Time-harmonic “complex source” wavefields and their sources in real space

The paper concerns the complexified Green function of the 3D Helmholtz equation in the free space, which is interesting as an exact solution demonstrating Gaussian-beam behavior. This function involves a square root and satisfies an inhomogeneous Helmholtz equation, the right-hand side of which depends on the cut and on the branch of the root. We deal with the explicit description of this generalized function.