A gain-assisted atomic medium controls and modifies spatial solitons of reflection and transmission of structured light. Structured light pulses of reflection and transmission are generated and analyzed by azimuthal quantum numbers dependent on control driving fields in the medium. The study revealed the formation of spatial bright and dark solitons. The bright and dark soliton splitting regions are linearly increasing according to azimuthal quantum numbers of formula. Two, four, six, and eight bright and dark soliton regions are investigated with the azimuthal quantum number of. The structured light of the reflection pulse maintained a constant shape, exhibiting weak nonlinearity along the x-axis and strong nonlinearity along the y-axis. However, the structured light transmission pulse displayed varying shapes, influenced by the balanced nonlinearities along both the x- and y-axes at higher azimuthal quantum number, leading to stable propagation of spatial bright solitons. These findings highlight the significant role of the structured light effect in controlling and stabilizing soliton dynamics, with potential applications in nonlinear optics, traffic flow, signal processing, plasma physics, quantum field theory, and optical soliton interferometry.

The generation of spatial bright solitons of reflection and transmission pulses and their intensities are investigated in a sodium atomic medium using Gaussian Milnor polynomial control fields. Significant bright and dark ring-shaped solitons are controlled by balancing nonlinearity and dispersion along two spatial coordinates. The intensity is more localized along one of the spatial coordinates due to larger nonlinearity and spread along other spatial coordinates due to smaller nonlinearity in the reflection pulse. A circular, crater-type bright soliton intensity is also maintained around the origin of the x and y coordinates, exhibiting varying intensity along the circumference. A large, bright intensity peak is observed around the origin, with the intensity minima at the center in reflection. The intensity peaks are enhanced in one of the spatial coordinates and localized in another coordinate in reflection. A large Gaussian-type bright solitonic intensity distribution is investigated at approximately (Formula presented.) throughout the variation along the x-axis in the transmission pulse pattern. The reflection and transmission pulse intensities vary from (Formula presented.) to (Formula presented.), and at least (Formula presented.) of the intensity of the incident pulse is lost by attenuation. The modified results are useful in optical communications, fiber optics, optical computation, signal processing, radar technology, and artificial neural networks.

The superluminal solitonic propagation behavior of left- and right-circularly polarized (LCP/RCP) light beams is investigated in a chiral medium. RCP and LCP beam absorption exhibits super-Gaussian-type peak behavior with spatial coordinate fluctuation around the origin. The RCP beam’s subluminal phase velocity is vp(+)=c/nr(+)[jls-end-space/], and its refractive index is 5.47. On the other hand, the LCP beam’s superluminal phase velocity is vp(−)=c/nr(−)[jls-end-space/], and its refractive index is −3.65. Both LCP and RCP beams propagate at superluminal group speeds in the medium. The RCP and LCP beams’ maximum group index values are determined to be Ng(+)=−33522 and Ng(−)=−1305[jls-end-space/]. The group velocities that correspond to this are vg(+)=−c/33522 and vg(−)=−c/1305[jls-end-space/]. With the position of greater nonlinearity and periodicity changing with forward time flowing, the RCP and LCP pulses E(r,t)⁽⁺⁾ and E(r,t)⁽⁻⁾ exhibit superluminal-peaked soliton characteristics. With increasing forward time, the LCP pulse intensity shifts to a positive position while the RCP pulse intensity shifts to a negative position. The bright superluminal solitonic intensities are modified and controlled. For both polarized light beams in a chiral atomic medium. The obtained results may be useful for soliton radar technology and time cloak equipment to reduce information hacking from outside hackers.