Out-of-plane beam shaping with UV-written tilted Bragg gratings for beam delivery on quantum chips

We theoretically and numerically investigate the performance of tilted Bragg gratings in planar waveguides, fabricated by direct UV writing in photosensitive silica, to couple light out of a chip. An analytic expression is derived for the coupling efficiency and validated numerically by finite element simulations. Using the analytic result, we can design gratings to generate output beams in free space of any specific shape and calculate their overall power coupling efficiency. Our simulations indicate that for currently achievable grating index contrasts devices of millimeter length are most suitable for this technology.