Controllable three-dimensional helical energy backflow in optical focusing field

The energy of light generally moves forward along the light propagation direction. However, in recent years, a counter-intuitive effect has been discovered that energy backflow can occur in certain special light fields. Presently, controlling the energy backflow of light for application requirements is becoming a significant challenge. Here we propose a method to generate and control a three-dimensional helical energy backflow (HEB) optical field. By designing an exponential helical conical phase mask, the energy backflow region in a common tightly focused field can be stretched into a three-dimensional helical shape with an ultra-long longitudinal length. The length of the HEB region can be flexibly extended up to 47.6λ by varying the exponential phase index and the initial topological charge. Furthermore, we demonstrate that nanoparticles within the HEB field are subjected to optical pulling forces, thereby drawing the nanoparticles back to the light source. This work presents a new, to the best of our knowledge, approach for the three-dimensional manipulation of the energy backflow field with potential applications in nanoparticle manipulation and detection.