The uncertainty in the number and position of laser filaments, caused by random noise and competition between filamentation and surrounding energy, severely limits their practical applications. Generating filaments with a regular distribution and a controllable number is therefore crucial for both fundamental research and technological advancements. Recent studies on femtosecond vortex beams have focused primarily on filamentation using conventional focusing lenses. However, tilting the lens can significantly influence filamentation behavior. Previous research has shown that adjusting the lens’s tilt angle allows precise control over the number, distribution, and spatial stability of femtosecond Gaussian laser filaments, effectively managing and suppressing multiple filaments. Moreover, tilted lenses are commonly used to determine a vortex beam’s topological charge, as the beam evolves into a stripe-shaped pattern characterized by alternating bright and dark fringes, with the topological charge calculated as the number of bright spots minus one. In this paper, we explore the filamentation and control of femtosecond vortex beams in fused silica using a tilted lens.

Initially, vortex beams with varying topological charges are focused on fused silica using a stationary lens to generate filaments. An imaging lens is used to capture the filament distribution at different propagation distances in fused silica, recorded by a digital camera. The vortex waveplate is replaced to incrementally increase the topological charge of the incident laser beam from 4 to 6 and 8, with corresponding increases in laser power due to higher self-focusing critical power. Linear propagation in air is then studied by removing the fused silica and varying the tilt angles of the focusing lens to examine the intensity distributions at different propagation distances. Subsequently, filamentation is analyzed for vortex beams in fused silica under tilted lens conditions. Finally, vortex beams with different topological charges are focused into fused silica through a tilted lens at a fixed tilt angle of 20° to evaluate the effect of topological charge on filamentation.

Without tilting the lens, vortex beams with varying topological charges form regular ring-shaped filament arrays in fused silica. As the topological charge increases, the filament count and ring radius also increase. Along the propagation direction, re-focusing occurs, with multiple millimeter-scale filaments forming periodically within a centimeter-scale envelope. By incrementally increasing the tilt angle of the lens from 0° in steps of 3°, and selecting typical angles of 17°, 20°, and 23°, the laser beam distribution evolves significantly. At 17°, the filaments exhibit an elliptical ring-shaped pattern with uneven intensity. As propagation continues, the distribution transitions to an elliptical form, with enhanced intensity at the long-axis ends, resulting in stripe-like patterns. At larger tilt angles, these evolve into rectangular filament distributions. Under filamentation conditions, regular filament arrays form at the positions corresponding to intensity fringes observed during linear propagation. This method resembles interference fringe generation to create filament arrays, offering a novel approach for filamentation control. Moreover, the filament fringe count increases with the beam’s topological charge, indicating that filament formation depends not only on incident energy but also on the number of bright intensity fringes in the focused beam.

In this paper, we explore the filamentation distribution and evolution of femtosecond vortex beams in fused silica using a tilted focusing lens. A stable and controllable filament array is achieved, with its distribution tailored by adjusting the tilt angle of the lens. By modifying the lens’s tilt angle, the filament distribution transforms from a circular pattern to an array structure. Moreover, the filament distribution and number can be precisely controlled by altering the vortex beam’s topological charge and the incident laser energy. The proposed method not only introduces a novel approach for controlling laser filaments but also holds significant potential for applications in research and technical fields such as laser micro- and nano-processing.