Intensity representation of nonparaxial vectorial Gaussian beams

Based on the vectorial Rayleigh-Sommerfeld diffraction integrals, the two expressions for the intensity of nonparaxial vectorial beams, i.e., the conventional intensity expression and the z component of the time-averaged Poynting vector, are studied without using any approximation. A detailed numerical comparison for nonparaxial vectorial Gaussian beams shows that the discrepancy between the two expressions, namely, the relative error, depends on the ratio of the waist width to the propagation distance and that of the wavelength to the propagation distance, respectively, and the error decreases with the increase of the two ratios. For nonparaxial vectorial Gaussian beams, if the ratio of the wavelength to the propagation distance is 10, and the ratio of the waist width to the propagation i