Virtual Source for an Odd Mathieu-Gauss Beam and Compare of the Functional Images of the Odd And Even

摘要

Based on the beam superposition, we identify a group of virtual sources for generating a 2n+2-th order Mathieu-Gauss beam with odd modes. The integral and differential representations for the Mathieu-Gauss wave are derived,which, in some conditions, yields the corresponding paraxial Mathieu-Gauss beam.Based on the same theory, we can get the integral and differential representations and the functional images of the 2n+1-th order Mathieu-Gauss beam with odd modes, the 2n-th order Mathieu-Gauss beam with even modes and the 2n+1-th order Mathieu-Gauss beam with even modes. Then compare the four kinds of functions.