  We report on the efficacy of a novel design for dielectric laser accelerators
by adding a distributed Bragg reflector (DBR) to a dual pillar grating
accelerating structure. This mimics a double-sided laser illumination,
resulting in an enhanced longitudinal electric field while reducing the
deflecting transverse effects, when compared to single-sided illumination. We
improve the coupling efficiency of the incident electric field into the
accelerating mode by 57 percent. The 12 $\mu$m long structures accelerate
sub-relativistic 28 keV electrons with gradients of up to 200 MeV/m in theory
and 133 MeV/m in practice. Our work shows how lithographically produced
nano-structures help to make novel laser accelerators more efficient.
