We investigate the intra-pulse quantum structure of an ultrafast optical pulse that propagates through an AlGaAs waveguide at the band-gap energy where nonlinear refraction is negative, i.e., the self-defocusing regime. In this regime, the sign of the group velocity dispersion parameter is positive to counteract the Kerr effects in frequency chirping. We show the evolution of the quantum spectral correlation with increasing pulse energy. A positive correlation between the two wings of the pulse spectrum is seen to occur as well as the spectral self-correlation, leading to a cross-shaped correlation structure in the quantum spectral correlation map. The pulse energy that supports the broadened spectra produces increased complexity in the correlation structure. Our calculation shows a spectral correlation map that is different from the fibre optical solitonic case due to the different nonlinear dynamics of interplay between the self-phase modulation and the group velocity dispersion for the quantum correlation structure.