Abstract
<jats:p>This study presents a numerical verification of the physical validity of using a quadratic dependence of the laser beamradius in modeling stimulated Raman scattering (SRS) in self-focusing media, such as toluene. The influence of various powerlawdependencies of the gain coefficient on the beam radius (n = 1, n = 2, n = 3) is analyzed in terms of numerical stability andresult accuracy. Two numerical approaches are developed: the Adams method with adaptive step size and the Euler iterativemethod with fixed step size, both based on energy conservation laws and the Kerr effect. The simulations are performed usingparameters typical for toluene (initial beam radius of 113 μm, refractive index of 1.49, laser wavelength of 694.3 nm, and criticalpower of 25 kW). The results show that the quadratic model (n = 2) provides the optimal combination of stability and physicalcorrectness, accurately capturing the Stokes generation threshold (zf ≈ 0.083 m) and power stabilization. The linear model (n =1) underestimates the self-focusing effect, violating energy conservation, while the cubic model (n = 3) exhibits numericalinstability. This work has practical significance for optimizing laser systems in spectroscopy, optoelectronics, and biomedicine.Moreover, an important aspect of developing numerical programs was to improve computational efficiency. Implementing themodeling in the form of standalone programs allows for a significant reduction in calculation time compared to manual analysisor the use of general-purpose software packages. This enables the investigation of complex nonlinear effects under realisticconditions with high spatial resolution</jats:p>