Research of the narrow-angle beam diffraction

摘要

The diffraction of narrow sharply focused beam propagating through the free space and nonlinear medium was studied. The validity of two approximated approaches for analysis of narrow beam diffraction was studied on the base of comparison with the solution of Kirchgof-Helmholtz diffraction. Both of these approaches is based on the particular solution of Helmholtz equation, which is corresponded with propagation of unidirectional wave. In the first of them attenuating waves are taken into account for the case where the spatial spectrum width is greater than the wave number. The second one is based on the neglect of contribution from attenuating waves. Also, validity of a parabolic wave equation for these situations was researched.