On far-field approximation of parabolic equation

The far-field approximation of Parabolic Equation (PE) and the numerical calculation of PE starter are studied.The relationship between the allowable error and the minimum reference range is analyzed and it is pointed out that within the minimum reference range the far-field approximation will cause considerable calculation error through the PE propagator,and so which can not be used to calculate PE self-starter,A new propagator,which has no far-field limitation and can be unitedly used for PE self-starter and far field calculation is derived.The numerical result in the Pekeris channel shows that the propagator is quite accurate for calculation of PE self-starter and transmission loss.