2012/10/25 by Paul Kinsler, Kinsler, Paul
Engineering · #FOS: Physical sciences #Geophysics and Sensor Technology #Geotechnical Engineering and Underground Structures #Optics (physics.optics)
paper · pdf · doi:10.48550/arxiv.1210.6794
openalex publication_date 2012/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
I derive directional wave equations useful for pulses propagating in beam, rod, pipe, and disk geometries by using a cylindrical coordinate system; the scheme works equally well for either long multi-cycle or single-cycle ultrashort pulses. This is achieved by means of a factorization procedure that conveniently generates exact bi-directional and first order wave equations after the selection of propagation direction - either axial, radial, or even angular. I then discuss how to reduce these to a uni-directional form, and discuss the necessary approximation, which is essentially a paraxial approximation as appropriately generalized to the specific geometry.