Nonparaxial analysis of far-field properties of Gaussian beams diffracted at a circular aperture.

On the basis of angular spectrum representation and the stationary-phase method, a far-field expression for nonparaxial Gaussian beams diffracted at a circular aperture is derived, which permits us to study the far-field nonparaxial properties of apertured Gaussian beams both analytically and numerically. It is shown that for the apertured case, the f -parameter and the truncation parameter affect the beam's far-field properties. The f -parameter plays the more important role in determining the beam nonparaxiality than does the truncation parameter, whereas the truncation parameter additionally influences the beam diffraction. A comparison with the paraxial case is made. For the unapertured case our results reduce to the previous ones.