I am trying to find the inverse Fourier transform of: $$ F(k_x,k_y)=e^{ikz} e^{-ik_\rho ^2 z /2k}, $$ where $k^2 = k_x^2 +k_y^2 +k_z^2 = k_\rho ^2 +k_z^2 $ is a constant.
I am getting confused as to how to go about this. Inverse fourier transform of $F(k_x)$ would be given by $ \int F(k_x)e^{-ik_x x} \frac{dk_x}{2\pi} $? How do I change this when there is a function of two variables?
Furthermore, could anyone explain what is meant by the prefactor of the exponential?