Design Blueprint: Purcell Enhancement and Collection Efficiency for a Quantum Dot in a Micropillar Cavity

Design blueprint derived from the source paper (DOI 10.5281/zenodo.24159668): A semiconductor quantum dot placed at the antinode of a micropillar resonator emits preferentially into the cavity mode when the Purcell factor is large. The same geometry that raises the emission rate also directs the light into a narrow cone, which is why micropillars are used as bright single-photon sources. This study computes the quantities that follow from stated assumptions for an InAs quantum dot at 930 nm in a micropillar with mode volume 5 cubic wavelengths in the material and quality factors from 1000 to 50000, using the relations set out in the Methods. The headline results are Purcell at Q 10000 = 152, beta at Q 10000 = 0.9935, collection at Q 10000 = 0.76, Purcell detuned one linewidth = 30.4, collection at Q 50000 = 0.764. The central question is stated as follows: For a stated mode volume and quality factor, what Purcell factor, fraction of emission into the mode, and photon collection probability follow, and how sensitive is the result to detuning between dot and cavity? The answer obtained here is conditional on the assumptions listed in the paper and in the deposited calculation; changing an assumption changes the numbers in the way the sensitivity discussion describes. Reported micropillar sources reach collection efficiencies of several tens of percent and Purcell factors near ten, so the computed range can be compared directly with that scale. The work is a computation, not a laboratory measurement, and it is labelled accordingly. Where the computed result is unfavourable to the device or effect under study, that outcome is reported in the same terms as a favourable one, because a bound that only appears when it is welcome is not a bound at all. All numerical statements in this abstract are reproduced by the deposited script from the stated inputs. Status: DESIGN BLUEPRINT — SIMULATED, NOT MEASURED — NOT BUILT. All numbers are simulated values from the source paper's computation, deposited with this blueprint as compute.py and results.json. AI-use disclosure: Dave, an AI research system, assisted with the computation and drafting under the author's direction; author of record William Alexander Aldred.