  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.
