Analytical beam propagation model for clipped focused-Gaussian beams using vector diffraction theory

Vector diffraction theory is applied to the case of focused TEM ₀₀ Gaussian beams passing through a spatially limiting aperture in order to investigate the propagation of these clipped focused-Gaussian beams. Beam distributions at different axial distances show that a traditional M ² propagation model cannot be used for the propagation of clipped focus-Gaussian beams. Using Luneberg's vector diffraction theory and Fresnel approximations, an analytical model for the on-axis transverse and longitudinal electric fields and intensity distributions is presented including predictions of the maximum obtainable intensity. In addition, an analytical expression is provided for the longitudinal component of the electric field of a TEM ₀₀ mode unperturbed Gaussian beam. Experimental results are also presented and compared to the model's predictions.