We present an experimental and theoretical study of the intensity noise correlation between the two orthogonally polarized modes in a dual frequency Vertical External Cavity Surface Emitting Laser (VECSEL). The dependence of the noise correlation spectra on the non-linear coupling between the two orthogonally polarized modes is put into evidence. Our results show that for small coupling the noise correlation amplitude and phase spectra remain nearly flat (around -6 dB and 0 degrees respectively) within the frequency range of our interest (from 100 kHz to 100 MHz). But for higher values of the coupling constant the low frequency behaviors (below 1-2 MHz) of the correlation amplitude and phase spectra are drastically changed, whereas above this cut-off frequency (1-2 MHz) the correlation spectra are almost independent of coupling strength. The theoretical model is based on the assumptions that the only source of noise in the frequency range of our interest for the two modes are pump noises, which are white noises of equal amplitude but partially correlated. (C) 2013 Optical Society of America.