Cubic–Quintic Stabilization of Hyper-Gaussian Solitons in AlGaAs Photonic Crystal Fibers

The integration of aluminum gallium arsenide (AlGaAs) into microstructured photonic crystal fibers (PCFs) creates a highly nonlinear platform promising for compact photonic devices. This work presents a comprehensive numerical investigation of ultrashort pulse propagation in AlGaAs glass PCFs using a generalized nonlinear Schrödinger equation model that incorporates higher-order dispersion, self-steepening, stimulated Raman scattering, and a competing cubic-quintic nonlinearity. The designed PCF geometry, featuring a seven-ring hexagonal lattice with graded air-hole diameters, is first analyzed to demonstrate strong modal confinement and engineerable anomalous dispersion at telecommunication wavelengths. The exceptionally high nonlinear coefficients, reaching γ 1 = 24359 W −1 km −1 and γ 2 = −285 W −2 km −1 , facilitate nonlinear processes at femtojoule energy levels. Subsequent analysis reveals the profound influence of higher-order effects on modulational instability (MI) gain spectra and soliton dynamics. Self-steepening introduces spectral asymmetry with blue-side suppression, while the Raman response causes a continuous red-shift and temporal delay of solitons via the soliton self-frequency shift. A parametric study further elucidates how pump power, dispersion, and nonlinearity systematically control MI gain bandwidth and amplitude. These findings provide a foundational framework for designing and optimizing AlGaAs PCF-based devices for applications in supercontinuum generation, wavelength conversion, and integrated nonlinear photonics. The results underscore the critical importance of including higher-order nonlinear terms when modeling pulse propagation in semiconductor-doped microstructured fibers. Keywords: Hyper-Gaussian solitons; Quintic nonlinearity; AlGaAs photonic crystal fiber; Nonlinear Schrödinger equation; Higher-order dispersion; Soliton stability; Nonlinear pulse propagation.