  III-V semiconductor quantum dots (QDs) are near-ideal and versatile
single-photon sources. Because of the capacity for monolithic integration with
photonic structures as well as optoelectronic and optomechanical systems, they
are proving useful in an increasingly broad application space. Here, we develop
monolithic circular dielectric gratings on bulk substrates -- as opposed to
suspended or wafer-bonded substrates -- for greatly improved photon collection
from InAs quantum dots. The structures utilize a unique two-tiered distributed
Bragg reflector (DBR) structure for vertical electric field confinement over a
broad angular range. Opposing ``openings" in the cavities induce strongly
polarized QD luminescence without harming collection efficiencies. We describe
how measured enhancements depend critically on the choice of collection optics.
This is important to consider when evaluating the performance of any photonic
structure that concentrates farfield emission intensity. Our cavity designs are
useful for integrating QDs with other quantum systems that require bulk
substrates, such as surface acoustic wave phonons.
