Reflectionless potentials following the prescription of Kay and Moses allow for total transmission of incoming waves of any kinetic energy. The optical analogue of such potentials occur as dielectric stratified media that can offer null reflectivity and near total transmission over a large range of incidence angles and wavelengths. In a previous work (S. Dutta Gupta and G. S. Agarwal, Opt. Express 15, 9614-9624, 2007), this was demonstrated for linearly polarized plane waves. We extend the earlier work valid for plane waves to structured beams to show near-total transmission of beams across the reflectionless dielectric profile. The analysis is based on the angular spectrum decomposition treating the beam as a collection of plane waves. Gaussian and Laguerre-Gaussian beams are shown to be transmitted through the film with <1% reflection in most scenarios. We also discuss the superlative performance of our proposed profile in preserving the beam shape during transmission comparing these results to a conventional lambda/2 antireflection coating.
