Direct determination of the on-axis intensity maximum of diffracted Gaussian beams

In lasers, the use of diffracting apertures involves many effects and applications. This goes from the selection of only one eigenmode to oscillate inside the resonator, often called the fundamental mode, the discrimination of the opposite travelling waves within ring resonators, to the control of the beam parameters like diffraction losses, the phase shift and the angular divergence. However, diffraction upon the aperture edge shifts along the optical axis the diffracted beam waist from the position where it would occur for a non apertured beam. The determination of the axial position of the beam waist is important insofar as it indicates the adequate position, inside the resonator, for small amplifying or absorbing media. Realizing that there is no effective treatment of this issue anywhere in literature, we attempt, in this work, to establish formulae which give the axial position for the effective waist of a diffracted beam by one aperture. This position will be expressed as a function of the beam parameters as well as those of the aperture.