Designing a self-accelerating beam by Wigner transform

Abstract

Based on the Wigner transform, a method for designing a self-accelerating beam is proposed. As an example, a beam traveling along an arbitrary path has been studied by modulating the phase of an optical field. Meanwhile, the effect of the amplitude modulation of Gaussian distribution on the beam propagation is analyzed. One can see that the phase mask obtained with our method is the same as existing results. Furthermore, an analytical expression for the intensity evolution with the identity phase and the Gaussian window has been derived. From the analytical expression, it can be found that the waist width of the Gaussian beam is a tunable factor to modulate the beam size during propagating along the expected trajectory. Using the derived analytical expression, the intensity distribution along the expected trajectory can be optimized.

Keywords

• Self-accelerating beam
• Wigner transform
• Phase modulation