda = 938 and 976 nm). The main visible emission band is observed in the green with its peak at lambda ~540 nm) and measured to be about 10% with respect to Yb3+ IR luminescence (lambda ~1000 nm). Red (lambda ~650 nm) and near-IR (lambda ~755 nm) emission bands are also observed but are weaker (about 3-5%). Analysis of the crystal absorption and luminescence spectra allows one to conclude that Yb3+ - Ho3+ stepwise up-conversion is the mechanism explaining the phenomenon. Ho3+ ions embedded in the crystal in small concentration are shown to form an effective reservoir for energy transferred from the excited Yb3+ subsystem and to be an efficient source of the visible emission.

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We demonstrate the cnoidal wave formation in a two-laser system with a saturable absorber in the cavity of one of the lasers. Another laser is used to activate the saturable absorber in order to control the pulse shape, width, intensity and frequency. Using the three-level laser model based on the Statz--De Mars equations, we show that for any value of the saturable absorber parameter there exists a certain modulation frequency for which the pulse shape is very close to a soliton shape with less than 5% error at the pulse base. Such a device may be prominent for optical communication and laser engineering applications.