In the conventional ray theory with real-valued travel time, the initial amplitude profile is represented by the initial conditions for amplitude. Since the accuracy of the ray theory suffers from the amplitude changes along wavefronts, this approach is considerably inaccurate for beams, because it does not provide the spreading of the beams caused by diffraction.
The representation of the initial Gaussian amplitude profile in terms of the imaginary part of the initial complex-valued travel time with the constant initial conditions for amplitude yields satisfactorily accurate paraxial Gaussian beams.
In this paper, we demonstrate that the representation of the initial Super-Gaussian amplitude profile in terms of the imaginary part of the initial complex-valued travel time with the constant initial conditions for amplitude yields the Super-Gaussian beams whose lowest-order paraxial approximation is identical to the conventional ray theory solution with real-valued travel time, without the diffracted wavefield which could result from the representation theorem.
Wave propagation, ray theory, complex-valued travel time, paraxial approximation, Gaussian beams, Super-Gaussian beams.
The paper is available in PDF (81 kB).