Focal Shift in Elegant sin-Gaussian Beam s Using Second-OrderM omentM ethod

The focal shiftof elegant sin-Gaussian beams passing through a lenswas studied using the Collin s formula. Itwas found that the axial intensity intensity of a focused elegant sin-Gaussian beam was nul.l The second-ordermomentmethod was used to derive the analytical formulas for both beam waist and the position of thewaistof the focused elegantsin-Gaussian beam. The focal shifts ofelegant sin-Gaussian beams can be obtained using the derived formulas. The analytical formulas for the relative focus shifts of focused elegantsin-Gaussian beamswere presented as examples. Numerical calculations demonstrate that focal shifts of focused elegant sin-Gaussian beams depend on optical system parameters, beam parameters and Fressnel number. Proper choice of the distance from the incidence plane to the lens leads to disappearance of focal shift.