On the validity of Rayleigh-Sommerfeld propagation formulas

Results of simulation by first Rayleigh-Sommerfeld integral formula (RS1),second Rayleigh-Sommerfeld integral formula (RS2) and Helmholtz-Kirchoff integral formula (HK) in studying beam propagation are compared by known rigorous solutions according the Mie theory in spherical coordinates and corresponding more simple expansions in cylindrical 2D-geometry. For simplicity, the monochromatic field propagation in cylindrical coordinates when the beam propagates along x-axis and is homogeneous to z is used. This model well approximates radiation of a most part of diode lasers.