This study theoretically examines the chirping of spatial frequency in \(q\) -Gaussian laser beams that interact nonlinearly with Kerr media possessing electromagnetically induced transparency (EIT). Due to Kerr nonlinearity the medium’s refractive index resembles that of a convex lens. Chirping, or the modulation of spatial frequency, also known as the phase anomaly, arises from the position-momentum uncertainty of photons. The intensity gradient across the laser beam's cross-section generates a transverse gradient in the index of refraction, stimulating self-focusing of the laser beam. As the beam's transverse dimensions decrease, the transverse momentum of its photons spreads, modifying its axial phase. Using Moment theory, we derived equations of motion for the beam's radius and spatial frequency. Numerical solutions of these equations reveal the effects of various laser and medium parameters on the beam's envelope evolution. The relationship between the axial phase and Berry phase is also discussed.
