The diode-pumped Nd: Vanadate laser is one of the most widely used lasers in the near-infrared range. With the passive Q-switching technique, a compact and robust system can be obtained, capable of self-pulsing at the tens of kHz range with pulses of duration in the order of nanoseconds. For this reason, it is found in a wide variety of applications such as material micromachining, medicine, metrology, sensors, and spectroscopy. The saturable absorber (SA) is a Cr:YAG crystal. This laser is known for exhibiting low-dimensional deterministic chaos [1] and extreme events (EE) [2].

In this work, we present experimental evidence of the presence of a strange non-chaotic attractor (SNA)[3] with extreme events. SNAs exhibit complex dynamical behavior that is neither strictly periodic nor chaotic, making them difficult to detect in real-world systems. They are typically observed in systems modeled by equations.

By experimentally obtaining time series of two laser variables—pulse intensity and time between successive pulses—the underlying attractor is reconstructed. The control parameter is the energy density over the SA, which is modified by varying the position of the SA within the laser cavity. For a certain position of the SA, we found that all Lyapunov exponents are negative, indicating that the attractor is non-chaotic. Several methods for estimating the fractal dimension are presented, with the Higuchi dimension yielding the best results [4]. To our knowledge, this is the first report of the experimental observation of a strange non chaotic attractor.

[1]  Optics Letters    Vol. 30,  No 20, pg 3498 -3500 (2010)

“Chaos in the pulse spacing of passive Q – switched all- solid state lasers”

M.G. Kovalsky, A.A. Hnilo

[2] Physical  Review  A 92, 053816  (2015)

“Features of the extreme events observed in an all-solid-state laser with a saturable absorber”

Carlos R. Bonazzola, Alejandro A. Hnilo, Marcelo G. Kovalsky, and Jorge R. Tredicce

[3] PhysicaD 13 261 – 268 (1984)

Strange attractors that are non chaotic

C. Grebogi, E. Ott, S. Pelikan and J. Yorke

[4] Physica D, 31, 277-283 (1988)

Approach to an Irregular Time Series on the Basis of the Fractal Theory.

Higuchi, T.