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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 investigates this general modelling approach for focused THz radiation generation in electro-optical crystals. Different implementations are employed for the near- and far-field regime. While a numerical approach is required to characterize near-field intensity distributions, a semi-analytical model is sufficient for far-field considerations. The near-field study has ramifications in THz near-field focused beam techniques while far-field investigations elucidate the radiation pattern shape and hence the detectable SNR.