Focusing properties of Hermite-Gaussian beams passing through an aperture-lens system

The focusing properties of Hermite-Gaussian(H-G)beams in passage through an aperture-lens separation optical system are studied based on the Collins formula.The axial intensity distribution and focal shift of H-G beams with even mode numbers are analyzed and illustrated with detailed numerical examples.It is found that the inverse focal shift and focusing without focal shift can be achieved by a suitable choice of the beam and optical system parameters.In particular,for the TEM22-mode H-G beam,there may be two equal axial maximum intensity points located on two sides of the geometrical focal plane,thus there are two focal shifts with opposite signs.