  In this paper, we present the theoretical studies of a refractive index map
to implement a Gauss to J0-Bessel-Gauss convertor. We theoretically demonstrate
the viability of such device by solving the inverse electromagnetic problem.
The computed conversion efficiency is 90%. The theoretical results, obtained
from the beam conversion efficiency, self-regeneration, and propagation through
an opaque obstruction; demonstrate that a 2D graded index map of the refractive
index can be used to transform a Gauss beam into a J0-Bessel-Gauss beam. To the
best of our knowledge, this is the first demonstration of such beam
transformation by means of a 2D index-mapping which is fully integrable in
silicon photonics based planar lightwave circuits (PLC). The concept device is
significant for the eventual development of a new array of technologies, such
as micro optical tweezers, optical traps, beam reshaping and non-linear beam
diode lasers.
