Generation of an Optical Spatial Array Oscillating According to Tunable Trajectories and Velocities

Beside the numerous applications obtained by the interaction of a laser beam with acoustic waves, another application have recently emerged that allows generating an optical dynamic spatial array (ODSA) using two orthogonal acoustic waves. In this paper, we demonstrate theoretically and illustrate numerically the possibility of generating an ODSA composed of many diffracted orders. The obtained results show that each diffracted order navigates in space according to its own trajectory and its own velocity. These trajectories are sometimes linear with sinusoidal velocities, sometimes circular with constant velocities and often elliptical with variable velocities. Moreover, the high diffracted orders of this ODSA, which are characterized by a high velocity and a large scanned area, can be controlled by varying the Raman–Nath parameter. The outstanding point is that all these diffracted orders navigate in space with the same sweep frequency despite the diversity of trajectories and velocities. The borrowing of Poincaré and Bloch spheres allows enumerating all these trajectories and presenting them in an elegant and attractive method. This technique can be used in metrology for rotation measurements based on Doppler effect. In addition, we can used it to develop a spatial display allows tracing Lissajous trajectories rather than using an oscilloscope.