The filamentation process of ultra-intense femtosecond lasers in the atmosphere is accompanied by significant nonlinear optical effects such as self-focusing, self-steepening, and plasma defocusing. This is essential for studying lidar, new light sources, artificial rainfall, air pollution detection, and laser remote sensing. When the femtosecond laser pulse is propagated into the atmosphere, a random multifilament phenomenon occurs owing to air refractive index perturbation caused by atmospheric turbulence and the initial inhomogeneous energy distribution of the femtosecond laser. This affects the energy distribution of the filament, shortens the propagation distance of the filament, and reduces the spot quality of the beam, therefore limits the practical application of the filament. This review summarizes local and international research progress on multifilaments in the past two decades. A series of multifilament control methods are reviewed, including the introduction of the elliptical rate of the incident beam, variation of the laser field gradient, modulation of the laser phase, and introduction of image dispersion to establish a reference for the study of multifilament regulation in femtosecond lasers.

With continuous advancements in laser technology, the peak intensity of femtosecond laser pulse obtained in laboratory tests has far exceeded the relativistic threshold (10¹⁸ W/cm²) and even reaches 10²³ W/cm², which significantly reduces the difficulty of femtosecond laser atmospheric filamentation. This serves as a foundation for experimental research and the practical application of the filament. Researchers have found that the multifilament phenomenon is mainly caused by the perturbation of the refractive index of air and the initial uneven energy distribution of the femtosecond laser. Further studies have also shown that during the formation of femtosecond laser filaments, only a small portion of the laser energy is concentrated in the filament, and most of the laser energy is stored around the filaments as background energy, which is often called the background energy reservoir. In this regard, Mlejnek et al. proposed the theory of dynamic energy compensation for optical filament propagation. It is believed that an energy reservoir with a low light intensity concentrated around the optical filament provides energy for the propagation of the laser filament, and the interaction between background energy reservoirs can sustain the filament. This theory was experimentally confirmed in 2005. Liu et al. interrupted the transmission of background energy by shielding the filament's outer ring, immediately stopping the filament's propagation. In subsequent simulation studies, they found that the required background energy must be at least 50% higher than the total energy required to sustain the self-guided propagation of the filament. The main reasons for the multifilament phenomenon are atmospheric turbulence caused disturbance of air refractive index and the uneven distribution of the initial energy of the femtosecond laser. To effectively control the generation of a stable multifilament structure, researchers have proposed several methods; these methods include introducing ellipticity in the incident beam, changing the laser field intensity gradient (Fig. 1, Fig. 2), introducing astigmatism (Fig. 3), modulating the wavefront phase (Fig. 4), introducing axicon, introducing optical anisotropy of the introduced species (Fig. 5), and using polarization axis symmetry breaking (Fig. 6). These methods reduce and even eliminate the effect of random perturbations on femtosecond filament transmission by modulating the initial energy distribution of the femtosecond laser or the perturbation of the air refractive index cause by atmospheric turbulence, thereby achieving experimentally reproducible femtosecond laser transmission processes. In addition, by increasing the distance between the background energy reservoirs of the filaments and reducing the mutual interference between the energy pools, a multifilament structure with stable transmission can also be produced. Another method to control the orderly spatial distribution of femtosecond multifilaments involves inhibiting the generation of multifilaments, that is, turning the multifilaments into single filaments during laser transmission. Similar to regulating multifilaments, inhibiting multifilament production can also produce controllable filaments. One of the main ways of suppressing the generation of multifilaments is by making the initial light intensity distribution of the laser pulse as smooth as possible, thus reducing the influence of the initial uneven distribution of light intensity and preventing the generation of multiple"hot spots". Another method is to reduce the distance between "hot spots", causing the energy pools of each "hot spot" to overlap with each other so that the multifilaments are fused into a single filament. Based on these two techniques, researchers have proposed the use of telescopic systems for beam reduction (Fig. 7), the introduction of astigmatism, the use of spatial light modulators or phase templates (Fig. 8), and the use of iris diaphragms and axicons to control multifilaments.

The formation process of femtosecond laser filaments is accompanied by rich optical effects such as fluorescence radiation, pulse self-compression, and supercontinuum generation. It has important application prospects in atmospheric pollution detection, new light sources, laser triggering, and terahertz radiation sources. Moreover, the study of femtosecond laser filamentation processes also benefits the development of the optics theory. Random multifilaments limit the practical applications of laser filamentation; hence, the significance of regulating multifilaments is to expand the practical applications of femtosecond lasers. Existing regulation methods for the multifilament phenomenon focus on generating controllable and stable structures and inhibiting multifilament production. Various research methods can be used to eliminate the randomness of multifilaments when the femtosecond laser is propagated to a certain extent in the atmosphere. However, there are still certain problems in multifilament control such as a low distribution control accuracy and shortened laser transmission distance due to laser energy loss. Therefore, the regulation of multifilaments needs to be studied further before it can be widely applied to various fields.