The THz emission point on a nonlinear electro-optical crystal for generating broadband THz radiation is modeled as a radiating Gaussian aperture. With the wavelengths of the infrared pump beam being much smaller than the wavelength components of the generated THz pulse, a THz sub-wavelength radiating aperture with Gaussian profile is effectively created. This paper comprehensively investigates Gaussian apertures in focused THz radiation generation in electro-optical crystals and illustrates the break-down of the paraxial approximation at low THz frequencies. The findings show that the shape of the radiation pattern causes a reduction in detectable THz radiation and hence contributes significantly to low signal-to-noise ratio in THz radiation generation. Whilst we have demonstrated the findings on optical rectification in this paper, the model may apply without a loss of generality to other types of apertures sources in THz radiation generation.