An integral expression for thermal blooming equation of high power laser propagation through atmosphere

On the basis of Fresnel Kirchhoff approximation,the integral expression for the thermal blooming of high power lasers propagating through atmosphere has been derived by Green's function method,and numerical simulations of CW steady state thermal blooming have been performed to show the feasibility of our method.We have also shown that the well known Fresnel Kirchhoff diffraction integral is a limiting case of the generalized integral expression,where the refactive index is a constant.