Investigation of the diffraction of a focused Gaussian beam by a half-plane near the beam waist

Diffraction of a focused Gaussian beam in the vicinity of the waist region at the edge of the screen is considered on the basis of numerical simulation and experimental investigation. The Gaussian beam propagation has been simulated on the basis of the Helmholtz equation solution by the spectral method. The diffraction of coherent laser radiation (wavelength of 0,63 $\mu$m) at the edge of a rectangular screen overlapping half the beam in the transverse direction has been analyzed experimentally. The laser beam is focused by the lens of focal length of 4 cm. A dependence of the diffraction pattern on the screen position relative to the focal waist position is observed. It is found that if the screen is located at distances less than the focal length, then the diffraction pattern is observed in the dark region and represents a semicircle with diffraction fringes. If the screen is placed in the waist region, then the diffraction pattern becomes symmetrical with respect to the screen edge, and if the screen is located at a distance greater than the focal length, then the diffraction pattern is observed in bright area with the diffraction fringes appearing on the other side. The results can be used for the accurate determination of the focused Gaussian beams waist position.