Spatial representation of Lissajous trajectories by an optical method

Acousto-optic deflectors (AODs) do not contain moving parts and therefore they are free of drawbacks associated with mechanical deflectors and exhibit tunable trajectories and velocities. We have hitherto demonstrated that two of them, orthogonally placed, permit the steering of a laser beam according to linear trajectories with sinusoidal velocities, circular trajectories with constant velocities and elliptical trajectories with variable velocities. In this paper, we propose another study displays other trajectories, more complex than the previous ones, known as Lissajous trajectories. This technique is based on tracking the maximum intensity position of a diffracted spot. The obtained results show that the laser beam can be steered according to Lissajous trajectories when the two modulation frequencies, \(\nu_{X}\) ${\nu }_X$ and \(\nu_{Y}\) ${\nu }_Y$ , are desynchronized. The simplest trajectory of them, called Besace, is obtained when one of the modulation frequencies is double the second. Under certain conditions, such a trajectory can transform into a parabola or even a Gerono Lemniscate. The convexity and shape of these last trajectories can be controlled by acting on frequency amplitudes \(\Delta f_{X}\) $\mathrm{\Delta }{f}_X$ and \(\Delta f_{Y}\) $\mathrm{\Delta }{f}_Y$ . In addition, the synchronization between the two modulation frequencies makes it possible to steer the laser beam according to linear, circular and elliptical trajectories. This new optical technique makes it possible to spatially represent all Lissajous curves rather than using an electronic method (the oscilloscope).