Pulsed beam propagation in plane stratified media: Asymptotically exact solutions

Closed form solutions for pulsed beam (PB) propagation in general inhomogeneous media can be obtained via paraxial wave tracking along the curved propagation trajectories. As a test bed to validate these solutions, we derive here an asymptotically exact solution for a PB in a general plane stratified medium. Such a solution can be derived via the complex source (CS) approach, but this requires an extension of the inhomogeneous wave-speed to the complex coordinates space. To circumvent this difficulty, we use a generalized plane-wave representation in which the CS field is used as the initial condition in the aperture plane. The spectral integral for the 3D PB field is then evaluated via the spectral theory of transients (STT) which expresses the field as a spectral integral of transient plane-waves that can be contracted to a simple and compact 1D integral.